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index f81c4d1091b661865f34757176484d614fc0fe38..d0c3cbf1020d5c292abdedf27627c6abe25e2293 100644
--- a/Makefile
+++ b/Makefile
@@ -1,12 +1,20 @@
-default: convert
-convert:
-	bash publication.sh
-clean:
-git:
-  # git add files
-  #git add whitepaper.md whitepaper.html
-  #git add chapters/1_intro.md.txt chapters/2_looking_at_Bitcoin.md.txt chapters/3_blockchain.md.txt chapters/4_Web_Of_Trust.md.txt chapters/5_individualized_difficulty.md.txt chapters/6_conclusion.md.txt chapters/9_sources.md.txt
-  #git add publication.sh
-
-  #we want to add the .pdf only for publication
-  # git add whitepaper.pdf
+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?=
+SPHINXBUILD   ?= sphinx-build
+SOURCEDIR     = source
+BUILDDIR      = build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
diff --git a/README.md b/README.md
index 0fe884efa29f73fee6d5395d2d30b52dafa8f8a6..d60f0fa68e2a56acf09eb457b76149c60bc27e2b 100644
--- a/README.md
+++ b/README.md
@@ -4,20 +4,17 @@ Rédaction d'un Whitepaper pour le projet Duniter.
 
 Je ne suis pas compétent pour entrer dans les détails du projet. Cependant, je le suis assez pour rédiger la majeure partie du texte explicatif. J'invite qui le souhaite à m'accompagner dans cette rédaction.
 ## Installation et compilation sur système Debian
+
+Les sources sont rédigées en syntaxe RestructuredText et compilées avec Sphinx.
+
 Pour compiler les sources markdown vers les versions html, ebook et pdf vous allez avoir besoin de ces dépendances:
 ```bash
-sudo apt install texlive-latex-base pandoc texlive-fonts-recommended calibre
+sudo apt install latexmk pip3
+python3 -m pip install sphinx --user
 make
 ```
 
 ## TODO
-* grouper les assets dans ce dépot dans src/img et non les mettre en hotlink.
-* Table Of Content sur la version HTML.
-* afficher les formules mathématiques en syntaxe laTex.
-* compléter les chapitres
-    * chap 1 Abstract
-    * chap 2 Proof-of-Work mining : a power race
-    * chap 3 Spam countermeasures (TODO)
 * traduire en Français les chapitres
 
 ### Références
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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 6e10d8e2c38b36a46552ef0d7e72044a
+tags: 645f666f9bcd5a90fca523b33c5a78b7
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@@ -0,0 +1,12 @@
+.. Duniter technical description documentation master file, created by
+   sphinx-quickstart on Sat Jun 20 12:05:38 2020.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Duniter technical description
+=============================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
diff --git a/build/_sources/index.rst.txt b/build/_sources/index.rst.txt
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--- /dev/null
+++ b/build/_sources/index.rst.txt
@@ -0,0 +1,1458 @@
+.. Duniter technical description documentation master file, created by
+   sphinx-quickstart on Sat Jun 20 12:05:38 2020.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Duniter technical description
+=============================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
+.. Duniter: A libre currency blockchain generator.
+
+.. ===============================================
+
+Abstract
+--------
+
+Many currency principles involve non-equal rights to monetary creation
+between humans. We propose a monetary creation based on the Relative
+Theory of Money, which guarantee equal monetary creation for each
+willing human. This type of currency can be centralised, however, this
+could lead to censorship and arbitrary choices of the central
+institution. Thus, strongly inspired by Bitcoin example, we want the
+currency to be as decentralised as possible, in the transaction network
+as in the human identification process. We use a Web of Trust between
+living humans for identification. This web of trust allows us to impose
+personalised difficulty for transaction validation, keeping the
+calculation accessible to low-end hardware and allowing all competent
+members to secure the currency.
+
+Introduction
+------------
+
+Duniter is a software to create and manage “libre currencies”. Libre
+currency is a concept defined by S.Laborde in the Relative Theory of
+Money (RTM) that was published in 2010. This theory demonstrates the
+possibility of an invariant monetary unit : the Universal Dividend.
+Doing so, the RTM answers the question :
+
+   How should a currency be created to match the principle of equality
+   between all humans, now and between generations ?
+
+The results of this demonstration implies a monetary creation :
+
+-  on a regular basis
+-  for each human being
+-  which amount has to be reassessed on fixed intervals according to a
+   fixed formula.
+
+Thus, Duniter project will associate a human to a digital identity. It
+will use a Web of Trust with specific rules. As the number of members
+may evolve, the Universal Dividend has to be created according to the
+formula :
+
+.. math::  UD(t+1) = UD(t) + c^2 \times {M(t) \over N(t)} 
+
+Duniter is based on a decentralized Blockchain. This technical choice
+allows irreversibility of transaction and uncensorability of trades and
+identities. While inspired by Bitcoin, Duniter uses a Web of Trust and
+the Proof of Work to secure the computation network, thus making
+obsolete the power race model used in Bitcoin.
+
+The first currency created through Duniter is Ğ1, pronounced “June”. It
+was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters
+as examples ; however, one can create another libre currency with custom
+parameters while still using Duniter software.
+
+1. State of the art : Bitcoin case
+----------------------------------
+
+.. raw:: html
+
+   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniter uses the crypto-currency concept introduced by Bitcoin [1]_,
+which is to use cryptographic tools such as signatures to create
+trustless digital currencies. Duniter fits this definition, but it has
+two completely different principles than Bitcoin : the Web of Trust and
+the Universal Dividend . These differences are on both monetary and
+technical aspects.
+
+.. _monetary-creation-a-space-time-asymmetry:
+
+1.1. Monetary creation of Bitcoin : a space-time asymmetry
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Space-time asymmetry refers to the relative access of individuals to
+newly created money [2]_. Concretely, most existing currencies (c. 2020)
+are both spatially and temporally asymmetrical for their users. Let's
+take Bitcoin as an example to understand why.
+
+1.1.1. Spatial asymmetry
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+When new Bitcoins are created, only some Bitcoin users (the miners) are
+given new Bitcoins, while everyone else get nothing. We believe this is
+the first injustice. However, some might say:
+
+   "Miners used their electricity and time to get it!"
+
+... we would answer that this work should not have been rewarded by
+newly created Bitcoins. New units should be distributed to the whole
+community. Miners should be rewared another way, but not by money
+issuance. Of course, Bitcoin cannot create money through Basic Income
+since Bitcoin users are not strongly identified, and one might benefit
+from money creation multiple times if they owned several wallets.
+Duniter gets rid of this problem by identifying its users and creating
+the same amount of Basic Income to everyone.
+
+1.1.2. Temporal-asymmetry
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
+which means ever fewer bitcoins will be created over time until no new
+BTC are being generated. So, once the first adopters have mined every
+bitcoin, how will future joiners get Bitcoins? Just like most of us do
+for Euros or Dollars: to get money, they will have to work for the ones
+who already own it.
+
+We believe this is the second injustice. Every member of a monetary
+community should be equal concerning monetary creation, and get the same
+relative amount of money over time, even if they are a late adopter.
+Duniter aims to fix this by making the Universal Dividend (a.k.a. UD)
+grow by the time according to precise rules, thus making members equal
+toward money issuance on a half-lifespan.
+
+Most currencies present one of these two asymmetries, including metal
+currencies and mutual credit, as exposed in the RTM.
+
+1.1.3. A solution
+^^^^^^^^^^^^^^^^^
+
+Bitcoin has taught us that it is possible to create a currency system
+allowing one to both create digital money and to exchange it without a
+central authority. What we need to change is the way money is issued so
+we finally have a symmetrical system. We need **Bitcoin + Universal
+Dividend**. But Universal Dividend implies that the community consists
+of only identified people. This is where the Web of Trust (WoT) comes
+into place.
+
+This concept, introduced by cryptography with the OpenPGP format [3]_,
+allows us to identify people in a decentralized manner. It works as
+follows: each person creates a personal identity that is linked to its
+cyptographic certificate. The identity must be confirmed by others
+members who use their own cryptographic key. It is that simple: people
+choose who is part of the community and who is not, not a central
+authority.
+
+However, Duniter will not use OpenPGP for its cryptographic features:
+Elliptic Curves [4]_ will be used instead for the conciseness of its
+generated keys and its pratical advantages. Duniter has its own Web of
+Trust principles, that will be exposed later.
+
+1.2. Proof-of-Work mining : a power race
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+In Bitcoin Model, the calculation and incentive principles cause a power
+race : new Bitcoins are created for the owners of the most numerous,
+powerful (and energy-consuming) computers. This leads to a power race an
+places the control over the currency in the hands of the richest
+hardware owners. We want to make Duniter blockchain validation much less
+energy and hardware consuming while keeping a strong level of security.
+This will be further explained later. A consequence of this choice is
+the participation of low-end hardware in the Duniter network, leading to
+a better decentralization of blockchain validation.
+
+1.2.1 What about Proof of Stake ?
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Proof of stake consensus algorythm was first introduced in 2012 [5]_.
+The basic principle is to allow the richest wallets to issue blocks,
+putting their coin balance as a “stake” they would lose in case of
+cheat.
+
+At the time of conceiving Duniter, the PoS algorythms had not been
+tested enough to be used as a fundamental base. We did not chose this
+consensus principle. Moreover, the principle of allowing owners of large
+amounts of money to validate transaction can only lead to placing power
+over the currency in the richests hands : this is contrary to the
+symmetical principles of a libre currency.
+
+.. [1]
+   Bitcoin Whitepaper, S.Nakamoto, 2008:
+   `bitcoin.org/bitcoin.pdf <https://bitcoin.org/bitcoin.pdf>`__
+
+.. [2]
+   Relative Theory of Money, S.Laborde, 2010:
+   `en.trm.creationmonetaire.info/ <http://en.trm.creationmonetaire.info/>`__
+
+.. [3]
+   OpenPGP protocol defines standard formats for encrypted messages,
+   signatures, private keys, and certificates for exchanging public
+   keys. The GNU Privacy Handbook, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+
+.. [4]
+   High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+   P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+   77–89.
+   `cr.yp.to/papers.html#ed25519 <https://cr.yp.to/papers.html#ed25519>`__.
+
+.. [5]
+   PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &
+   S.Nadal, 2012 :
+   `archive.org/details/PPCoinPaper <https://archive.org/details/PPCoinPaper>`__
+2. Duniters Blockchain
+----------------------
+
+..   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniters Blockchain follows the basic principles of Bitcoins. This is
+essential for synchronization between peers, as to prevent double-spend
+attacks. However, Duniters Blockchain will store different informations
+than Bitcoins.
+
+The basic use of Blockchain will be registering transactions. For this
+part, we use the same principles as Bitcoin : transactions have inputs
+(spending accounts) and outputs (receiving accounts). But contrary to
+Bitcoin, no generation transaction exists : monetary creation happens
+only through UD. So, in Duniters Blockchain, Inputs can be either:
+
+-  a former transaction (as in Bitcoin)
+-  a Universal Dividend (specific to Duniter).
+
+Duniters Web of Trust is also written in the Blockchain. The identity of
+each member gets registered much like transactions are, with a strong
+link to the time reference. Thus, the Blockchain is a representation of
+a space-time frame of reference, where “space” are members of the WoT
+and “time” the basic blockchain units : the blocks. On each point of
+time, one can determine which account is legitimate to create the UD,
+only with a blockchain analysis.
+
+2.1. Spam countermeasures
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+An issue of most cryptocurrency projects is to prevent the common ledger
+from growing too much. This would require nodes to have a lot of storage
+and computing power to be usable. In particular, we don’t want an
+attacker to be able to make the Blockchain grow too fast. Most projects
+implement transaction fees as a way to prevent this, making the attacker
+lose money. We don’t want to introduce this mean since a currency with
+automatic fees on transactions is no more neutral. Several
+countermeasuers against such spam attacks are implemented.
+
+..   <!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
+
+2.1.1. Minimum output amount
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. raw:: html
+
+   <!-- This has to be implemented in DUBPv13. -->
+
+Fixing a minimal output amount reduces the power of an attack. Duniter
+deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could
+create thousand accounts with only 1 UD. To prevent this, a valid
+transaction must have output amounts of minimum 1Ğ1. This reduces the
+power an attack by 100.
+
+2.1.2. Limited block size and chainability
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The block size is always limited. While the protocol allows this limit
+to evolve to address scaling issues, an attacker cannot register as many
+transaction as they wish.
+
+With the same goal to prevent too many transactions to get registered,
+while transactions can be “chained” (refer to another transaction in the
+same block), the chainability of transactions is limited to 5.
+
+2.2. Scaling
+~~~~~~~~~~~~
+
+Most of the time, the scaling issue rises for distributed systems that
+should work on a very large scale. This is not the case of Duniter, for
+multiple reasons :
+
+-  Ğ1 is the first libre currency, and is still experimental on the
+   monetary creation principle. We don’t want it to reach the whole
+   world, we only want it to work, to validate or invalidate the RTM.
+   Moreover, the rules chosen for the Ğ1 WoT should limit its size to
+   around 16 million members.
+-  Duniter’s aim is to be used to create multiple libre currencies, that
+   would fit local or regional economies. As a consequence, it would
+   deal with less transactions than if it was a world-scale system. The
+   RTM proposes a formula to calculate the exchange rate between two
+   currencies, that could be used to create automatic exchanges for a
+   member travelling away from their community.
+
+However, Duniter has assets that will help if the number of users and
+transactions grow.
+
+2.2.1 Dynamic block size
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+While Bitcoin has a fixed block size, Duniters blocks size can evolve.
+On low use of the blockchain, the maximal block size is 500 bytes. On
+high use of the blockchain, the maximal block size would be 110% of the
+average size of the current window blocks(see “personalised difficulty”
+part for more information). This way, the blocks are bounded in size,
+but can slowly grow if a massive and legitimate use of the blockchain
+needs it. The block size (in bytes) is limited as so :
+
+.. math::  \textrm{blockSize} < \max \left({500 ; \textrm{CEIL}(1.10 \times (\textrm{average block size}))}\right) 
+
+2.2.2. Lightning Networks
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The Lightning Networks [1]_ allow almost instant and off-chain
+transactions. They were first implemented on Lightcoin, and are now on
+Bitcoin. One of their benefits is to make the blockchain store a lot of
+transactions at once, thus reducing the groth of the blockchain. The
+Duniter protocol allows XHX() and CSV() unlock conditions that are
+necessary to implement Lightning Networks. While not available yet, this
+payment channel might get implemented when needed.
+
+2.2.3. Unit base
+^^^^^^^^^^^^^^^^
+
+As the Universal Dividend grows exponentially, with time Duniter nodes
+would have had to deal with always largest amounts, eventually reaching
+the BIGINT limit. To avoid this, the amounts are expressed with a unit
+base in base 10. We want the UD amount to always fit in 4 digits. To
+manage it, the ``unitbase`` is updated each time the UD value reaches
+100.00 : it goes from ``99.99*10^(unitbase)`` to
+``10.00*10^(unitbase+1)``. All the unit amounts are thus divided by 10.
+While this might seem strange, this process has already hapened in state
+currencies. Moreover, the amounts expressed in UD will not change.
+
+With a monetary growth of 10% each year and a stable population, such a
+change of unit base would happen each 25 years.
+
+.. [1]
+   The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 :
+   `lightning.network/lightning-network-paper.pdf <http://lightning.network/lightning-network-paper.pdf>`__
+3. Duniter Web of Trust
+-----------------------
+
+.. _duniter-wot-basic-principles:
+
+3.1. Basic Principles
+~~~~~~~~~~~~~~~~~~~~~
+
+In order to identify “members” accounts - which create monetary units -
+and other accounts, Duniter uses a Web of Trust. This can be summarized
+into few principles:
+
+-  Each account becomes a member if it received a minimal number of
+   certifications - 5 for Ğ1 currency.
+-  Only members accounts can send certifications. Certifications have a
+   limited lifespan.
+-  A certification indicates that the sender accepts the receiver as a
+   legitimate identity.
+
+The aim of the WoT is to identify a blockchain account to a living
+human. According to Lauterbach et.al [1]_, the strengh of a relationship
+should be considered when building a vouch system. For this reason, the
+Ğ1 Web of Trust rules are expressed in a licence stating what WoT
+certifications are. A certification represents a strong human
+relationship : one may certify a close relative, not an acquaintance.
+Each member has to accept this licence before being included in the WoT.
+Thus, if a member is part of an attack on the currency, they can be
+found by mutual relatives. Additional security rules occur to prevent
+cheat and attacks on a large scale.
+
+Note that non-members accounts can use the currency, but cannot create
+money. Non-members accounts can be used by individuals as secondary
+wallets, or by institutions.
+
+We were inspired by the OpenPGP Trust system [2]_. However, the OpenPGP
+trust principles aim at defining trust from a particular point of view
+while Duniter needs to identify humans for the whole community. To
+achieve this goal, while OpenPGP allows each user to tweak its trust
+parameters individually, Duniter sets rules in the “genesis” block for
+the whole community.
+
+3.2. Why do we need a Web of Trust ?
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+There are two reasons we need it :
+
+1. To make sure that only one Universal Dividend is produced per member
+   at each specified creation interval. In the Ğ1’s case this interval
+   is set as daily ``86 400`` seconds, it is the *monetary parameter*
+   known as ``dt``.
+2. To identify the nodes hashing the blocks and assign each a
+   personalised difficulty. This custom difficulty proof of work is
+   there to avoid the blockchain’s validation mechanism becoming too
+   centralised as is the case with many 'non-libre’ cryptocurrencies.
+
+**Monetary parameter**:
+   Each currency that use Duniter has its own
+   blockchain whose behaviour is dictated by a set of ‘parameters’
+   defined in block zero - the so-called genesis block - that can be
+   tweaked to achieve the desired results. At the time of writing the
+   Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21
+   parameters of which 10 are for the WoT alone. We’ll focus on these
+   10.
+
+   Suffice to say that in the Ğ1’s case, the DU is created every 24
+   hours - 86 400 seconds. This interval is set through the time
+   derivative ``dt`` parameter and can have a different value in other
+   implementations of the protocol.
+
+We want to make sure that each member can only have one account. As we
+all know, achieving zero-risk isn’t possible [3]_. Our goal is therefore
+not to create a WoT within which fraud would be absolutely impossible,
+but instead to discourage it. Here is a rewording of our goal in 4
+smaller ones :
+
+1. Make the certification process lengthy enough that all members
+   exercise due diligence and are wary of risks.
+2. Make fraudulent acts as hard as we can to the extent that they become
+   pointless.
+3. Ensure that any Sybil attacks have a negligible impact on the
+   currency by ensuring that illegitimate double Universal Dividends
+   have no significant bearing on the legitimate monetary mass
+4. Slow the growth of ‘Sybil regions’ to give enough time for the
+   community to react and isolate the threat.
+
+**Sybil attack**:
+   A Sybil attack is an attack perpetrated on a
+   reputation system through the creation of fake identities. A Web of
+   Trust is a specific instance of a Reputation System.
+
+There are plenty of Sybil attack scenarios we can think of and just as
+many reasons why their perpetrators would want to carry them out. Our
+objective is that the configuration of the WoT protects both users and
+its IT backbone infrastructure against these attacks.
+
+This means that micro-attacks performed by small groups of individuals
+looking for personal enrichment are of no interest to us. The web’s role
+isn’t to deter these attacks, this being instead the role of the
+community. Just like the town you live in is responsible for providing
+your tap water and electricity but isn’t responsible for any burglaries,
+etc. Much in the same way, Duniter’s WoT guarantees us all a functional
+currency, but do not detect small fraud.
+
+.. _own-certification-system:
+
+3.3. The importance of having our own certification system
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Centralized identification systems can achieve the goal we want. State
+Identification is an example. However, this has many drawbacks :
+
+-  The authority may have arbitrary criteria for identification, for
+   example preventing people without an official state-provided identity
+   or homeless people to be included in the WoT.
+-  Payment might be required to get identified, thus making the monetary
+   creation not “free”.
+-  The authority is a point of failure for any attacker.
+
+It is of the utmost importance that we remain free from any state or
+corporation. The WoT is an answer to this criterium. To this day we
+depend only on the Internet and yet, were it to fail, there are already
+alternatives being tested around the world for a decentralised
+communication network.
+
+.. _graph-theory-vocabulary:
+
+3.4. A few foundational concepts on graph theory : a bit of vocabulary
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+-  **Graph**: set of points -called ‘vertices’- joined by edges -called
+   paths/walks-.
+
+-  **Simple graph**: a graph with no loops and with no multiple edges.
+   That is, each edge connects two distinct endpoints and no two edges
+   have the same endpoints. A simple edge is an edge that is not part of
+   a multiple adjacency -of edges-. In many cases, graphs are assumed to
+   be simple unless specified otherwise.
+
+-  **Directed graph**: a graph in which the edges have a distinguished
+   direction, from one vertex to another. A directed edge can also be
+   called a path or walk. Arrow A –> B is therefore different from arrow
+   B –> A.
+
+-  **Endpoints**: the edge with vertex A –> B has A and B as endpoints,
+   respectively as start and end of the path/walk.
+
+-  **Isolated vertex**: a vertex whose degree is zero, that is, a vertex
+   with no incident edges.
+
+-  **Degree of a vertex**: number of its incident edges -in and out-.
+
+-  **Out-degree of vertex A**: number of outbound edges / tail ends from
+   A.
+
+-  **In-degree of vertex A**: number of incoming edges / head ends to A.
+
+.. figure:: img/degrees_en.jpg
+   :alt: degrees of a vertex diagram
+   :width: 40%
+
+   degrees of a vertex diagram
+
+-  **Path**: -aka “walk”- path to follow to get from vertex A to vertex
+   B.
+
+3.5. Definition of the Duniter Web of Trust
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The Duniter WoTs -one per currency- are simple directed graphs without
+isolated vertices. The vertices are the members and the edges are the
+certifications given and received.
+
+*Directed* means that the responsibility of issuing a certification is
+unique and personal to the certifier. The trust they place in the
+receiver cannot be imposed in the other direction although in most
+circumstances both parties equally trust each other.
+
+In addition, all vertices are either currently active members or
+past-members. Past-member vertices are in a specific ‘deactivated state’
+and can no longer issue or receive certifications although the ones
+already issued or received to/from other members are still considered
+‘pending’ to avoid a collapse of the WoT. If these old members don’t
+come back into the WoT, their pending certifications will eventually
+expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.
+
+To wrap up with old members, after a certain period of time - set in the
+currency’s parameters - their deactivated vertex is removed from the web
+and the associated identity is ‘revoked’. The person who owned the
+account can no longer use this identity but is free to join the web with
+another one.
+
+**Identity**:
+   An identity is a set of three pieces of information: a
+   public key, a name and a blockstamp. A blockstamp points to a
+   specific block in the chain. Its main use is to freeze the point in
+   time at which an identity was created and to link this identity to a
+   specific chain and a currency - each currency having its own
+   blockchain.
+
+   An identity can be in any one of 5 different status: pending, member,
+   old member, revoked or excluded.
+
+Let’s take a simple example:
+
+::
+
+       A -> B -> C
+            |
+            \--> D
+
+If, for whatever reason, A were to lose its member status, the web would
+crumble and all other members would be excluded as a consequence. To
+avoid this, the certification from A –> B will remain valid until its
+expiry date, leaving enough time for B to receive certifications from C
+or D.
+
+Because our WoT doesn’t have any isolated vertices, each new identity
+created needs to be pulled into the web with all of the certifications
+it has received, all in the same block. This calls for a temporary
+‘buffer’ storage space for **pending** identities and the certifications
+they have received. This storage space is called ‘the pool’ of Duniter
+nodes, which we could also have called the ‘sandbox’ as that’s the name
+used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other
+documents and metadata not mentioned here.
+
+.. _exploring-the-rules-behind-duniter-wot:
+
+3.6. Exploring the rules behind a Duniter Web of Trust
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The Duniter WoTs - one per currency - works with a set of eight
+fundamental rules enforced through eleven different parameters. Ten of
+these parameters are set within the genesis block, the eleventh one -
+``msPeriod``- having being hard-coded in the Ğ1’s code subsequently.
+
+3.6.1. Distance rule and referent members (``stepMax`` and ``xPercent``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+These two parameters are closely linked and together define the
+‘distance rule’. The ‘distance rule’ can only be described after
+defining what a ‘referent member’ is:
+
+**Referent member**:
+   Member A is said to be ‘referent’ if and only if
+   the total of their degrees are greater than or equal to
+   ``CEIL-N^-1/stepMax`` where N is the total number of members. As the
+   size of the web will grow this number will grow too, meaning it will
+   take more certification issuances to become a referent member. The
+   number of certifications needed to become a member shouldn’t change.
+
+Let’s now define the distance rule:
+
+**Distance rule**:
+   M ember A is said to observe this rule if and only
+   if for a subset xPercent % of referent members R there exists a path
+   of length less than or equal to ``stepMax`` between R and A.
+
+Referent members only exist so that the distance rule can take effect,
+they have no special privileges over non-referent members. In a perfect
+web, that is one in which each member has certified all members they
+legitimately can, all members would be referent members. However,
+because the web progressively grows in size and because members die and
+are replaced by new ones, there are always members at any given time
+``t`` who haven’t yet certified all members they legitimately could.
+These members would hinder the evolution of the web if they were taken
+into account in the calculation of the distance rule and the web would
+effectively stop growing.
+
+Because verifying the application of the distance rule is
+calculation-greedy, it is only performed when a new identity gets
+confirmed into the web or an existing member gets renewed. There is an
+exception to this rule: the distance rule is not observed in the genesis
+block -when the web is first implemented.
+
+3.6.2. Rule of the minimum number of certifications needed (``sigQty``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This is the simplest rule, it essentially says that each member must at
+any given time -meaning in any single block- have received at least
+``sigQty`` active certifications. If, for whatever reason, member A were
+to have less than ``sigQty`` active certifications in a given block,
+they would cease to be a member and be required to publish a request for
+identity renewal.
+
+3.6.3. The membership renewal rule (``msValidity``, ``msPeriod`` and ``msWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Bear in mind that a membership doesn’t last a lifetime but instead has a
+lifespan set to ``msValidity`` seconds.
+
+Every single member -or old member who hasn’t revoked his identity or
+been excluded- can request a membership renewal so long as the last
+request was made more than ``msPeriod`` seconds ago. If a member has
+never requested a renewal, the date of last renewal is equal to the
+timestamp at which his membership was first created. A new request will
+be stored in the ‘pool’ for a maximum of ``msWindow`` seconds before
+it’s included in the blockchain. Once again, this can only happen
+once/if the member meets both the ``siqQty`` rule and the distance rule
+-if these criterion are already matched it’s just a case of waiting for
+a new block to be mined-.
+
+If a member hasn’t requested a renewal for longer than ``msValidity``
+seconds, they automatically cease to be a member. From this moment on,
+the ex-member has another ``msValidity`` window to renew their
+membership. When this period of ``2 × msValidity`` runs out, the
+membership will expire and this identity will never be available for use
+again in the web. If the person so desires, they will have to publish
+new identity and membership documents and find enough certifiers, as any
+newcomer.
+
+3.6.4. Rule of certification lifespan (``sigValidity``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+All certifications included in the blockchain expire **sigValidity**
+seconds after they were **issued**.
+
+   /!\\ The issuance and the inclusion of a certification in the
+   blockchain occur at different times. When member A issues a
+   certification at time t1, it gets stored in the pool starting at t1
+   and only finds its way into the blockchain at t2 when all of the
+   web’s rules are observed. Several weeks can thus go by between t1 and
+   t2!
+
+3.6.5. Rule of limited supply of active certifications (``sigStock``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+By ‘active certifications’ we refer to certifications included in the
+blockchain and that haven’t yet expired.
+
+The total of active certifications issued by any member at any single
+time must be less than or equal to ``sigStock``. When this threshold is
+reached the member will have to wait for one of his active
+certifications to expire before he/she can issue a new one.
+
+.. _rule-of-the-time-period-between-two-certification-issuances-sigperiod:
+
+3.6.6. Rule of the time period between two certification issuances. (``sigPeriod``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+As soon as a certification issued by member A gets included in the
+blockchain, they will be unable to issue a new one before another
+``sigPeriod`` seconds.
+
+3.6.7. Expiry of a certification issuance (``sigWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+When a certification is issued by member A, it will be stored in the
+‘pool’ for a maximum of ``sigWindow`` seconds. If the certification
+hasn’t been included in the blockchain by then, it will be cancelled and
+the member’s ``sigStock`` will be repleted by one.
+
+3.6.8. Lifespan of a ‘pending’ identity (``idtyWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+When a new identity is created, it is stored in the ‘pool’ for a maximum
+of ``idtyWindow`` seconds. If the person hasn’t achieved member status
+by then, the certification will simply be cancelled.
+
+3.7. Details on some of the WoT’s peculiarities at the genesis block
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The aforementioned rules can only be enforced with an existing web. They
+cannot be observed when first creating the web, that is when defining
+the genesis block.
+
+Only rules 2 and 5 can be observed at the genesis block.
+
+The genesis block has to be manually created by the founding members. In
+practice this means that there must be a choice on which identities to
+include on the premise that all of them observe rules 2 and 5. In
+addition, the genesis block must be signed with the private key of one
+of these identities.
+
+As soon as the genesis block has been created, the other identities can
+start mining the blockchain and the member who created block #0
+effectively looses the decision power he had at creation.
+
+.. _why-these-rules-and-application-cases-in-the-g1:
+
+3.8. Why these rules and application cases in the Ğ1
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+3.8.1. Distance and maximum size
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The distance rule is there to curb the maximum size of a Sybil region as
+well as that of the monetary community as a whole. The ``xpercent``
+parameter prevents the creation of a ‘faction’ that could take hold of
+the blockchain.
+
+.. figure:: img/wot-sybil.jpg
+   :alt: Sybil region
+   :width: 90%
+
+   Sybil region
+
+The Sybil regions are isolated from the rest of the graph in the sense
+that they can only receive certifications from other ill-intentioned
+Sybil members. As a consequence, the shortest edge/path between a
+legitimate member and a Sybil one has to have the attack’s author as an
+endpoint. The maximum depth the Sybil region can attain is therefore
+contingent on the distance between the attacking edge-s- and the
+xpercent% closest referent members, this distance is known as
+``stepAttackers``. The maximum size of a Sybil region created by
+``sigQty`` members depends on the L parameter, defined as
+``L = sigQty/sigStock``:
+
+.. math:: MaxSybilSize = (sigStock - sigQty) \times {1 - L^{(stepMax - stepAttackers)} \over 1 - L} 
+
+The maximum size of the Web of Trust is given by the following formula:
+
+.. math:: WoTmax = sigStock \times L^{(stepMax - 1)} 
+
+However we know for a fact that members will never use all of their
+available certifications. According to Dunbar [4]_, on average, one is
+able to maintain relationships to around 150 people. Being conservative,
+we will consider that on average, each person will certify 50 accounts.
+We can calculate the size of the average web of trust ``WoTavg`` :
+
+..   WoTavg= (50)*(sigQty/50)^(stepMax-1)
+
+.. math:: WotAvg = 50 \times \left(\frac{\textrm{sigQty}}{50}\right)^{stepMax - 1}
+
+Our goal with the Ğ1 is to create a community of about one million
+members to test the consequences of a libre monetary system. Let’s see
+how we can tweak the pair of sigQty and stepMax- to reach this size:
+
+.. figure:: img/wot-moy.png
+   :alt: Average WoT size graph as a function of sigQty and stepMax
+   :width: 90%
+
+   Average WoT size graph as a function of sigQty and stepMax
+
+The maximum size of a Sybil region grows linearly with ``sigQty`` but
+exponentially with ``stepMax``. Logic has it that we need to keep
+``stepMax`` as low as possible to ensure sufficient strength to the web.
+The above graph shows that the lowest value of ``stepMax`` for a web of
+a million members is of 5. This is an order of magnitude and is likely
+to be much higher in reality, we cannot measure it for sure.
+
+For ``sigQty`` we can choose a value of **4** for a web of **1.5 million
+members** or **5** for **half a million members**. Bear in mind these
+are gross figures and could be significantly higher, we are talking
+anywhere between 1 and 10 million in reality. Calculating WOTavg gives
+us a pretty good idea of how the web would scale bearing in mind that it
+considers all members are referent members too -which isn’t the case as
+explained previously-. Hence the maximum size of the web is likely
+larger, a ballpark figure of half a million is enough for now especially
+knowing that the smaller ``sigQty`` is, the easier it is to launch a
+Sybil attack -it’s easier to find four accomplices than five-. For
+security reasons we have settled on five:
+
+
+..   stepMax = 5
+..   sigQty = 5
+..   sigStock \>= 50
+
+.. math:: stepMax = 5
+.. math:: sigQty = 5
+.. math:: sigStock \geq 50
+
+The maximum size of a Sybil region therefore is:
+
+..   (sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))
+
+.. math:: (sigStock-sigQty) * {1 - \left({sigStock \over 5}\right)^{5-stepAttackers}} \over {1-{sigStock \over 5}}
+
+with sigStock = 50 we have a Sybil region of:
+
+..   45*(1-10^(5-stepAttackers))/(-9)
+
+.. math:: 45 \times {1 - 10^{5 - stepAttackers}} \over {- 9}
+
+A good practice for protecting the web is to maximise ``stepAttackers``.
+That’s why we decided that referent members in the genesis block had to
+be at least four steps away from each other.
+
+Another way to keep a Sybil attack at bay, were it slow enough for
+members to notice it, would be for referent members to ‘stretch’ the web
+intentionally to limit the growth of the region by ensuring that the
+attackers’ legitimate certifications received in the first place aren’t
+renewed. But what if bot accounts were created and certified each other
+super fast and following all rules, how would we counter that? By
+introducing a minimum length of time between two certifications!
+
+3.8.2. Time is our friend
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+To help us deter a Sybil attack, we’ve decided to impose a minimum
+period of time between any two certifications issued from a single
+account. This parameter called ``sigPeriod`` affords us a greater chance
+to detect the formation of a ‘hostile’ faction.
+
+Here is a graph showing the evolution of a Sybil region with the
+variation of ``sigPeriod``. The simulation considers that honest members
+and attackers both issue a certification each ``sigPeriod`` interval, in
+days:
+
+.. figure:: img/impact_sig_period.png
+   :alt: size of the WoT according to sigPeriod and stepAttackers
+   :width: 100%
+
+   size of the WoT according to sigPeriod and stepAttackers
+
+As we see, there is a strong link between the growth speed of the region
+and ``sigPeriod``. As evidenced here, we need a ``sigPeriod`` high
+enough in order to ensure that the legitimate web can grow at least as
+fast as a Sybil region. In addition, the higher ``sigPeriod`` is, the
+more members will exercise their certification power gingerly, the
+action coming at a higher ‘cost’.
+
+There are numerous advantages to giving ``sigPeriod`` a high value and
+no technical barriers to it, hence our choice of five days.
+
+We could have also gone for one week for the sake of simplicity. However
+there is an underlying idea behind our choice which was quite simply the
+pace of today’s life. Certifying someone can be a lengthy process as one
+needs to make sure they are correctly applying the Ğ1 licence and people
+nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
+to allow one to certify at the end of every working week -five days-
+instead of a whole calendar one.
+
+3.8.3. Trust me now, trust me forever ? (``sigValidity``, ``msValidity``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+There would be two main drawbacks to a lifetime membership in the Ğ1’s
+Web of Trust:
+
+-  First of all, some members will pass and those accounts should no
+   longer produce the Universal Dividend.
+-  Secondly it is of the utmost importance that ‘rogue’ accounts can be
+   excluded from the web at some point.
+
+To achieve this, certifications have a limited lifespan. Members need to
+seek renewal from their peers after ``sigValidity`` time. On the other
+hand, this time can’t be too short that members would spend more time
+seeking renewal than they would exchanging in the currency. Furthermore,
+a certification with too short a lifespan would foster careless
+certifying behaviours. The act of certifying must have a high-enough
+‘perceived’ cost to make it feel like an important act. Lastly, we also
+wanted this lifespan to be easy to remember. Historically speaking, we
+first settled on the values of ``sigPeriod`` and ``sigStock``, meant one
+could issue all of their certifications in 495 days, one year was
+therefore not long enough. We deemed three years to be too much and
+that’s how we agreed on two years in the end.
+
+Thinking that a deceased member could continue producing the UD for two
+long years without anyone benefitting from it was also something we
+needed to address. We chose a value of one year for **msValidity**. The
+act of renewing every year is done through one of the clients
+interacting with the blockchain, through a simple click on a button.
+This parameter is less important than others and is mostly there to
+‘prune’ the web of past or inactive members who don’t renew their
+membership.
+
+3.8.4. Keeping the pools free of information glut (``idtyWindow``, ``sigWindow``, ``msWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The pools need to be cleaned up on a regular basis to avoid them
+clogging up with information and to ensure that machines with less
+calculating power can still run a Duniter node.
+
+To achieve this, identities with pending membership approval and the
+corresponding certifications have to remain the shortest time possible
+in the pool while still having a chance of making it into the
+blockchain.
+
+For the Ğ1, our opinion was that two months would be enough for all
+potential certifiers to agree on a specific identity to certify. We also
+wanted a time period that would be easy enough to remember by all. We
+settled on two months, and gave this value to all three parameters
+``idtyWindow``, ``sigWindow`` and ``msWindow``.
+
+3.8.5. Avoiding single members from ‘knowing too many people’ (``sigStock``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+| We considered that on average, each person will certify 50 people.
+  However, we know for a fact that some members will use more than 50
+  certifications. The maximum social network of one individual is around
+  150 people [5]_. Being conservative, we settled on a maximum
+  certification number ``sigstock`` of 100.
+| Since ``sigStock``\ ’s impact on the size of a Sybil region is fairly
+  limited, we did not investigate further this parameter.
+
+3.8.6. Avoiding locking minorities (``xpercent``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+It’s easy enough to become a referent member, one of the Sybil
+strategies could therefore be to create a region of referent members.
+Such a region would grow slower than otherwise but could confer a
+locking power to its members by using the distance rule. That’s why the
+distance rule cannot be calculated on 100% of the referent members.
+Hence the introduction of the ``xpercent`` parameter which defines the
+percentage of referent members needing to be less than five edges
+-steps- from each other.
+
+This percentage needs to be low enough to prevent the formation of a
+locking minority -referent Sybil members being too far from legitimate
+referent members-. On the other hand, it needs to be high enough so as
+to restrict the maximum size of the Sybil region through the distance
+rule. The ``xpercent`` parameter was one of the hardest to define,
+therefore we might decide to change its value during the Ğ1 experiment.
+
+We were inspired by the Pareto principle [6]_: if at least 20% of
+members give good density to the web, 80% of the referent members will
+be five or less steps from any other member -referent or not-. The
+maximum value for ``xpercent`` is therefore 80%, anything above that and
+the distance rule could be too restrictive for legitimate use cases.
+With security our top concern, we chose the maximum value of 80%.
+
+3.8.7. Spam protection with (``msPeriod``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This parameter stands out a bit on its own, as it was added after the
+genesis block. It is there to protect the Duniter P2P infrastructure
+against ‘spam’ attacks. We had to think of a strategy against attacks
+such as high-frequency membership renewal requests -i.e: in every block,
+every five minutes- or worse still, hundreds of these requests per
+minute to flood the Duniter nodes. Without such limits, nodes are
+supposed to address all renewal requests, even in cases where they were
+last published five minutes ago! The ``msPeriod`` parameter was given
+the same value as ``idtyWindow``, ``sigWindow`` and ``msWindow``,
+i.e. two months.
+
+.. [1]
+   Surfing a Web of Trust, Reputation and Reciprocity on
+   CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic:
+   `snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf <http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf>`__
+
+.. [2]
+   Public key validation on GnuPG manual, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+
+.. [3]
+   The Sibyl Attack, J.R.Douceur:
+   `www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf <https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf>`__
+
+.. [4]
+   Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
+
+.. [5]
+   Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
+
+.. [6]
+   Pareto principle :
+   `en.wikipedia.org/wiki/Pareto_principle <https://en.wikipedia.org/wiki/Pareto_principle>`__
+.. _proof-of-work-with-personalized-difficulty:
+
+4. Proof of Work with personal difficulty
+-----------------------------------------
+
+As each P2P cryptocurrency, Duniter has a way to synchronize its peers.
+It uses a proof of Work (PoW) to write the Blockchain on a regular
+basis, much like BitCoin. However, Duniter has a unique asset : the WoT,
+where each member represents a unique living human.
+
+This difference might seem minimal, but it has an enormous consequence :
+while Bitcoin uses a race based on computing power only, Duniter creates
+a validation frame that is no race. It is more like a lottery where each
+“winning” member is excluded for a certain amount of time. Moreover,
+those who have more computing power get a handicap, as a way to let
+other peers win. All this is possible through the WoT, that allows
+personalised difficulty while PoW is used for synchronization. All the
+rules of this PoW/WoT mechanism can be verified by reading the
+blockchain. As a consequence, a peer only needs to have an up-to-date
+copy of the blockchain to apply the rules. A view of the whole network
+is not needed.
+
+Another strong difference is that forging peers are not rewarded by the
+protocol. There is no economical incentive on forging lots of blocs,
+neither on having a lot of computing power.
+
+One could say that Duniter uses a PoW that needs very low energy
+consumption compared to BitCoin : an “ecological” PoW ?
+
+.. <!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
+
+.. _why-proof-of-work:
+
+4.1. Why do we need Proof of Work ?
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Duniter nodes share a database as part of a p2p environment. The proof
+of work (PoW) allows machines to synchronize with each other. In
+Duniter’s case, the blockchain is our database, and acts as a ledger
+keeping a trace of all transactions, status of the WoT and more. How can
+we let several machines add data (ie: a transaction) at the same time?
+In addition, how do we settle on how much time has gone by since the
+blockchain was last updated? Agreement on time is of the utmost
+importance as we want to create Universal Dividends on a regular basis,
+and keep track of membership status, both in human time.
+
+Proof-of-work provides a clever solution to both problems:
+
+1. Any machine can write into the blockchain (create a new block) but is
+   only authorised to do so if it has previously solved a mathematical
+   equation that require a certain amount of work. The challenge has to
+   be hard enough to prevent two machines to solve it at the same time,
+   ensuring the unicity of a block’s creator.
+
+2. Solving this challenge takes a certain amount of time, which depends
+   on the calculating power of the whole network. This provides a common
+   ground for defining the needed time reference. A block time is set
+   (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to
+   get an average duration corresponding to this block time.
+
+4.2. Only members can “mine”
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+One of Duniter’s major differences with other PoW-based cryptocurrencies
+is that only members are allowed to author blocks. Each block is signed
+with the member’s private key, allowing the algorithm to determine a
+personalised difficulty.
+
+This personalised difficulty eliminates the rat-race for the most
+sophisticated and powerful mining equipment. Another benefit is the fact
+that no “supercomputer” can take control of the blockchain. Lastly,
+Duniter implements a rotation in forging members thanks to this
+personalized difficulty.
+
+This lightweight PoW is much less energy-consuming than other PoW
+cryptocurrencies. Members can mine with anything from a raspberry pi to
+a privacy-first internet cube.
+
+.. _how-does-duniter-pow-work:
+
+4.3. How does it work ?
+~~~~~~~~~~~~~~~~~~~~~~~
+
+.. _the-hash:
+
+4.3.1. The hash (aka digest)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Example of a valid hash:
+
+::
+
+   00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653
+
+As you can see this hash starts with five zeros which was very hard to
+achieve and took a lot of work for someone’s computer. Hence the term
+“proof of work”.
+
+.. _common-difficulty:
+
+4.3.2. The common difficulty
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+A common difficulty is needed to settle on a yardstick for our time
+reference. Its role is to make sure the blockchain moves forward at a
+steady pace - one block every ``avgGenTime`` seconds, ``avgGenTime``
+being one of the 20 parameters behind the Duniter protocol-.
+
+This difficulty’s initial value can be set to any arbitrary value
+(``70`` in Duniter ``v1.5.x``) and then acts as a spring, regulating
+blocktime creation by increasing itself if the creation interval drops
+under ``avgGenTime`` and vice-versa.
+
+4.3.2.1. How is difficulty applied ?
+''''''''''''''''''''''''''''''''''''
+
+The numeric value of difficulty is taken from an array of possible
+hashes out of all possible hashes. In DUBPv13 the hash of a block is its
+sha256 hexadecimal hash.
+
+To understand the difficulty, we make a euclidiean division of the
+difficulty by 16.
+
+Here’s an example with a difficulty value of 70 :
+
+..   70 // 16 = 4 with a remainder of 6. 
+
+   70 / 16 = 4 with a remainder of 6. 
+
+The valid hashes are the ones starting with four zeros and with the
+fifth character less than or equal to 9 (6 in hexadecimal notation). The
+valid hashes are then written as starting with : ``0000[0-9]``. This is
+a bit different from Bitcoin, where the difficulty is only ruled by the
+number of zeroes.
+
+4.3.2.2. The Nonce
+''''''''''''''''''
+
+When a member is forging a new block, his computer freezes the block’s
+content and changes the Nonce until the hash reaches the required number
+of zeroes.
+
+The nonce allows us to mine a new block by finding a hash. The hash
+value allows us to determine the difficulty level of the proof-of-work
+performed. Examples of possible Nonce values:
+
+-  10100000112275
+-  10300000288743
+-  10400000008538
+-  10700000079653
+-  10300000070919
+
+In reality the ``Nonce`` value follows a pre-determined format akin to
+``XYY00000000000``. The Nonce’s value isn’t the number of attempts but
+rather a value within a set of possible ones. This is how the Nonce is
+built:
+
+-  X is a number assigned to a specific peer. Let’s assume that someone
+   has several nodes each with the same private key, this would lead to
+   possible collisions if this person were to mine the same block with
+   different nodes. Each [STRIKEOUT:block] **node ?** will therefore
+   have its own unique X to prevent this from happening.
+
+-  Y is the number of cores of the processor. The Nonce starting with
+   ``107[…]`` belongs to a seven cores processor, while ``199[...]``
+   could be the proof generated by a 99 cores processor.
+
+The rest of the Nonce, the part that follows after the XYY, is the
+numerical space for this individual node and is unique to each of the
+CPU’s core. This space is comprised of eleven digits (``00000000000``).
+For the sake of accuracy, we use the term CPU in the wider sense, it can
+be understood as a bi-CPU for example. We take into consideration the
+number of cores for the resulting PoW.
+
+4.4. Personalised difficulty
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Earlier in this article, we explained that the personalised difficulty
+is the new and key concept that sets Duniter apart from other PoW-based
+cryptocurrencies.
+
+Here is how this personalised difficulty is calculated and assigned:
+
+It is determined by a combination of two different constraints with
+complimentary roles: the **exclusion factor** and the **handicap**.
+
+Let ``powMin`` be the common difficulty, ``exFact`` a member’s exclusion
+factor and ``handicap`` their handicap. This member’s personalised
+difficulty ``diff`` is:
+
+..   diff = powMin*exFact + handicap
+
+.. math:: {\textrm{diff} = \textrm{powMin} \times \textrm{exFact} + \textrm{handicap}}
+
+.. _the-exclusion-factor:
+
+4.4.1. Understanding ``exFact``, the exclusion factor
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Members who have never produced blocks or haven’t for quite some time
+are assigned an exclusion factor of ``1``. Their personalised difficulty
+is therefore simply the sum of ``powMin + handicap``.
+
+Before reading on, let’s precise the role of this exclusion factor. When
+a member adds a block to the chain, his ``exFact`` jumps up from one to
+a very high value, to prevent them from forging other blocks immediately
+after and taking control of the blockchain.
+
+The exclusion factor will then rapidly return to one. This delay is
+expressed as a number of blocks. It is calculated as a proportion of the
+number of members forging. In the Ğ1’s case, this proportion is 1/3,
+meaning that if there are fifteen members currently forging, the
+member’s exclusion factor will drop down to one after five blocks.
+
+4.4.1.1. What is intended by “the number of members forging” ?
+''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
+
+We mean the number of members trying to create the next block. In
+reality, there is no way to precisely know how many members are
+calculating at any given time, because it is impossible to view the
+entire network. But we need this information, whithout which assigning a
+personalised difficulty is impossible. To achieve this, Duniter looks
+back at the blockchain and assumes that there is as much members forging
+as those who have found at least one block in the last blocks in the
+current window, minus the very last one.
+
+4.4.1.2. Current window
+'''''''''''''''''''''''
+
+We use the concept of **current window**. The current window is the
+number of blocks we look back at to determine how many members are
+forging. Let’s see how it works:
+
+-  ``issuersFrame`` is the size of the current window in blocks.
+
+-  ``issuersCount`` the number of members who have calculated at least
+   one block during the current window.
+
+Both ``issuersFrame`` and ``issuersCount`` are block fields. When first
+starting a blockchain, the very first block has an ``issuersFrame=1``
+and an ``issuersCount=0``. The genesis block is excluded as there are no
+members in the current window!
+
+From the second block onwards (block #1) we track the variation of
+``issuersCount``. The member having mined block #0 enters the current
+window and in block #1 we will therefore mention ``issuersCount=1``.
+
+``issuersFrame`` then varies as follows:
+
+-  if ``issuersCount`` increases by N (with a maximum step of N = 1),
+   then ``issuersFrame`` will increase by one unit over a period of 5N
+   blocks.
+-  Conversely, if ``issuersCount`` decreases by Y (with a maximum step
+   of Y = 2 = current window inching forward + loss of one calculating
+   member), then ``issuersFrame`` will decrease by one unit during 5Y
+   blocks.
+-  When such events overlap, ``issuersFrame`` evolves as so :
+
+======= ============================================ ===============
+bloc    event                                        issuersFrame
+======= ============================================ ===============
+T       Babar writes a block and enters issuersCount 160
+T+1     Celeste leaves issuersCount                  160 +1 = 161
+T+2     N/a                                          161 +1 -1 = 161
+T+3/4/5 N/a                                          161 +1 -1 = 161
+T+6     N/a                                          161 -1 = 160
+======= ============================================ ===============
+
+The calculation can be found under rules
+`BR_G05 <https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe>`__
+and
+`BR_G06 <https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar>`__
+of the DUP protocol.
+
+4.4.1.3. exFact and the personalised difficulty
+'''''''''''''''''''''''''''''''''''''''''''''''
+
+We explained that ``exFact`` spikes immediately after the member has
+found a block. It decreases then rapidly to ``1`` after a number of
+blocks equal to ``1/3 * issuersCount``. Let’s see precisely how we
+calculate ``exFact``:
+
+-  ``nbPreviousIssuers`` is the value of issuersCount at the last block
+   ``N`` found by the member.
+
+-  ``nbBlocksSince`` is the number of blocks found by the rest of the
+   network since block ``N``.
+
+-  ``percentRot`` is the number of *not excluded* peers we want. It is a
+   monetary parameter, its value is 0.67 for Ğ1 currency.
+
+..   a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
+..   exFact = MAX [ 1 ; a ]
+
+.. math:: exFact = MAX[ 1 ; FLOOR ({{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}}) ]
+
+
+The FLOOR is a simple truncate function. For ``exFact`` to exclude the
+member, we need :
+
+..   (percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) >= 2
+
+.. math:: {{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}} >= 2
+
+We can see that the member is not excluded if ``nbBlocksSince`` is
+greater than 1/3 of the calculating members. Take as an example
+``nbPreviousIssuers = 6`` and ``nbBlocksSince = 3``:
+
+..   (0.67* 6 / (1 + 3)) = 1.005 -> exFact = 1
+
+.. math:: {0.67 \times {6 \over {1 + 3}} = 1.005} \Rightarrow exFact = 1
+
+
+However, if the member computed a block one block ago (nbBlocksSince =
+1), exFact = 2 and the forging peer is excluded:
+
+
+..   (0.67 * 6 / (1 + 1)) = 2.01 -> exFact = 2
+
+.. math:: {0.67 \times {6 \over {1 + 1}} = 2.01} \Rightarrow exFact = 2
+
+
+Moreover if the last block was authored by the said member, then:
+
+..   nbBlocksSince=0   and 
+..   exFact = 0.67 * nbPreviousIssuers
+
+.. math:: nbBlocksSince = 0  
+.. math:: exFact = 0.67 \times nbPreviousIssuers
+
+
+ExFact value increases according to the number of members calculating.
+Thus, if there is enough members calculating, even mining farms would be
+excluded. We have therefore succeeded in our intent to deter attempts to
+seize the blockchain and its currency.
+
+However, at any time ``t``, the two-thirds of calculating members all
+have an exclusion factor of ``1``, even though they might not all have
+the same computational power at hand. If the personalised difficulty
+only took into account the exclusion factor, then only the members with
+the highest computational power from the remaining third would be able
+to author new blocks and the other 2/3s would almost always be excluded.
+Lesser machines wouldn’t stand a chance…
+
+4.4.2. The handicap
+^^^^^^^^^^^^^^^^^^^
+
+The handicap is the second parameter of the personalised difficulty. Its
+main role is to improve the rotation of forging peers. A higher handicap
+is assigned to members with higher calculating power, so lesser machines
+can also compute blocks. As a consequence, there is no incentive on
+forging with powerful computers. Security can be achieved with less
+computing power than with pure PoW.
+
+The aim is to handicap the half that has authored most blocks (the most
+powerful half) to favour the other one. So, the handicap formula will
+use the median number of blocks authored by peers within the current
+window.
+
+-  ``nbPersonalBlocksInFrame`` is the number of blocks authored by a
+   single member within the current window.
+
+-  ``medianOfBlocksInFrame`` is the median number of blocks written by
+   the calculating members during the same timeframe.
+
+
+..   a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
+..   handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))
+
+.. math:: handicap = FLOOR( {\ln({ \max({ 1 ; {{nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame} )} )} \over \ln{1.189} })
+
+
+Let’s unwrap the formula:
+
+..   (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)
+
+.. math:: { {nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame}
+
+is simply the ratio between the number of blocks authored by the peer
+and the median number of blocks. For example, if a peer has authored
+``9`` blocks in the current window and the median is ``5``, then the
+ratio will be ``(9+1)/5 = 2``. 
+
+- The MAX function allows us to ensure that
+the handicap has a value at least equal to ``1``.
+
+- The Napierian Logarithm of this ratio prevents the handicap from
+becoming excluding. We want the handicap to level the calculating field
+so that all peers stand a chance, not to exclude peers.
+
+- If we wanted the handicap to be applied as soon as the median is
+reached, we would divide it by ``LN(1)``. The problem is that we have
+already set a minimum value of ``1`` with the MAX function. If we were
+to divide the ratio by ``LN(1)`` all calculating peers would have a
+handicap ``\>= 1``. In addition, is it really fair to handicap a member
+who is right on the median?
+
+That’s why we went for ``1.189`` rather than ``1``. A member has to be
+at least ``18.9%`` above the median to be assigned a handicap. 18.9% is
+actually 16^(1/16), the difficulty factor between two levels of the
+proof work (hexadecimal hash).
+
+To conclude, you have to remember that :
+
+-  The handicap is indexed on the logarithm of the ratio to the median,
+-  Handicap is only applied on members whose ratio to the median is
+   greater than the ratio between two levels of the proof-of-work’s
+   difficulty.
+Conclusion
+----------
+
+.. raw:: html
+
+   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniter’s Blockchain can be compared to Bitcoin’s : a common document
+retracing the history of the currency. However, Duniter registers not
+only trades, but also the history of relationships in the community as a
+mean to identify a human to a digital account. This way, Duniter has
+information about the fondamental reference of RTM : living humans. A
+libre Currency can be issued thanks to the Universal Dividend.
+
+More than that, Duniter proposes a new model for securing a Blockchain
+in an efficient and decentralized way. Basing the security on a Web of
+Trust with an individualised security makes the calculation rules more
+fair. A side-effect of this choice is a network consisting mostly of
+low-end computers, maintaining a good security and helping
+decentralization of calculation.
+
+The ultimate goal of Duniter project is to allow people to participate
+in a libre economy, thanks to a libre currency. What is a libre economy
+? The Relative Theory of Money defines it through four economic
+liberties :
+
+-  The freedom to choose your currency system: because money should not
+   be imposed.
+-  The freedom to access resources: because we all should have access to
+   economic & monetary resources.
+-  The freedom to estimate and produce value: because value is a purely
+   relative to each individual.
+-  The freedom to trade with the money: because we should not be limited
+   by the avaible money supply.
+
+Those 4 economic freedoms should be understood together, not
+exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So
+here, freedom does not mean the right to take all of a resource (like
+water source in a desert) so no more is available to the others. Now you
+get it, this is the goal: free economy through free currency.
+
+Sources :
+---------
+
+-  Relative Theory of Money, S.Laborde, 2010:
+   `en.trm.creationmonetaire.info/ <http://en.trm.creationmonetaire.info/>`__
+-  Bitcoin Whitepaper, S.Nakamoto, 2008:
+   `bitcoin.org/bitcoin.pdf <https://bitcoin.org/bitcoin.pdf>`__
+-  The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 :
+   `lightning.network/lightning-network-paper.pdf <http://lightning.network/lightning-network-paper.pdf>`__
+-  The GNU Privacy Handbook, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+-  High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+   P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+   77–89.
+   `cr.yp.to/papers.html#ed25519 <https://cr.yp.to/papers.html#ed25519>`__.
+-  PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &
+   S.Nadal, 2012 :
+   `archive.org/details/PPCoinPaper <https://archive.org/details/PPCoinPaper>`__
+-  Duniter Blockchain Protocol, v13, draft by Elois :
+   `git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md <https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md>`__
+-  The Sibyl Attack, J.R.Douceur:
+   `www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf <https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf>`__
+-  Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
diff --git a/build/_sources/parts/en/1_intro.rst.txt b/build/_sources/parts/en/1_intro.rst.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c4247f7f024e99c6fcf2faa76bd18f443d83e52
--- /dev/null
+++ b/build/_sources/parts/en/1_intro.rst.txt
@@ -0,0 +1,56 @@
+.. Duniter: A libre currency blockchain generator.
+
+.. ===============================================
+
+Abstract
+--------
+
+Many currency principles involve non-equal rights to monetary creation
+between humans. We propose a monetary creation based on the Relative
+Theory of Money, which guarantee equal monetary creation for each
+willing human. This type of currency can be centralised, however, this
+could lead to censorship and arbitrary choices of the central
+institution. Thus, strongly inspired by Bitcoin example, we want the
+currency to be as decentralised as possible, in the transaction network
+as in the human identification process. We use a Web of Trust between
+living humans for identification. This web of trust allows us to impose
+personalised difficulty for transaction validation, keeping the
+calculation accessible to low-end hardware and allowing all competent
+members to secure the currency.
+
+Introduction
+------------
+
+Duniter is a software to create and manage “libre currencies”. Libre
+currency is a concept defined by S.Laborde in the Relative Theory of
+Money (RTM) that was published in 2010. This theory demonstrates the
+possibility of an invariant monetary unit : the Universal Dividend.
+Doing so, the RTM answers the question :
+
+   How should a currency be created to match the principle of equality
+   between all humans, now and between generations ?
+
+The results of this demonstration implies a monetary creation :
+
+-  on a regular basis
+-  for each human being
+-  which amount has to be reassessed on fixed intervals according to a
+   fixed formula.
+
+Thus, Duniter project will associate a human to a digital identity. It
+will use a Web of Trust with specific rules. As the number of members
+may evolve, the Universal Dividend has to be created according to the
+formula :
+
+.. math::  UD(t+1) = UD(t) + c^2 \times {M(t) \over N(t)} 
+
+Duniter is based on a decentralized Blockchain. This technical choice
+allows irreversibility of transaction and uncensorability of trades and
+identities. While inspired by Bitcoin, Duniter uses a Web of Trust and
+the Proof of Work to secure the computation network, thus making
+obsolete the power race model used in Bitcoin.
+
+The first currency created through Duniter is Ğ1, pronounced “June”. It
+was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters
+as examples ; however, one can create another libre currency with custom
+parameters while still using Duniter software.
diff --git a/chapters/en/2_looking_at_Bitcoin.rst b/build/_sources/parts/en/2_looking_at_Bitcoin.rst.txt
similarity index 100%
rename from chapters/en/2_looking_at_Bitcoin.rst
rename to build/_sources/parts/en/2_looking_at_Bitcoin.rst.txt
diff --git a/chapters/en/3_blockchain.rst b/build/_sources/parts/en/3_blockchain.rst.txt
similarity index 100%
rename from chapters/en/3_blockchain.rst
rename to build/_sources/parts/en/3_blockchain.rst.txt
diff --git a/build/_sources/parts/en/4_Web_Of_Trust.rst.txt b/build/_sources/parts/en/4_Web_Of_Trust.rst.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5fc1f51b2dbedb588d5724b4c20fb388de503dcf
--- /dev/null
+++ b/build/_sources/parts/en/4_Web_Of_Trust.rst.txt
@@ -0,0 +1,648 @@
+3. Duniter Web of Trust
+-----------------------
+
+.. _duniter-wot-basic-principles:
+
+3.1. Basic Principles
+~~~~~~~~~~~~~~~~~~~~~
+
+In order to identify “members” accounts - which create monetary units -
+and other accounts, Duniter uses a Web of Trust. This can be summarized
+into few principles:
+
+-  Each account becomes a member if it received a minimal number of
+   certifications - 5 for Ğ1 currency.
+-  Only members accounts can send certifications. Certifications have a
+   limited lifespan.
+-  A certification indicates that the sender accepts the receiver as a
+   legitimate identity.
+
+The aim of the WoT is to identify a blockchain account to a living
+human. According to Lauterbach et.al [1]_, the strengh of a relationship
+should be considered when building a vouch system. For this reason, the
+Ğ1 Web of Trust rules are expressed in a licence stating what WoT
+certifications are. A certification represents a strong human
+relationship : one may certify a close relative, not an acquaintance.
+Each member has to accept this licence before being included in the WoT.
+Thus, if a member is part of an attack on the currency, they can be
+found by mutual relatives. Additional security rules occur to prevent
+cheat and attacks on a large scale.
+
+Note that non-members accounts can use the currency, but cannot create
+money. Non-members accounts can be used by individuals as secondary
+wallets, or by institutions.
+
+We were inspired by the OpenPGP Trust system [2]_. However, the OpenPGP
+trust principles aim at defining trust from a particular point of view
+while Duniter needs to identify humans for the whole community. To
+achieve this goal, while OpenPGP allows each user to tweak its trust
+parameters individually, Duniter sets rules in the “genesis” block for
+the whole community.
+
+3.2. Why do we need a Web of Trust ?
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+There are two reasons we need it :
+
+1. To make sure that only one Universal Dividend is produced per member
+   at each specified creation interval. In the Ğ1’s case this interval
+   is set as daily ``86 400`` seconds, it is the *monetary parameter*
+   known as ``dt``.
+2. To identify the nodes hashing the blocks and assign each a
+   personalised difficulty. This custom difficulty proof of work is
+   there to avoid the blockchain’s validation mechanism becoming too
+   centralised as is the case with many 'non-libre’ cryptocurrencies.
+
+**Monetary parameter**:
+   Each currency that use Duniter has its own
+   blockchain whose behaviour is dictated by a set of ‘parameters’
+   defined in block zero - the so-called genesis block - that can be
+   tweaked to achieve the desired results. At the time of writing the
+   Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21
+   parameters of which 10 are for the WoT alone. We’ll focus on these
+   10.
+
+   Suffice to say that in the Ğ1’s case, the DU is created every 24
+   hours - 86 400 seconds. This interval is set through the time
+   derivative ``dt`` parameter and can have a different value in other
+   implementations of the protocol.
+
+We want to make sure that each member can only have one account. As we
+all know, achieving zero-risk isn’t possible [3]_. Our goal is therefore
+not to create a WoT within which fraud would be absolutely impossible,
+but instead to discourage it. Here is a rewording of our goal in 4
+smaller ones :
+
+1. Make the certification process lengthy enough that all members
+   exercise due diligence and are wary of risks.
+2. Make fraudulent acts as hard as we can to the extent that they become
+   pointless.
+3. Ensure that any Sybil attacks have a negligible impact on the
+   currency by ensuring that illegitimate double Universal Dividends
+   have no significant bearing on the legitimate monetary mass
+4. Slow the growth of ‘Sybil regions’ to give enough time for the
+   community to react and isolate the threat.
+
+**Sybil attack**:
+   A Sybil attack is an attack perpetrated on a
+   reputation system through the creation of fake identities. A Web of
+   Trust is a specific instance of a Reputation System.
+
+There are plenty of Sybil attack scenarios we can think of and just as
+many reasons why their perpetrators would want to carry them out. Our
+objective is that the configuration of the WoT protects both users and
+its IT backbone infrastructure against these attacks.
+
+This means that micro-attacks performed by small groups of individuals
+looking for personal enrichment are of no interest to us. The web’s role
+isn’t to deter these attacks, this being instead the role of the
+community. Just like the town you live in is responsible for providing
+your tap water and electricity but isn’t responsible for any burglaries,
+etc. Much in the same way, Duniter’s WoT guarantees us all a functional
+currency, but do not detect small fraud.
+
+.. _own-certification-system:
+
+3.3. The importance of having our own certification system
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Centralized identification systems can achieve the goal we want. State
+Identification is an example. However, this has many drawbacks :
+
+-  The authority may have arbitrary criteria for identification, for
+   example preventing people without an official state-provided identity
+   or homeless people to be included in the WoT.
+-  Payment might be required to get identified, thus making the monetary
+   creation not “free”.
+-  The authority is a point of failure for any attacker.
+
+It is of the utmost importance that we remain free from any state or
+corporation. The WoT is an answer to this criterium. To this day we
+depend only on the Internet and yet, were it to fail, there are already
+alternatives being tested around the world for a decentralised
+communication network.
+
+.. _graph-theory-vocabulary:
+
+3.4. A few foundational concepts on graph theory : a bit of vocabulary
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+-  **Graph**: set of points -called ‘vertices’- joined by edges -called
+   paths/walks-.
+
+-  **Simple graph**: a graph with no loops and with no multiple edges.
+   That is, each edge connects two distinct endpoints and no two edges
+   have the same endpoints. A simple edge is an edge that is not part of
+   a multiple adjacency -of edges-. In many cases, graphs are assumed to
+   be simple unless specified otherwise.
+
+-  **Directed graph**: a graph in which the edges have a distinguished
+   direction, from one vertex to another. A directed edge can also be
+   called a path or walk. Arrow A –> B is therefore different from arrow
+   B –> A.
+
+-  **Endpoints**: the edge with vertex A –> B has A and B as endpoints,
+   respectively as start and end of the path/walk.
+
+-  **Isolated vertex**: a vertex whose degree is zero, that is, a vertex
+   with no incident edges.
+
+-  **Degree of a vertex**: number of its incident edges -in and out-.
+
+-  **Out-degree of vertex A**: number of outbound edges / tail ends from
+   A.
+
+-  **In-degree of vertex A**: number of incoming edges / head ends to A.
+
+.. figure:: img/degrees_en.jpg
+   :alt: degrees of a vertex diagram
+   :width: 40%
+
+   degrees of a vertex diagram
+
+-  **Path**: -aka “walk”- path to follow to get from vertex A to vertex
+   B.
+
+3.5. Definition of the Duniter Web of Trust
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The Duniter WoTs -one per currency- are simple directed graphs without
+isolated vertices. The vertices are the members and the edges are the
+certifications given and received.
+
+*Directed* means that the responsibility of issuing a certification is
+unique and personal to the certifier. The trust they place in the
+receiver cannot be imposed in the other direction although in most
+circumstances both parties equally trust each other.
+
+In addition, all vertices are either currently active members or
+past-members. Past-member vertices are in a specific ‘deactivated state’
+and can no longer issue or receive certifications although the ones
+already issued or received to/from other members are still considered
+‘pending’ to avoid a collapse of the WoT. If these old members don’t
+come back into the WoT, their pending certifications will eventually
+expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.
+
+To wrap up with old members, after a certain period of time - set in the
+currency’s parameters - their deactivated vertex is removed from the web
+and the associated identity is ‘revoked’. The person who owned the
+account can no longer use this identity but is free to join the web with
+another one.
+
+**Identity**:
+   An identity is a set of three pieces of information: a
+   public key, a name and a blockstamp. A blockstamp points to a
+   specific block in the chain. Its main use is to freeze the point in
+   time at which an identity was created and to link this identity to a
+   specific chain and a currency - each currency having its own
+   blockchain.
+
+   An identity can be in any one of 5 different status: pending, member,
+   old member, revoked or excluded.
+
+Let’s take a simple example:
+
+::
+
+       A -> B -> C
+            |
+            \--> D
+
+If, for whatever reason, A were to lose its member status, the web would
+crumble and all other members would be excluded as a consequence. To
+avoid this, the certification from A –> B will remain valid until its
+expiry date, leaving enough time for B to receive certifications from C
+or D.
+
+Because our WoT doesn’t have any isolated vertices, each new identity
+created needs to be pulled into the web with all of the certifications
+it has received, all in the same block. This calls for a temporary
+‘buffer’ storage space for **pending** identities and the certifications
+they have received. This storage space is called ‘the pool’ of Duniter
+nodes, which we could also have called the ‘sandbox’ as that’s the name
+used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other
+documents and metadata not mentioned here.
+
+.. _exploring-the-rules-behind-duniter-wot:
+
+3.6. Exploring the rules behind a Duniter Web of Trust
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The Duniter WoTs - one per currency - works with a set of eight
+fundamental rules enforced through eleven different parameters. Ten of
+these parameters are set within the genesis block, the eleventh one -
+``msPeriod``- having being hard-coded in the Ğ1’s code subsequently.
+
+3.6.1. Distance rule and referent members (``stepMax`` and ``xPercent``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+These two parameters are closely linked and together define the
+‘distance rule’. The ‘distance rule’ can only be described after
+defining what a ‘referent member’ is:
+
+**Referent member**:
+   Member A is said to be ‘referent’ if and only if
+   the total of their degrees are greater than or equal to
+   ``CEIL-N^-1/stepMax`` where N is the total number of members. As the
+   size of the web will grow this number will grow too, meaning it will
+   take more certification issuances to become a referent member. The
+   number of certifications needed to become a member shouldn’t change.
+
+Let’s now define the distance rule:
+
+**Distance rule**:
+   M ember A is said to observe this rule if and only
+   if for a subset xPercent % of referent members R there exists a path
+   of length less than or equal to ``stepMax`` between R and A.
+
+Referent members only exist so that the distance rule can take effect,
+they have no special privileges over non-referent members. In a perfect
+web, that is one in which each member has certified all members they
+legitimately can, all members would be referent members. However,
+because the web progressively grows in size and because members die and
+are replaced by new ones, there are always members at any given time
+``t`` who haven’t yet certified all members they legitimately could.
+These members would hinder the evolution of the web if they were taken
+into account in the calculation of the distance rule and the web would
+effectively stop growing.
+
+Because verifying the application of the distance rule is
+calculation-greedy, it is only performed when a new identity gets
+confirmed into the web or an existing member gets renewed. There is an
+exception to this rule: the distance rule is not observed in the genesis
+block -when the web is first implemented.
+
+3.6.2. Rule of the minimum number of certifications needed (``sigQty``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This is the simplest rule, it essentially says that each member must at
+any given time -meaning in any single block- have received at least
+``sigQty`` active certifications. If, for whatever reason, member A were
+to have less than ``sigQty`` active certifications in a given block,
+they would cease to be a member and be required to publish a request for
+identity renewal.
+
+3.6.3. The membership renewal rule (``msValidity``, ``msPeriod`` and ``msWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Bear in mind that a membership doesn’t last a lifetime but instead has a
+lifespan set to ``msValidity`` seconds.
+
+Every single member -or old member who hasn’t revoked his identity or
+been excluded- can request a membership renewal so long as the last
+request was made more than ``msPeriod`` seconds ago. If a member has
+never requested a renewal, the date of last renewal is equal to the
+timestamp at which his membership was first created. A new request will
+be stored in the ‘pool’ for a maximum of ``msWindow`` seconds before
+it’s included in the blockchain. Once again, this can only happen
+once/if the member meets both the ``siqQty`` rule and the distance rule
+-if these criterion are already matched it’s just a case of waiting for
+a new block to be mined-.
+
+If a member hasn’t requested a renewal for longer than ``msValidity``
+seconds, they automatically cease to be a member. From this moment on,
+the ex-member has another ``msValidity`` window to renew their
+membership. When this period of ``2 × msValidity`` runs out, the
+membership will expire and this identity will never be available for use
+again in the web. If the person so desires, they will have to publish
+new identity and membership documents and find enough certifiers, as any
+newcomer.
+
+3.6.4. Rule of certification lifespan (``sigValidity``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+All certifications included in the blockchain expire **sigValidity**
+seconds after they were **issued**.
+
+   /!\\ The issuance and the inclusion of a certification in the
+   blockchain occur at different times. When member A issues a
+   certification at time t1, it gets stored in the pool starting at t1
+   and only finds its way into the blockchain at t2 when all of the
+   web’s rules are observed. Several weeks can thus go by between t1 and
+   t2!
+
+3.6.5. Rule of limited supply of active certifications (``sigStock``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+By ‘active certifications’ we refer to certifications included in the
+blockchain and that haven’t yet expired.
+
+The total of active certifications issued by any member at any single
+time must be less than or equal to ``sigStock``. When this threshold is
+reached the member will have to wait for one of his active
+certifications to expire before he/she can issue a new one.
+
+.. _rule-of-the-time-period-between-two-certification-issuances-sigperiod:
+
+3.6.6. Rule of the time period between two certification issuances. (``sigPeriod``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+As soon as a certification issued by member A gets included in the
+blockchain, they will be unable to issue a new one before another
+``sigPeriod`` seconds.
+
+3.6.7. Expiry of a certification issuance (``sigWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+When a certification is issued by member A, it will be stored in the
+‘pool’ for a maximum of ``sigWindow`` seconds. If the certification
+hasn’t been included in the blockchain by then, it will be cancelled and
+the member’s ``sigStock`` will be repleted by one.
+
+3.6.8. Lifespan of a ‘pending’ identity (``idtyWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+When a new identity is created, it is stored in the ‘pool’ for a maximum
+of ``idtyWindow`` seconds. If the person hasn’t achieved member status
+by then, the certification will simply be cancelled.
+
+3.7. Details on some of the WoT’s peculiarities at the genesis block
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The aforementioned rules can only be enforced with an existing web. They
+cannot be observed when first creating the web, that is when defining
+the genesis block.
+
+Only rules 2 and 5 can be observed at the genesis block.
+
+The genesis block has to be manually created by the founding members. In
+practice this means that there must be a choice on which identities to
+include on the premise that all of them observe rules 2 and 5. In
+addition, the genesis block must be signed with the private key of one
+of these identities.
+
+As soon as the genesis block has been created, the other identities can
+start mining the blockchain and the member who created block #0
+effectively looses the decision power he had at creation.
+
+.. _why-these-rules-and-application-cases-in-the-g1:
+
+3.8. Why these rules and application cases in the Ğ1
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+3.8.1. Distance and maximum size
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The distance rule is there to curb the maximum size of a Sybil region as
+well as that of the monetary community as a whole. The ``xpercent``
+parameter prevents the creation of a ‘faction’ that could take hold of
+the blockchain.
+
+.. figure:: img/wot-sybil.jpg
+   :alt: Sybil region
+   :width: 90%
+
+   Sybil region
+
+The Sybil regions are isolated from the rest of the graph in the sense
+that they can only receive certifications from other ill-intentioned
+Sybil members. As a consequence, the shortest edge/path between a
+legitimate member and a Sybil one has to have the attack’s author as an
+endpoint. The maximum depth the Sybil region can attain is therefore
+contingent on the distance between the attacking edge-s- and the
+xpercent% closest referent members, this distance is known as
+``stepAttackers``. The maximum size of a Sybil region created by
+``sigQty`` members depends on the L parameter, defined as
+``L = sigQty/sigStock``:
+
+.. math:: MaxSybilSize = (sigStock - sigQty) \times {1 - L^{(stepMax - stepAttackers)} \over 1 - L} 
+
+The maximum size of the Web of Trust is given by the following formula:
+
+.. math:: WoTmax = sigStock \times L^{(stepMax - 1)} 
+
+However we know for a fact that members will never use all of their
+available certifications. According to Dunbar [4]_, on average, one is
+able to maintain relationships to around 150 people. Being conservative,
+we will consider that on average, each person will certify 50 accounts.
+We can calculate the size of the average web of trust ``WoTavg`` :
+
+..   WoTavg= (50)*(sigQty/50)^(stepMax-1)
+
+.. math:: WotAvg = 50 \times \left(\frac{\textrm{sigQty}}{50}\right)^{stepMax - 1}
+
+Our goal with the Ğ1 is to create a community of about one million
+members to test the consequences of a libre monetary system. Let’s see
+how we can tweak the pair of sigQty and stepMax- to reach this size:
+
+.. figure:: img/wot-moy.png
+   :alt: Average WoT size graph as a function of sigQty and stepMax
+   :width: 90%
+
+   Average WoT size graph as a function of sigQty and stepMax
+
+The maximum size of a Sybil region grows linearly with ``sigQty`` but
+exponentially with ``stepMax``. Logic has it that we need to keep
+``stepMax`` as low as possible to ensure sufficient strength to the web.
+The above graph shows that the lowest value of ``stepMax`` for a web of
+a million members is of 5. This is an order of magnitude and is likely
+to be much higher in reality, we cannot measure it for sure.
+
+For ``sigQty`` we can choose a value of **4** for a web of **1.5 million
+members** or **5** for **half a million members**. Bear in mind these
+are gross figures and could be significantly higher, we are talking
+anywhere between 1 and 10 million in reality. Calculating WOTavg gives
+us a pretty good idea of how the web would scale bearing in mind that it
+considers all members are referent members too -which isn’t the case as
+explained previously-. Hence the maximum size of the web is likely
+larger, a ballpark figure of half a million is enough for now especially
+knowing that the smaller ``sigQty`` is, the easier it is to launch a
+Sybil attack -it’s easier to find four accomplices than five-. For
+security reasons we have settled on five:
+
+
+..   stepMax = 5
+..   sigQty = 5
+..   sigStock \>= 50
+
+.. math:: stepMax = 5
+.. math:: sigQty = 5
+.. math:: sigStock \geq 50
+
+The maximum size of a Sybil region therefore is:
+
+..   (sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))
+
+.. math:: (sigStock-sigQty) * {1 - \left({sigStock \over 5}\right)^{5-stepAttackers}} \over {1-{sigStock \over 5}}
+
+with sigStock = 50 we have a Sybil region of:
+
+..   45*(1-10^(5-stepAttackers))/(-9)
+
+.. math:: 45 \times {1 - 10^{5 - stepAttackers}} \over {- 9}
+
+A good practice for protecting the web is to maximise ``stepAttackers``.
+That’s why we decided that referent members in the genesis block had to
+be at least four steps away from each other.
+
+Another way to keep a Sybil attack at bay, were it slow enough for
+members to notice it, would be for referent members to ‘stretch’ the web
+intentionally to limit the growth of the region by ensuring that the
+attackers’ legitimate certifications received in the first place aren’t
+renewed. But what if bot accounts were created and certified each other
+super fast and following all rules, how would we counter that? By
+introducing a minimum length of time between two certifications!
+
+3.8.2. Time is our friend
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+To help us deter a Sybil attack, we’ve decided to impose a minimum
+period of time between any two certifications issued from a single
+account. This parameter called ``sigPeriod`` affords us a greater chance
+to detect the formation of a ‘hostile’ faction.
+
+Here is a graph showing the evolution of a Sybil region with the
+variation of ``sigPeriod``. The simulation considers that honest members
+and attackers both issue a certification each ``sigPeriod`` interval, in
+days:
+
+.. figure:: img/impact_sig_period.png
+   :alt: size of the WoT according to sigPeriod and stepAttackers
+   :width: 100%
+
+   size of the WoT according to sigPeriod and stepAttackers
+
+As we see, there is a strong link between the growth speed of the region
+and ``sigPeriod``. As evidenced here, we need a ``sigPeriod`` high
+enough in order to ensure that the legitimate web can grow at least as
+fast as a Sybil region. In addition, the higher ``sigPeriod`` is, the
+more members will exercise their certification power gingerly, the
+action coming at a higher ‘cost’.
+
+There are numerous advantages to giving ``sigPeriod`` a high value and
+no technical barriers to it, hence our choice of five days.
+
+We could have also gone for one week for the sake of simplicity. However
+there is an underlying idea behind our choice which was quite simply the
+pace of today’s life. Certifying someone can be a lengthy process as one
+needs to make sure they are correctly applying the Ğ1 licence and people
+nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
+to allow one to certify at the end of every working week -five days-
+instead of a whole calendar one.
+
+3.8.3. Trust me now, trust me forever ? (``sigValidity``, ``msValidity``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+There would be two main drawbacks to a lifetime membership in the Ğ1’s
+Web of Trust:
+
+-  First of all, some members will pass and those accounts should no
+   longer produce the Universal Dividend.
+-  Secondly it is of the utmost importance that ‘rogue’ accounts can be
+   excluded from the web at some point.
+
+To achieve this, certifications have a limited lifespan. Members need to
+seek renewal from their peers after ``sigValidity`` time. On the other
+hand, this time can’t be too short that members would spend more time
+seeking renewal than they would exchanging in the currency. Furthermore,
+a certification with too short a lifespan would foster careless
+certifying behaviours. The act of certifying must have a high-enough
+‘perceived’ cost to make it feel like an important act. Lastly, we also
+wanted this lifespan to be easy to remember. Historically speaking, we
+first settled on the values of ``sigPeriod`` and ``sigStock``, meant one
+could issue all of their certifications in 495 days, one year was
+therefore not long enough. We deemed three years to be too much and
+that’s how we agreed on two years in the end.
+
+Thinking that a deceased member could continue producing the UD for two
+long years without anyone benefitting from it was also something we
+needed to address. We chose a value of one year for **msValidity**. The
+act of renewing every year is done through one of the clients
+interacting with the blockchain, through a simple click on a button.
+This parameter is less important than others and is mostly there to
+‘prune’ the web of past or inactive members who don’t renew their
+membership.
+
+3.8.4. Keeping the pools free of information glut (``idtyWindow``, ``sigWindow``, ``msWindow``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The pools need to be cleaned up on a regular basis to avoid them
+clogging up with information and to ensure that machines with less
+calculating power can still run a Duniter node.
+
+To achieve this, identities with pending membership approval and the
+corresponding certifications have to remain the shortest time possible
+in the pool while still having a chance of making it into the
+blockchain.
+
+For the Ğ1, our opinion was that two months would be enough for all
+potential certifiers to agree on a specific identity to certify. We also
+wanted a time period that would be easy enough to remember by all. We
+settled on two months, and gave this value to all three parameters
+``idtyWindow``, ``sigWindow`` and ``msWindow``.
+
+3.8.5. Avoiding single members from ‘knowing too many people’ (``sigStock``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+| We considered that on average, each person will certify 50 people.
+  However, we know for a fact that some members will use more than 50
+  certifications. The maximum social network of one individual is around
+  150 people [5]_. Being conservative, we settled on a maximum
+  certification number ``sigstock`` of 100.
+| Since ``sigStock``\ ’s impact on the size of a Sybil region is fairly
+  limited, we did not investigate further this parameter.
+
+3.8.6. Avoiding locking minorities (``xpercent``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+It’s easy enough to become a referent member, one of the Sybil
+strategies could therefore be to create a region of referent members.
+Such a region would grow slower than otherwise but could confer a
+locking power to its members by using the distance rule. That’s why the
+distance rule cannot be calculated on 100% of the referent members.
+Hence the introduction of the ``xpercent`` parameter which defines the
+percentage of referent members needing to be less than five edges
+-steps- from each other.
+
+This percentage needs to be low enough to prevent the formation of a
+locking minority -referent Sybil members being too far from legitimate
+referent members-. On the other hand, it needs to be high enough so as
+to restrict the maximum size of the Sybil region through the distance
+rule. The ``xpercent`` parameter was one of the hardest to define,
+therefore we might decide to change its value during the Ğ1 experiment.
+
+We were inspired by the Pareto principle [6]_: if at least 20% of
+members give good density to the web, 80% of the referent members will
+be five or less steps from any other member -referent or not-. The
+maximum value for ``xpercent`` is therefore 80%, anything above that and
+the distance rule could be too restrictive for legitimate use cases.
+With security our top concern, we chose the maximum value of 80%.
+
+3.8.7. Spam protection with (``msPeriod``)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This parameter stands out a bit on its own, as it was added after the
+genesis block. It is there to protect the Duniter P2P infrastructure
+against ‘spam’ attacks. We had to think of a strategy against attacks
+such as high-frequency membership renewal requests -i.e: in every block,
+every five minutes- or worse still, hundreds of these requests per
+minute to flood the Duniter nodes. Without such limits, nodes are
+supposed to address all renewal requests, even in cases where they were
+last published five minutes ago! The ``msPeriod`` parameter was given
+the same value as ``idtyWindow``, ``sigWindow`` and ``msWindow``,
+i.e. two months.
+
+.. [1]
+   Surfing a Web of Trust, Reputation and Reciprocity on
+   CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic:
+   `snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf <http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf>`__
+
+.. [2]
+   Public key validation on GnuPG manual, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+
+.. [3]
+   The Sibyl Attack, J.R.Douceur:
+   `www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf <https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf>`__
+
+.. [4]
+   Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
+
+.. [5]
+   Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
+
+.. [6]
+   Pareto principle :
+   `en.wikipedia.org/wiki/Pareto_principle <https://en.wikipedia.org/wiki/Pareto_principle>`__
diff --git a/chapters/en/5_individualized_difficulty.rst b/build/_sources/parts/en/5_individualized_difficulty.rst.txt
similarity index 100%
rename from chapters/en/5_individualized_difficulty.rst
rename to build/_sources/parts/en/5_individualized_difficulty.rst.txt
diff --git a/chapters/en/6_conclusion.rst b/build/_sources/parts/en/6_conclusion.rst.txt
similarity index 100%
rename from chapters/en/6_conclusion.rst
rename to build/_sources/parts/en/6_conclusion.rst.txt
diff --git a/chapters/en/9_sources.rst b/build/_sources/parts/en/9_sources.rst.txt
similarity index 100%
rename from chapters/en/9_sources.rst
rename to build/_sources/parts/en/9_sources.rst.txt
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new file mode 100644
index 0000000000000000000000000000000000000000..56f5efc61ec4910592264c70ea1ae538fa83522d
--- /dev/null
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+
+/* -- main layout ----------------------------------------------------------- */
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+div.clearer {
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+}
+
+/* -- relbar ---------------------------------------------------------------- */
+
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+    font-size: 90%;
+}
+
+div.related h3 {
+    display: none;
+}
+
+div.related ul {
+    margin: 0;
+    padding: 0 0 0 10px;
+    list-style: none;
+}
+
+div.related li {
+    display: inline;
+}
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+div.sphinxsidebarwrapper {
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+div.sphinxsidebar {
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+    font-size: 90%;
+    word-wrap: break-word;
+    overflow-wrap : break-word;
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+div.sphinxsidebar ul {
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+}
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+    border-left: none;
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+    box-sizing: border-box;
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+
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+img {
+    border: 0;
+    max-width: 100%;
+}
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+/* -- search page ----------------------------------------------------------- */
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+    padding: 0;
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+}
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+}
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+    float: right;
+    margin-left: 1em;
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+img.align-center, .figure.align-center, object.align-center {
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+  margin-left: auto;
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
+
+div.body div.math p {
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+}
+
+span.eqno {
+    float: right;
+}
+
+span.eqno a.headerlink {
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+    z-index: 1;
+}
+
+div.math:hover a.headerlink {
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+}
+
+/* -- printout stylesheet --------------------------------------------------- */
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+@media print {
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+    div.documentwrapper,
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+
+    div.sphinxsidebar,
+    div.related,
+    div.footer,
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+}
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diff --git a/build/_static/doctools.js b/build/_static/doctools.js
new file mode 100644
index 0000000000000000000000000000000000000000..daccd209dab05a75f5627390e37a6b764e93f547
--- /dev/null
+++ b/build/_static/doctools.js
@@ -0,0 +1,315 @@
+/*
+ * doctools.js
+ * ~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for all documentation.
+ *
+ * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
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+
+/**
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+ */
+$u = _.noConflict();
+
+/**
+ * make the code below compatible with browsers without
+ * an installed firebug like debugger
+if (!window.console || !console.firebug) {
+  var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
+    "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
+    "profile", "profileEnd"];
+  window.console = {};
+  for (var i = 0; i < names.length; ++i)
+    window.console[names[i]] = function() {};
+}
+ */
+
+/**
+ * small helper function to urldecode strings
+ */
+jQuery.urldecode = function(x) {
+  return decodeURIComponent(x).replace(/\+/g, ' ');
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+  if (typeof s === 'undefined')
+    s = document.location.search;
+  var parts = s.substr(s.indexOf('?') + 1).split('&');
+  var result = {};
+  for (var i = 0; i < parts.length; i++) {
+    var tmp = parts[i].split('=', 2);
+    var key = jQuery.urldecode(tmp[0]);
+    var value = jQuery.urldecode(tmp[1]);
+    if (key in result)
+      result[key].push(value);
+    else
+      result[key] = [value];
+  }
+  return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+  function highlight(node, addItems) {
+    if (node.nodeType === 3) {
+      var val = node.nodeValue;
+      var pos = val.toLowerCase().indexOf(text);
+      if (pos >= 0 &&
+          !jQuery(node.parentNode).hasClass(className) &&
+          !jQuery(node.parentNode).hasClass("nohighlight")) {
+        var span;
+        var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+        if (isInSVG) {
+          span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+        } else {
+          span = document.createElement("span");
+          span.className = className;
+        }
+        span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+        node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+          document.createTextNode(val.substr(pos + text.length)),
+          node.nextSibling));
+        node.nodeValue = val.substr(0, pos);
+        if (isInSVG) {
+          var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+          var bbox = node.parentElement.getBBox();
+          rect.x.baseVal.value = bbox.x;
+          rect.y.baseVal.value = bbox.y;
+          rect.width.baseVal.value = bbox.width;
+          rect.height.baseVal.value = bbox.height;
+          rect.setAttribute('class', className);
+          addItems.push({
+              "parent": node.parentNode,
+              "target": rect});
+        }
+      }
+    }
+    else if (!jQuery(node).is("button, select, textarea")) {
+      jQuery.each(node.childNodes, function() {
+        highlight(this, addItems);
+      });
+    }
+  }
+  var addItems = [];
+  var result = this.each(function() {
+    highlight(this, addItems);
+  });
+  for (var i = 0; i < addItems.length; ++i) {
+    jQuery(addItems[i].parent).before(addItems[i].target);
+  }
+  return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+  jQuery.uaMatch = function(ua) {
+    ua = ua.toLowerCase();
+
+    var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+      /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+      /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+      /(msie) ([\w.]+)/.exec(ua) ||
+      ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+      [];
+
+    return {
+      browser: match[ 1 ] || "",
+      version: match[ 2 ] || "0"
+    };
+  };
+  jQuery.browser = {};
+  jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+var Documentation = {
+
+  init : function() {
+    this.fixFirefoxAnchorBug();
+    this.highlightSearchWords();
+    this.initIndexTable();
+    if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
+      this.initOnKeyListeners();
+    }
+  },
+
+  /**
+   * i18n support
+   */
+  TRANSLATIONS : {},
+  PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
+  LOCALE : 'unknown',
+
+  // gettext and ngettext don't access this so that the functions
+  // can safely bound to a different name (_ = Documentation.gettext)
+  gettext : function(string) {
+    var translated = Documentation.TRANSLATIONS[string];
+    if (typeof translated === 'undefined')
+      return string;
+    return (typeof translated === 'string') ? translated : translated[0];
+  },
+
+  ngettext : function(singular, plural, n) {
+    var translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated === 'undefined')
+      return (n == 1) ? singular : plural;
+    return translated[Documentation.PLURALEXPR(n)];
+  },
+
+  addTranslations : function(catalog) {
+    for (var key in catalog.messages)
+      this.TRANSLATIONS[key] = catalog.messages[key];
+    this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
+    this.LOCALE = catalog.locale;
+  },
+
+  /**
+   * add context elements like header anchor links
+   */
+  addContextElements : function() {
+    $('div[id] > :header:first').each(function() {
+      $('<a class="headerlink">\u00B6</a>').
+      attr('href', '#' + this.id).
+      attr('title', _('Permalink to this headline')).
+      appendTo(this);
+    });
+    $('dt[id]').each(function() {
+      $('<a class="headerlink">\u00B6</a>').
+      attr('href', '#' + this.id).
+      attr('title', _('Permalink to this definition')).
+      appendTo(this);
+    });
+  },
+
+  /**
+   * workaround a firefox stupidity
+   * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
+   */
+  fixFirefoxAnchorBug : function() {
+    if (document.location.hash && $.browser.mozilla)
+      window.setTimeout(function() {
+        document.location.href += '';
+      }, 10);
+  },
+
+  /**
+   * highlight the search words provided in the url in the text
+   */
+  highlightSearchWords : function() {
+    var params = $.getQueryParameters();
+    var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
+    if (terms.length) {
+      var body = $('div.body');
+      if (!body.length) {
+        body = $('body');
+      }
+      window.setTimeout(function() {
+        $.each(terms, function() {
+          body.highlightText(this.toLowerCase(), 'highlighted');
+        });
+      }, 10);
+      $('<p class="highlight-link"><a href="javascript:Documentation.' +
+        'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
+          .appendTo($('#searchbox'));
+    }
+  },
+
+  /**
+   * init the domain index toggle buttons
+   */
+  initIndexTable : function() {
+    var togglers = $('img.toggler').click(function() {
+      var src = $(this).attr('src');
+      var idnum = $(this).attr('id').substr(7);
+      $('tr.cg-' + idnum).toggle();
+      if (src.substr(-9) === 'minus.png')
+        $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
+      else
+        $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
+    }).css('display', '');
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
+        togglers.click();
+    }
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords : function() {
+    $('#searchbox .highlight-link').fadeOut(300);
+    $('span.highlighted').removeClass('highlighted');
+  },
+
+  /**
+   * make the url absolute
+   */
+  makeURL : function(relativeURL) {
+    return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
+  },
+
+  /**
+   * get the current relative url
+   */
+  getCurrentURL : function() {
+    var path = document.location.pathname;
+    var parts = path.split(/\//);
+    $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
+      if (this === '..')
+        parts.pop();
+    });
+    var url = parts.join('/');
+    return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
+  },
+
+  initOnKeyListeners: function() {
+    $(document).keydown(function(event) {
+      var activeElementType = document.activeElement.tagName;
+      // don't navigate when in search box or textarea
+      if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
+          && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) {
+        switch (event.keyCode) {
+          case 37: // left
+            var prevHref = $('link[rel="prev"]').prop('href');
+            if (prevHref) {
+              window.location.href = prevHref;
+              return false;
+            }
+          case 39: // right
+            var nextHref = $('link[rel="next"]').prop('href');
+            if (nextHref) {
+              window.location.href = nextHref;
+              return false;
+            }
+        }
+      }
+    });
+  }
+};
+
+// quick alias for translations
+_ = Documentation.gettext;
+
+$(document).ready(function() {
+  Documentation.init();
+});
diff --git a/build/_static/documentation_options.js b/build/_static/documentation_options.js
new file mode 100644
index 0000000000000000000000000000000000000000..dbef29e6db8094003dc7e5496ca64994b9c8b26b
--- /dev/null
+++ b/build/_static/documentation_options.js
@@ -0,0 +1,12 @@
+var DOCUMENTATION_OPTIONS = {
+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
+    VERSION: '0.0.2',
+    LANGUAGE: 'None',
+    COLLAPSE_INDEX: false,
+    BUILDER: 'html',
+    FILE_SUFFIX: '.html',
+    LINK_SUFFIX: '.html',
+    HAS_SOURCE: true,
+    SOURCELINK_SUFFIX: '.txt',
+    NAVIGATION_WITH_KEYS: false
+};
\ No newline at end of file
diff --git a/build/_static/epub.css b/build/_static/epub.css
new file mode 100644
index 0000000000000000000000000000000000000000..270e9570e4b085b37e513cb11757eab46e69d395
--- /dev/null
+++ b/build/_static/epub.css
@@ -0,0 +1,310 @@
+/*
+ * default.css_t
+ * ~~~~~~~~~~~~~
+ *
+ * Sphinx stylesheet -- default theme.
+ *
+ * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+@import url("basic.css");
+
+/* -- page layout ----------------------------------------------------------- */
+
+body {
+    font-family: {{ theme_bodyfont }};
+    font-size: 100%;
+    background-color: {{ theme_footerbgcolor }};
+    color: #000;
+    margin: 0;
+    padding: 0;
+}
+
+div.document {
+    background-color: {{ theme_sidebarbgcolor }};
+}
+
+div.documentwrapper {
+    float: left;
+    width: 100%;
+}
+
+div.bodywrapper {
+    margin: 0 0 0 230px;
+}
+
+div.body {
+    background-color: {{ theme_bgcolor }};
+    color: {{ theme_textcolor }};
+    padding: 0 20px 30px 20px;
+}
+
+{%- if theme_rightsidebar|tobool %}
+div.bodywrapper {
+    margin: 0 230px 0 0;
+}
+{%- endif %}
+
+div.footer {
+    color: {{ theme_footertextcolor }};
+    width: 100%;
+    padding: 9px 0 9px 0;
+    text-align: center;
+    font-size: 75%;
+}
+
+div.footer a {
+    color: {{ theme_footertextcolor }};
+    text-decoration: underline;
+}
+
+div.related {
+    background-color: {{ theme_relbarbgcolor }};
+    line-height: 30px;
+    color: {{ theme_relbartextcolor }};
+}
+
+div.related a {
+    color: {{ theme_relbarlinkcolor }};
+}
+
+div.sphinxsidebar {
+    {%- if theme_stickysidebar|tobool %}
+    top: 30px;
+    bottom: 0;
+    margin: 0;
+    position: fixed;
+    overflow: auto;
+    height: auto;
+    {%- endif %}
+    {%- if theme_rightsidebar|tobool %}
+    float: right;
+    {%- if theme_stickysidebar|tobool %}
+    right: 0;
+    {%- endif %}
+    {%- endif %}
+}
+
+{%- if theme_stickysidebar|tobool %}
+/* this is nice, but it it leads to hidden headings when jumping
+   to an anchor */
+/*
+div.related {
+    position: fixed;
+}
+
+div.documentwrapper {
+    margin-top: 30px;
+}
+*/
+{%- endif %}
+
+div.sphinxsidebar h3 {
+    font-family: {{ theme_headfont }};
+    color: {{ theme_sidebartextcolor }};
+    font-size: 1.4em;
+    font-weight: normal;
+    margin: 0;
+    padding: 0;
+}
+
+div.sphinxsidebar h3 a {
+    color: {{ theme_sidebartextcolor }};
+}
+
+div.sphinxsidebar h4 {
+    font-family: {{ theme_headfont }};
+    color: {{ theme_sidebartextcolor }};
+    font-size: 1.3em;
+    font-weight: normal;
+    margin: 5px 0 0 0;
+    padding: 0;
+}
+
+div.sphinxsidebar p {
+    color: {{ theme_sidebartextcolor }};
+}
+
+div.sphinxsidebar p.topless {
+    margin: 5px 10px 10px 10px;
+}
+
+div.sphinxsidebar ul {
+    margin: 10px;
+    padding: 0;
+    color: {{ theme_sidebartextcolor }};
+}
+
+div.sphinxsidebar a {
+    color: {{ theme_sidebarlinkcolor }};
+}
+
+div.sphinxsidebar input {
+    border: 1px solid {{ theme_sidebarlinkcolor }};
+    font-family: sans-serif;
+    font-size: 1em;
+}
+
+{% if theme_collapsiblesidebar|tobool %}
+/* for collapsible sidebar */
+div#sidebarbutton {
+    background-color: {{ theme_sidebarbtncolor }};
+}
+{% endif %}
+
+/* -- hyperlink styles ------------------------------------------------------ */
+
+a {
+    color: {{ theme_linkcolor }};
+    text-decoration: none;
+}
+
+a:visited {
+    color: {{ theme_visitedlinkcolor }};
+    text-decoration: none;
+}
+
+a:hover {
+    text-decoration: underline;
+}
+
+{% if theme_externalrefs|tobool %}
+a.external {
+   text-decoration: none;
+   border-bottom: 1px dashed {{ theme_linkcolor }};
+}
+
+a.external:hover {
+   text-decoration: none;
+   border-bottom: none;
+}
+
+a.external:visited {
+    text-decoration: none;
+    border-bottom: 1px dashed {{ theme_visitedlinkcolor }};
+}
+{% endif %}
+
+/* -- body styles ----------------------------------------------------------- */
+
+div.body h1,
+div.body h2,
+div.body h3,
+div.body h4,
+div.body h5,
+div.body h6 {
+    font-family: {{ theme_headfont }};
+    background-color: {{ theme_headbgcolor }};
+    font-weight: normal;
+    color: {{ theme_headtextcolor }};
+    border-bottom: 1px solid #ccc;
+    margin: 20px -20px 10px -20px;
+    padding: 3px 0 3px 10px;
+}
+
+div.body h1 { margin-top: 0; font-size: 200%; }
+div.body h2 { font-size: 160%; }
+div.body h3 { font-size: 140%; }
+div.body h4 { font-size: 120%; }
+div.body h5 { font-size: 110%; }
+div.body h6 { font-size: 100%; }
+
+a.headerlink {
+    color: {{ theme_headlinkcolor }};
+    font-size: 0.8em;
+    padding: 0 4px 0 4px;
+    text-decoration: none;
+}
+
+a.headerlink:hover {
+    background-color: {{ theme_headlinkcolor }};
+    color: white;
+}
+
+div.body p, div.body dd, div.body li {
+    text-align: justify;
+    line-height: 130%;
+}
+
+div.admonition p.admonition-title + p {
+    display: inline;
+}
+
+div.admonition p {
+    margin-bottom: 5px;
+}
+
+div.admonition pre {
+    margin-bottom: 5px;
+}
+
+div.admonition ul, div.admonition ol {
+    margin-bottom: 5px;
+}
+
+div.note {
+    background-color: #eee;
+    border: 1px solid #ccc;
+}
+
+div.seealso {
+    background-color: #ffc;
+    border: 1px solid #ff6;
+}
+
+div.topic {
+    background-color: #eee;
+}
+
+div.warning {
+    background-color: #ffe4e4;
+    border: 1px solid #f66;
+}
+
+p.admonition-title {
+    display: inline;
+}
+
+p.admonition-title:after {
+    content: ":";
+}
+
+pre {
+    padding: 5px;
+    background-color: {{ theme_codebgcolor }};
+    color: {{ theme_codetextcolor }};
+    line-height: 120%;
+    border: 1px solid #ac9;
+    border-left: none;
+    border-right: none;
+}
+
+code {
+    background-color: #ecf0f3;
+    padding: 0 1px 0 1px;
+    font-size: 0.95em;
+}
+
+th {
+    background-color: #ede;
+}
+
+.warning code {
+    background: #efc2c2;
+}
+
+.note code {
+    background: #d6d6d6;
+}
+
+.viewcode-back {
+    font-family: {{ theme_bodyfont }};
+}
+
+div.viewcode-block:target {
+    background-color: #f4debf;
+    border-top: 1px solid #ac9;
+    border-bottom: 1px solid #ac9;
+}
diff --git a/build/_static/file.png b/build/_static/file.png
new file mode 100644
index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3
Binary files /dev/null and b/build/_static/file.png differ
diff --git a/build/_static/footerbg.png b/build/_static/footerbg.png
new file mode 100644
index 0000000000000000000000000000000000000000..1fbc873daa930207b3a5a07a4d34a9478241d67e
Binary files /dev/null and b/build/_static/footerbg.png differ
diff --git a/build/_static/headerbg.png b/build/_static/headerbg.png
new file mode 100644
index 0000000000000000000000000000000000000000..e1051af48e5ccbaf8d64c58cc993444b4675dabf
Binary files /dev/null and b/build/_static/headerbg.png differ
diff --git a/build/_static/ie6.css b/build/_static/ie6.css
new file mode 100644
index 0000000000000000000000000000000000000000..74baa5d5a9aff47f47bea2fee5b8f7b4ffb8f32b
--- /dev/null
+++ b/build/_static/ie6.css
@@ -0,0 +1,7 @@
+* html img,
+* html .png{position:relative;behavior:expression((this.runtimeStyle.behavior="none")&&(this.pngSet?this.pngSet=true:(this.nodeName == "IMG" && this.src.toLowerCase().indexOf('.png')>-1?(this.runtimeStyle.backgroundImage = "none",
+this.runtimeStyle.filter = "progid:DXImageTransform.Microsoft.AlphaImageLoader(src='" + this.src + "',sizingMethod='image')",
+this.src = "_static/transparent.gif"):(this.origBg = this.origBg? this.origBg :this.currentStyle.backgroundImage.toString().replace('url("','').replace('")',''),
+this.runtimeStyle.filter = "progid:DXImageTransform.Microsoft.AlphaImageLoader(src='" + this.origBg + "',sizingMethod='crop')",
+this.runtimeStyle.backgroundImage = "none")),this.pngSet=true)
+);}
diff --git a/build/_static/jquery-3.5.1.js b/build/_static/jquery-3.5.1.js
new file mode 100644
index 0000000000000000000000000000000000000000..50937333b99a5e168ac9e8292b22edd7e96c3e6a
--- /dev/null
+++ b/build/_static/jquery-3.5.1.js
@@ -0,0 +1,10872 @@
+/*!
+ * jQuery JavaScript Library v3.5.1
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2020-05-04T22:49Z
+ */
+( function( global, factory ) {
+
+	"use strict";
+
+	if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+		// For CommonJS and CommonJS-like environments where a proper `window`
+		// is present, execute the factory and get jQuery.
+		// For environments that do not have a `window` with a `document`
+		// (such as Node.js), expose a factory as module.exports.
+		// This accentuates the need for the creation of a real `window`.
+		// e.g. var jQuery = require("jquery")(window);
+		// See ticket #14549 for more info.
+		module.exports = global.document ?
+			factory( global, true ) :
+			function( w ) {
+				if ( !w.document ) {
+					throw new Error( "jQuery requires a window with a document" );
+				}
+				return factory( w );
+			};
+	} else {
+		factory( global );
+	}
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+      // Support: Chrome <=57, Firefox <=52
+      // In some browsers, typeof returns "function" for HTML <object> elements
+      // (i.e., `typeof document.createElement( "object" ) === "function"`).
+      // We don't want to classify *any* DOM node as a function.
+      return typeof obj === "function" && typeof obj.nodeType !== "number";
+  };
+
+
+var isWindow = function isWindow( obj ) {
+		return obj != null && obj === obj.window;
+	};
+
+
+var document = window.document;
+
+
+
+	var preservedScriptAttributes = {
+		type: true,
+		src: true,
+		nonce: true,
+		noModule: true
+	};
+
+	function DOMEval( code, node, doc ) {
+		doc = doc || document;
+
+		var i, val,
+			script = doc.createElement( "script" );
+
+		script.text = code;
+		if ( node ) {
+			for ( i in preservedScriptAttributes ) {
+
+				// Support: Firefox 64+, Edge 18+
+				// Some browsers don't support the "nonce" property on scripts.
+				// On the other hand, just using `getAttribute` is not enough as
+				// the `nonce` attribute is reset to an empty string whenever it
+				// becomes browsing-context connected.
+				// See https://github.com/whatwg/html/issues/2369
+				// See https://html.spec.whatwg.org/#nonce-attributes
+				// The `node.getAttribute` check was added for the sake of
+				// `jQuery.globalEval` so that it can fake a nonce-containing node
+				// via an object.
+				val = node[ i ] || node.getAttribute && node.getAttribute( i );
+				if ( val ) {
+					script.setAttribute( i, val );
+				}
+			}
+		}
+		doc.head.appendChild( script ).parentNode.removeChild( script );
+	}
+
+
+function toType( obj ) {
+	if ( obj == null ) {
+		return obj + "";
+	}
+
+	// Support: Android <=2.3 only (functionish RegExp)
+	return typeof obj === "object" || typeof obj === "function" ?
+		class2type[ toString.call( obj ) ] || "object" :
+		typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+	version = "3.5.1",
+
+	// Define a local copy of jQuery
+	jQuery = function( selector, context ) {
+
+		// The jQuery object is actually just the init constructor 'enhanced'
+		// Need init if jQuery is called (just allow error to be thrown if not included)
+		return new jQuery.fn.init( selector, context );
+	};
+
+jQuery.fn = jQuery.prototype = {
+
+	// The current version of jQuery being used
+	jquery: version,
+
+	constructor: jQuery,
+
+	// The default length of a jQuery object is 0
+	length: 0,
+
+	toArray: function() {
+		return slice.call( this );
+	},
+
+	// Get the Nth element in the matched element set OR
+	// Get the whole matched element set as a clean array
+	get: function( num ) {
+
+		// Return all the elements in a clean array
+		if ( num == null ) {
+			return slice.call( this );
+		}
+
+		// Return just the one element from the set
+		return num < 0 ? this[ num + this.length ] : this[ num ];
+	},
+
+	// Take an array of elements and push it onto the stack
+	// (returning the new matched element set)
+	pushStack: function( elems ) {
+
+		// Build a new jQuery matched element set
+		var ret = jQuery.merge( this.constructor(), elems );
+
+		// Add the old object onto the stack (as a reference)
+		ret.prevObject = this;
+
+		// Return the newly-formed element set
+		return ret;
+	},
+
+	// Execute a callback for every element in the matched set.
+	each: function( callback ) {
+		return jQuery.each( this, callback );
+	},
+
+	map: function( callback ) {
+		return this.pushStack( jQuery.map( this, function( elem, i ) {
+			return callback.call( elem, i, elem );
+		} ) );
+	},
+
+	slice: function() {
+		return this.pushStack( slice.apply( this, arguments ) );
+	},
+
+	first: function() {
+		return this.eq( 0 );
+	},
+
+	last: function() {
+		return this.eq( -1 );
+	},
+
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
+	eq: function( i ) {
+		var len = this.length,
+			j = +i + ( i < 0 ? len : 0 );
+		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+	},
+
+	end: function() {
+		return this.prevObject || this.constructor();
+	},
+
+	// For internal use only.
+	// Behaves like an Array's method, not like a jQuery method.
+	push: push,
+	sort: arr.sort,
+	splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+	var options, name, src, copy, copyIsArray, clone,
+		target = arguments[ 0 ] || {},
+		i = 1,
+		length = arguments.length,
+		deep = false;
+
+	// Handle a deep copy situation
+	if ( typeof target === "boolean" ) {
+		deep = target;
+
+		// Skip the boolean and the target
+		target = arguments[ i ] || {};
+		i++;
+	}
+
+	// Handle case when target is a string or something (possible in deep copy)
+	if ( typeof target !== "object" && !isFunction( target ) ) {
+		target = {};
+	}
+
+	// Extend jQuery itself if only one argument is passed
+	if ( i === length ) {
+		target = this;
+		i--;
+	}
+
+	for ( ; i < length; i++ ) {
+
+		// Only deal with non-null/undefined values
+		if ( ( options = arguments[ i ] ) != null ) {
+
+			// Extend the base object
+			for ( name in options ) {
+				copy = options[ name ];
+
+				// Prevent Object.prototype pollution
+				// Prevent never-ending loop
+				if ( name === "__proto__" || target === copy ) {
+					continue;
+				}
+
+				// Recurse if we're merging plain objects or arrays
+				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+					( copyIsArray = Array.isArray( copy ) ) ) ) {
+					src = target[ name ];
+
+					// Ensure proper type for the source value
+					if ( copyIsArray && !Array.isArray( src ) ) {
+						clone = [];
+					} else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+						clone = {};
+					} else {
+						clone = src;
+					}
+					copyIsArray = false;
+
+					// Never move original objects, clone them
+					target[ name ] = jQuery.extend( deep, clone, copy );
+
+				// Don't bring in undefined values
+				} else if ( copy !== undefined ) {
+					target[ name ] = copy;
+				}
+			}
+		}
+	}
+
+	// Return the modified object
+	return target;
+};
+
+jQuery.extend( {
+
+	// Unique for each copy of jQuery on the page
+	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+	// Assume jQuery is ready without the ready module
+	isReady: true,
+
+	error: function( msg ) {
+		throw new Error( msg );
+	},
+
+	noop: function() {},
+
+	isPlainObject: function( obj ) {
+		var proto, Ctor;
+
+		// Detect obvious negatives
+		// Use toString instead of jQuery.type to catch host objects
+		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+			return false;
+		}
+
+		proto = getProto( obj );
+
+		// Objects with no prototype (e.g., `Object.create( null )`) are plain
+		if ( !proto ) {
+			return true;
+		}
+
+		// Objects with prototype are plain iff they were constructed by a global Object function
+		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+	},
+
+	isEmptyObject: function( obj ) {
+		var name;
+
+		for ( name in obj ) {
+			return false;
+		}
+		return true;
+	},
+
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
+	},
+
+	each: function( obj, callback ) {
+		var length, i = 0;
+
+		if ( isArrayLike( obj ) ) {
+			length = obj.length;
+			for ( ; i < length; i++ ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		} else {
+			for ( i in obj ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		}
+
+		return obj;
+	},
+
+	// results is for internal usage only
+	makeArray: function( arr, results ) {
+		var ret = results || [];
+
+		if ( arr != null ) {
+			if ( isArrayLike( Object( arr ) ) ) {
+				jQuery.merge( ret,
+					typeof arr === "string" ?
+					[ arr ] : arr
+				);
+			} else {
+				push.call( ret, arr );
+			}
+		}
+
+		return ret;
+	},
+
+	inArray: function( elem, arr, i ) {
+		return arr == null ? -1 : indexOf.call( arr, elem, i );
+	},
+
+	// Support: Android <=4.0 only, PhantomJS 1 only
+	// push.apply(_, arraylike) throws on ancient WebKit
+	merge: function( first, second ) {
+		var len = +second.length,
+			j = 0,
+			i = first.length;
+
+		for ( ; j < len; j++ ) {
+			first[ i++ ] = second[ j ];
+		}
+
+		first.length = i;
+
+		return first;
+	},
+
+	grep: function( elems, callback, invert ) {
+		var callbackInverse,
+			matches = [],
+			i = 0,
+			length = elems.length,
+			callbackExpect = !invert;
+
+		// Go through the array, only saving the items
+		// that pass the validator function
+		for ( ; i < length; i++ ) {
+			callbackInverse = !callback( elems[ i ], i );
+			if ( callbackInverse !== callbackExpect ) {
+				matches.push( elems[ i ] );
+			}
+		}
+
+		return matches;
+	},
+
+	// arg is for internal usage only
+	map: function( elems, callback, arg ) {
+		var length, value,
+			i = 0,
+			ret = [];
+
+		// Go through the array, translating each of the items to their new values
+		if ( isArrayLike( elems ) ) {
+			length = elems.length;
+			for ( ; i < length; i++ ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+
+		// Go through every key on the object,
+		} else {
+			for ( i in elems ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+		}
+
+		// Flatten any nested arrays
+		return flat( ret );
+	},
+
+	// A global GUID counter for objects
+	guid: 1,
+
+	// jQuery.support is not used in Core but other projects attach their
+	// properties to it so it needs to exist.
+	support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+function( _i, name ) {
+	class2type[ "[object " + name + "]" ] = name.toLowerCase();
+} );
+
+function isArrayLike( obj ) {
+
+	// Support: real iOS 8.2 only (not reproducible in simulator)
+	// `in` check used to prevent JIT error (gh-2145)
+	// hasOwn isn't used here due to false negatives
+	// regarding Nodelist length in IE
+	var length = !!obj && "length" in obj && obj.length,
+		type = toType( obj );
+
+	if ( isFunction( obj ) || isWindow( obj ) ) {
+		return false;
+	}
+
+	return type === "array" || length === 0 ||
+		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.5
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2020-03-14
+ */
+( function( window ) {
+var i,
+	support,
+	Expr,
+	getText,
+	isXML,
+	tokenize,
+	compile,
+	select,
+	outermostContext,
+	sortInput,
+	hasDuplicate,
+
+	// Local document vars
+	setDocument,
+	document,
+	docElem,
+	documentIsHTML,
+	rbuggyQSA,
+	rbuggyMatches,
+	matches,
+	contains,
+
+	// Instance-specific data
+	expando = "sizzle" + 1 * new Date(),
+	preferredDoc = window.document,
+	dirruns = 0,
+	done = 0,
+	classCache = createCache(),
+	tokenCache = createCache(),
+	compilerCache = createCache(),
+	nonnativeSelectorCache = createCache(),
+	sortOrder = function( a, b ) {
+		if ( a === b ) {
+			hasDuplicate = true;
+		}
+		return 0;
+	},
+
+	// Instance methods
+	hasOwn = ( {} ).hasOwnProperty,
+	arr = [],
+	pop = arr.pop,
+	pushNative = arr.push,
+	push = arr.push,
+	slice = arr.slice,
+
+	// Use a stripped-down indexOf as it's faster than native
+	// https://jsperf.com/thor-indexof-vs-for/5
+	indexOf = function( list, elem ) {
+		var i = 0,
+			len = list.length;
+		for ( ; i < len; i++ ) {
+			if ( list[ i ] === elem ) {
+				return i;
+			}
+		}
+		return -1;
+	},
+
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
+
+	// Regular expressions
+
+	// http://www.w3.org/TR/css3-selectors/#whitespace
+	whitespace = "[\\x20\\t\\r\\n\\f]",
+
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+		// Operator (capture 2)
+		"*([*^$|!~]?=)" + whitespace +
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
+
+	pseudos = ":(" + identifier + ")(?:\\((" +
+
+		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+		// 1. quoted (capture 3; capture 4 or capture 5)
+		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+		// 2. simple (capture 6)
+		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+		// 3. anything else (capture 2)
+		".*" +
+		")\\)|)",
+
+	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+	rwhitespace = new RegExp( whitespace + "+", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
+
+	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
+	rdescend = new RegExp( whitespace + "|>" ),
+
+	rpseudo = new RegExp( pseudos ),
+	ridentifier = new RegExp( "^" + identifier + "$" ),
+
+	matchExpr = {
+		"ID": new RegExp( "^#(" + identifier + ")" ),
+		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
+		"ATTR": new RegExp( "^" + attributes ),
+		"PSEUDO": new RegExp( "^" + pseudos ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+		// For use in libraries implementing .is()
+		// We use this for POS matching in `select`
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+	},
+
+	rhtml = /HTML$/i,
+	rinputs = /^(?:input|select|textarea|button)$/i,
+	rheader = /^h\d$/i,
+
+	rnative = /^[^{]+\{\s*\[native \w/,
+
+	// Easily-parseable/retrievable ID or TAG or CLASS selectors
+	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+	rsibling = /[+~]/,
+
+	// CSS escapes
+	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
+			high < 0 ?
+				String.fromCharCode( high + 0x10000 ) :
+				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+	},
+
+	// CSS string/identifier serialization
+	// https://drafts.csswg.org/cssom/#common-serializing-idioms
+	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+	fcssescape = function( ch, asCodePoint ) {
+		if ( asCodePoint ) {
+
+			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+			if ( ch === "\0" ) {
+				return "\uFFFD";
+			}
+
+			// Control characters and (dependent upon position) numbers get escaped as code points
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+		}
+
+		// Other potentially-special ASCII characters get backslash-escaped
+		return "\\" + ch;
+	},
+
+	// Used for iframes
+	// See setDocument()
+	// Removing the function wrapper causes a "Permission Denied"
+	// error in IE
+	unloadHandler = function() {
+		setDocument();
+	},
+
+	inDisabledFieldset = addCombinator(
+		function( elem ) {
+			return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+		},
+		{ dir: "parentNode", next: "legend" }
+	);
+
+// Optimize for push.apply( _, NodeList )
+try {
+	push.apply(
+		( arr = slice.call( preferredDoc.childNodes ) ),
+		preferredDoc.childNodes
+	);
+
+	// Support: Android<4.0
+	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
+	arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+	push = { apply: arr.length ?
+
+		// Leverage slice if possible
+		function( target, els ) {
+			pushNative.apply( target, slice.call( els ) );
+		} :
+
+		// Support: IE<9
+		// Otherwise append directly
+		function( target, els ) {
+			var j = target.length,
+				i = 0;
+
+			// Can't trust NodeList.length
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+			target.length = j - 1;
+		}
+	};
+}
+
+function Sizzle( selector, context, results, seed ) {
+	var m, i, elem, nid, match, groups, newSelector,
+		newContext = context && context.ownerDocument,
+
+		// nodeType defaults to 9, since context defaults to document
+		nodeType = context ? context.nodeType : 9;
+
+	results = results || [];
+
+	// Return early from calls with invalid selector or context
+	if ( typeof selector !== "string" || !selector ||
+		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+		return results;
+	}
+
+	// Try to shortcut find operations (as opposed to filters) in HTML documents
+	if ( !seed ) {
+		setDocument( context );
+		context = context || document;
+
+		if ( documentIsHTML ) {
+
+			// If the selector is sufficiently simple, try using a "get*By*" DOM method
+			// (excepting DocumentFragment context, where the methods don't exist)
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+				// ID selector
+				if ( ( m = match[ 1 ] ) ) {
+
+					// Document context
+					if ( nodeType === 9 ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
+
+							// Support: IE, Opera, Webkit
+							// TODO: identify versions
+							// getElementById can match elements by name instead of ID
+							if ( elem.id === m ) {
+								results.push( elem );
+								return results;
+							}
+						} else {
+							return results;
+						}
+
+					// Element context
+					} else {
+
+						// Support: IE, Opera, Webkit
+						// TODO: identify versions
+						// getElementById can match elements by name instead of ID
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+							contains( context, elem ) &&
+							elem.id === m ) {
+
+							results.push( elem );
+							return results;
+						}
+					}
+
+				// Type selector
+				} else if ( match[ 2 ] ) {
+					push.apply( results, context.getElementsByTagName( selector ) );
+					return results;
+
+				// Class selector
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+					context.getElementsByClassName ) {
+
+					push.apply( results, context.getElementsByClassName( m ) );
+					return results;
+				}
+			}
+
+			// Take advantage of querySelectorAll
+			if ( support.qsa &&
+				!nonnativeSelectorCache[ selector + " " ] &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+				// Support: IE 8 only
+				// Exclude object elements
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+				newSelector = selector;
+				newContext = context;
+
+				// qSA considers elements outside a scoping root when evaluating child or
+				// descendant combinators, which is not what we want.
+				// In such cases, we work around the behavior by prefixing every selector in the
+				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
+				// Thanks to Andrew Dupont for this technique.
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
+					}
+
+					// Prefix every selector in the list
+					groups = tokenize( selector );
+					i = groups.length;
+					while ( i-- ) {
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
+					}
+					newSelector = groups.join( "," );
+				}
+
+				try {
+					push.apply( results,
+						newContext.querySelectorAll( newSelector )
+					);
+					return results;
+				} catch ( qsaError ) {
+					nonnativeSelectorCache( selector, true );
+				} finally {
+					if ( nid === expando ) {
+						context.removeAttribute( "id" );
+					}
+				}
+			}
+		}
+	}
+
+	// All others
+	return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ *	deleting the oldest entry
+ */
+function createCache() {
+	var keys = [];
+
+	function cache( key, value ) {
+
+		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+			// Only keep the most recent entries
+			delete cache[ keys.shift() ];
+		}
+		return ( cache[ key + " " ] = value );
+	}
+	return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+	fn[ expando ] = true;
+	return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+	var el = document.createElement( "fieldset" );
+
+	try {
+		return !!fn( el );
+	} catch ( e ) {
+		return false;
+	} finally {
+
+		// Remove from its parent by default
+		if ( el.parentNode ) {
+			el.parentNode.removeChild( el );
+		}
+
+		// release memory in IE
+		el = null;
+	}
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+	var arr = attrs.split( "|" ),
+		i = arr.length;
+
+	while ( i-- ) {
+		Expr.attrHandle[ arr[ i ] ] = handler;
+	}
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+	var cur = b && a,
+		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+			a.sourceIndex - b.sourceIndex;
+
+	// Use IE sourceIndex if available on both nodes
+	if ( diff ) {
+		return diff;
+	}
+
+	// Check if b follows a
+	if ( cur ) {
+		while ( ( cur = cur.nextSibling ) ) {
+			if ( cur === b ) {
+				return -1;
+			}
+		}
+	}
+
+	return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return name === "input" && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return ( name === "input" || name === "button" ) && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+	return function( elem ) {
+
+		// Only certain elements can match :enabled or :disabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+		if ( "form" in elem ) {
+
+			// Check for inherited disabledness on relevant non-disabled elements:
+			// * listed form-associated elements in a disabled fieldset
+			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+			// * option elements in a disabled optgroup
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+			// All such elements have a "form" property.
+			if ( elem.parentNode && elem.disabled === false ) {
+
+				// Option elements defer to a parent optgroup if present
+				if ( "label" in elem ) {
+					if ( "label" in elem.parentNode ) {
+						return elem.parentNode.disabled === disabled;
+					} else {
+						return elem.disabled === disabled;
+					}
+				}
+
+				// Support: IE 6 - 11
+				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
+				return elem.isDisabled === disabled ||
+
+					// Where there is no isDisabled, check manually
+					/* jshint -W018 */
+					elem.isDisabled !== !disabled &&
+					inDisabledFieldset( elem ) === disabled;
+			}
+
+			return elem.disabled === disabled;
+
+		// Try to winnow out elements that can't be disabled before trusting the disabled property.
+		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+		// even exist on them, let alone have a boolean value.
+		} else if ( "label" in elem ) {
+			return elem.disabled === disabled;
+		}
+
+		// Remaining elements are neither :enabled nor :disabled
+		return false;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+	return markFunction( function( argument ) {
+		argument = +argument;
+		return markFunction( function( seed, matches ) {
+			var j,
+				matchIndexes = fn( [], seed.length, argument ),
+				i = matchIndexes.length;
+
+			// Match elements found at the specified indexes
+			while ( i-- ) {
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
+				}
+			}
+		} );
+	} );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+	return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+	var namespace = elem.namespaceURI,
+		docElem = ( elem.ownerDocument || elem ).documentElement;
+
+	// Support: IE <=8
+	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+	// https://bugs.jquery.com/ticket/4833
+	return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+	var hasCompare, subWindow,
+		doc = node ? node.ownerDocument || node : preferredDoc;
+
+	// Return early if doc is invalid or already selected
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+		return document;
+	}
+
+	// Update global variables
+	document = doc;
+	docElem = document.documentElement;
+	documentIsHTML = !isXML( document );
+
+	// Support: IE 9 - 11+, Edge 12 - 18+
+	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+		// Support: IE 11, Edge
+		if ( subWindow.addEventListener ) {
+			subWindow.addEventListener( "unload", unloadHandler, false );
+
+		// Support: IE 9 - 10 only
+		} else if ( subWindow.attachEvent ) {
+			subWindow.attachEvent( "onunload", unloadHandler );
+		}
+	}
+
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
+	/* Attributes
+	---------------------------------------------------------------------- */
+
+	// Support: IE<8
+	// Verify that getAttribute really returns attributes and not properties
+	// (excepting IE8 booleans)
+	support.attributes = assert( function( el ) {
+		el.className = "i";
+		return !el.getAttribute( "className" );
+	} );
+
+	/* getElement(s)By*
+	---------------------------------------------------------------------- */
+
+	// Check if getElementsByTagName("*") returns only elements
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
+
+	// Support: IE<9
+	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+	// Support: IE<10
+	// Check if getElementById returns elements by name
+	// The broken getElementById methods don't pick up programmatically-set names,
+	// so use a roundabout getElementsByName test
+	support.getById = assert( function( el ) {
+		docElem.appendChild( el ).id = expando;
+		return !document.getElementsByName || !document.getElementsByName( expando ).length;
+	} );
+
+	// ID filter and find
+	if ( support.getById ) {
+		Expr.filter[ "ID" ] = function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				return elem.getAttribute( "id" ) === attrId;
+			};
+		};
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var elem = context.getElementById( id );
+				return elem ? [ elem ] : [];
+			}
+		};
+	} else {
+		Expr.filter[ "ID" ] =  function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				var node = typeof elem.getAttributeNode !== "undefined" &&
+					elem.getAttributeNode( "id" );
+				return node && node.value === attrId;
+			};
+		};
+
+		// Support: IE 6 - 7 only
+		// getElementById is not reliable as a find shortcut
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var node, i, elems,
+					elem = context.getElementById( id );
+
+				if ( elem ) {
+
+					// Verify the id attribute
+					node = elem.getAttributeNode( "id" );
+					if ( node && node.value === id ) {
+						return [ elem ];
+					}
+
+					// Fall back on getElementsByName
+					elems = context.getElementsByName( id );
+					i = 0;
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
+						if ( node && node.value === id ) {
+							return [ elem ];
+						}
+					}
+				}
+
+				return [];
+			}
+		};
+	}
+
+	// Tag
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
+		function( tag, context ) {
+			if ( typeof context.getElementsByTagName !== "undefined" ) {
+				return context.getElementsByTagName( tag );
+
+			// DocumentFragment nodes don't have gEBTN
+			} else if ( support.qsa ) {
+				return context.querySelectorAll( tag );
+			}
+		} :
+
+		function( tag, context ) {
+			var elem,
+				tmp = [],
+				i = 0,
+
+				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+				results = context.getElementsByTagName( tag );
+
+			// Filter out possible comments
+			if ( tag === "*" ) {
+				while ( ( elem = results[ i++ ] ) ) {
+					if ( elem.nodeType === 1 ) {
+						tmp.push( elem );
+					}
+				}
+
+				return tmp;
+			}
+			return results;
+		};
+
+	// Class
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+			return context.getElementsByClassName( className );
+		}
+	};
+
+	/* QSA/matchesSelector
+	---------------------------------------------------------------------- */
+
+	// QSA and matchesSelector support
+
+	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+	rbuggyMatches = [];
+
+	// qSa(:focus) reports false when true (Chrome 21)
+	// We allow this because of a bug in IE8/9 that throws an error
+	// whenever `document.activeElement` is accessed on an iframe
+	// So, we allow :focus to pass through QSA all the time to avoid the IE error
+	// See https://bugs.jquery.com/ticket/13378
+	rbuggyQSA = [];
+
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+		// Build QSA regex
+		// Regex strategy adopted from Diego Perini
+		assert( function( el ) {
+
+			var input;
+
+			// Select is set to empty string on purpose
+			// This is to test IE's treatment of not explicitly
+			// setting a boolean content attribute,
+			// since its presence should be enough
+			// https://bugs.jquery.com/ticket/12359
+			docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
+				"<select id='" + expando + "-\r\\' msallowcapture=''>" +
+				"<option selected=''></option></select>";
+
+			// Support: IE8, Opera 11-12.16
+			// Nothing should be selected when empty strings follow ^= or $= or *=
+			// The test attribute must be unknown in Opera but "safe" for WinRT
+			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+			}
+
+			// Support: IE8
+			// Boolean attributes and "value" are not treated correctly
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+			}
+
+			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
+			}
+
+			// Webkit/Opera - :checked should return selected option elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			// IE8 throws error here and will not see later tests
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
+			}
+
+			// Support: Safari 8+, iOS 8+
+			// https://bugs.webkit.org/show_bug.cgi?id=136851
+			// In-page `selector#id sibling-combinator selector` fails
+			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+				rbuggyQSA.push( ".#.+[+~]" );
+			}
+
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
+			el.innerHTML = "<a href='' disabled='disabled'></a>" +
+				"<select disabled='disabled'><option/></select>";
+
+			// Support: Windows 8 Native Apps
+			// The type and name attributes are restricted during .innerHTML assignment
+			var input = document.createElement( "input" );
+			input.setAttribute( "type", "hidden" );
+			el.appendChild( input ).setAttribute( "name", "D" );
+
+			// Support: IE8
+			// Enforce case-sensitivity of name attribute
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
+				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+			}
+
+			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+			// IE8 throws error here and will not see later tests
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: IE9-11+
+			// IE's :disabled selector does not pick up the children of disabled fieldsets
+			docElem.appendChild( el ).disabled = true;
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: Opera 10 - 11 only
+			// Opera 10-11 does not throw on post-comma invalid pseudos
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
+	}
+
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+		docElem.webkitMatchesSelector ||
+		docElem.mozMatchesSelector ||
+		docElem.oMatchesSelector ||
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
+
+			// Check to see if it's possible to do matchesSelector
+			// on a disconnected node (IE 9)
+			support.disconnectedMatch = matches.call( el, "*" );
+
+			// This should fail with an exception
+			// Gecko does not error, returns false instead
+			matches.call( el, "[s!='']:x" );
+			rbuggyMatches.push( "!=", pseudos );
+		} );
+	}
+
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+	/* Contains
+	---------------------------------------------------------------------- */
+	hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+	// Element contains another
+	// Purposefully self-exclusive
+	// As in, an element does not contain itself
+	contains = hasCompare || rnative.test( docElem.contains ) ?
+		function( a, b ) {
+			var adown = a.nodeType === 9 ? a.documentElement : a,
+				bup = b && b.parentNode;
+			return a === bup || !!( bup && bup.nodeType === 1 && (
+				adown.contains ?
+					adown.contains( bup ) :
+					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+			) );
+		} :
+		function( a, b ) {
+			if ( b ) {
+				while ( ( b = b.parentNode ) ) {
+					if ( b === a ) {
+						return true;
+					}
+				}
+			}
+			return false;
+		};
+
+	/* Sorting
+	---------------------------------------------------------------------- */
+
+	// Document order sorting
+	sortOrder = hasCompare ?
+	function( a, b ) {
+
+		// Flag for duplicate removal
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		// Sort on method existence if only one input has compareDocumentPosition
+		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+		if ( compare ) {
+			return compare;
+		}
+
+		// Calculate position if both inputs belong to the same document
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+			a.compareDocumentPosition( b ) :
+
+			// Otherwise we know they are disconnected
+			1;
+
+		// Disconnected nodes
+		if ( compare & 1 ||
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+			// Choose the first element that is related to our preferred document
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
+				return -1;
+			}
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
+				return 1;
+			}
+
+			// Maintain original order
+			return sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+		}
+
+		return compare & 4 ? -1 : 1;
+	} :
+	function( a, b ) {
+
+		// Exit early if the nodes are identical
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		var cur,
+			i = 0,
+			aup = a.parentNode,
+			bup = b.parentNode,
+			ap = [ a ],
+			bp = [ b ];
+
+		// Parentless nodes are either documents or disconnected
+		if ( !aup || !bup ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
+				aup ? -1 :
+				bup ? 1 :
+				sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+
+		// If the nodes are siblings, we can do a quick check
+		} else if ( aup === bup ) {
+			return siblingCheck( a, b );
+		}
+
+		// Otherwise we need full lists of their ancestors for comparison
+		cur = a;
+		while ( ( cur = cur.parentNode ) ) {
+			ap.unshift( cur );
+		}
+		cur = b;
+		while ( ( cur = cur.parentNode ) ) {
+			bp.unshift( cur );
+		}
+
+		// Walk down the tree looking for a discrepancy
+		while ( ap[ i ] === bp[ i ] ) {
+			i++;
+		}
+
+		return i ?
+
+			// Do a sibling check if the nodes have a common ancestor
+			siblingCheck( ap[ i ], bp[ i ] ) :
+
+			// Otherwise nodes in our document sort first
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
+			0;
+	};
+
+	return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+	return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+	setDocument( elem );
+
+	if ( support.matchesSelector && documentIsHTML &&
+		!nonnativeSelectorCache[ expr + " " ] &&
+		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
+
+		try {
+			var ret = matches.call( elem, expr );
+
+			// IE 9's matchesSelector returns false on disconnected nodes
+			if ( ret || support.disconnectedMatch ||
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
+				return ret;
+			}
+		} catch ( e ) {
+			nonnativeSelectorCache( expr, true );
+		}
+	}
+
+	return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
+		setDocument( context );
+	}
+	return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
+		setDocument( elem );
+	}
+
+	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+		// Don't get fooled by Object.prototype properties (jQuery #13807)
+		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+			fn( elem, name, !documentIsHTML ) :
+			undefined;
+
+	return val !== undefined ?
+		val :
+		support.attributes || !documentIsHTML ?
+			elem.getAttribute( name ) :
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
+				val.value :
+				null;
+};
+
+Sizzle.escape = function( sel ) {
+	return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+	throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+	var elem,
+		duplicates = [],
+		j = 0,
+		i = 0;
+
+	// Unless we *know* we can detect duplicates, assume their presence
+	hasDuplicate = !support.detectDuplicates;
+	sortInput = !support.sortStable && results.slice( 0 );
+	results.sort( sortOrder );
+
+	if ( hasDuplicate ) {
+		while ( ( elem = results[ i++ ] ) ) {
+			if ( elem === results[ i ] ) {
+				j = duplicates.push( i );
+			}
+		}
+		while ( j-- ) {
+			results.splice( duplicates[ j ], 1 );
+		}
+	}
+
+	// Clear input after sorting to release objects
+	// See https://github.com/jquery/sizzle/pull/225
+	sortInput = null;
+
+	return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+	var node,
+		ret = "",
+		i = 0,
+		nodeType = elem.nodeType;
+
+	if ( !nodeType ) {
+
+		// If no nodeType, this is expected to be an array
+		while ( ( node = elem[ i++ ] ) ) {
+
+			// Do not traverse comment nodes
+			ret += getText( node );
+		}
+	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+		// Use textContent for elements
+		// innerText usage removed for consistency of new lines (jQuery #11153)
+		if ( typeof elem.textContent === "string" ) {
+			return elem.textContent;
+		} else {
+
+			// Traverse its children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				ret += getText( elem );
+			}
+		}
+	} else if ( nodeType === 3 || nodeType === 4 ) {
+		return elem.nodeValue;
+	}
+
+	// Do not include comment or processing instruction nodes
+
+	return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+	// Can be adjusted by the user
+	cacheLength: 50,
+
+	createPseudo: markFunction,
+
+	match: matchExpr,
+
+	attrHandle: {},
+
+	find: {},
+
+	relative: {
+		">": { dir: "parentNode", first: true },
+		" ": { dir: "parentNode" },
+		"+": { dir: "previousSibling", first: true },
+		"~": { dir: "previousSibling" }
+	},
+
+	preFilter: {
+		"ATTR": function( match ) {
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+			// Move the given value to match[3] whether quoted or unquoted
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
+
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
+			}
+
+			return match.slice( 0, 4 );
+		},
+
+		"CHILD": function( match ) {
+
+			/* matches from matchExpr["CHILD"]
+				1 type (only|nth|...)
+				2 what (child|of-type)
+				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+				4 xn-component of xn+y argument ([+-]?\d*n|)
+				5 sign of xn-component
+				6 x of xn-component
+				7 sign of y-component
+				8 y of y-component
+			*/
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+				// nth-* requires argument
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
+				}
+
+				// numeric x and y parameters for Expr.filter.CHILD
+				// remember that false/true cast respectively to 0/1
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
+			}
+
+			return match;
+		},
+
+		"PSEUDO": function( match ) {
+			var excess,
+				unquoted = !match[ 6 ] && match[ 2 ];
+
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+				return null;
+			}
+
+			// Accept quoted arguments as-is
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+			// Strip excess characters from unquoted arguments
+			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
+				// Get excess from tokenize (recursively)
+				( excess = tokenize( unquoted, true ) ) &&
+
+				// advance to the next closing parenthesis
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+				// excess is a negative index
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
+			}
+
+			// Return only captures needed by the pseudo filter method (type and argument)
+			return match.slice( 0, 3 );
+		}
+	},
+
+	filter: {
+
+		"TAG": function( nodeNameSelector ) {
+			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+			return nodeNameSelector === "*" ?
+				function() {
+					return true;
+				} :
+				function( elem ) {
+					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+				};
+		},
+
+		"CLASS": function( className ) {
+			var pattern = classCache[ className + " " ];
+
+			return pattern ||
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
+		},
+
+		"ATTR": function( name, operator, check ) {
+			return function( elem ) {
+				var result = Sizzle.attr( elem, name );
+
+				if ( result == null ) {
+					return operator === "!=";
+				}
+				if ( !operator ) {
+					return true;
+				}
+
+				result += "";
+
+				/* eslint-disable max-len */
+
+				return operator === "=" ? result === check :
+					operator === "!=" ? result !== check :
+					operator === "^=" ? check && result.indexOf( check ) === 0 :
+					operator === "*=" ? check && result.indexOf( check ) > -1 :
+					operator === "$=" ? check && result.slice( -check.length ) === check :
+					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+					false;
+				/* eslint-enable max-len */
+
+			};
+		},
+
+		"CHILD": function( type, what, _argument, first, last ) {
+			var simple = type.slice( 0, 3 ) !== "nth",
+				forward = type.slice( -4 ) !== "last",
+				ofType = what === "of-type";
+
+			return first === 1 && last === 0 ?
+
+				// Shortcut for :nth-*(n)
+				function( elem ) {
+					return !!elem.parentNode;
+				} :
+
+				function( elem, _context, xml ) {
+					var cache, uniqueCache, outerCache, node, nodeIndex, start,
+						dir = simple !== forward ? "nextSibling" : "previousSibling",
+						parent = elem.parentNode,
+						name = ofType && elem.nodeName.toLowerCase(),
+						useCache = !xml && !ofType,
+						diff = false;
+
+					if ( parent ) {
+
+						// :(first|last|only)-(child|of-type)
+						if ( simple ) {
+							while ( dir ) {
+								node = elem;
+								while ( ( node = node[ dir ] ) ) {
+									if ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) {
+
+										return false;
+									}
+								}
+
+								// Reverse direction for :only-* (if we haven't yet done so)
+								start = dir = type === "only" && !start && "nextSibling";
+							}
+							return true;
+						}
+
+						start = [ forward ? parent.firstChild : parent.lastChild ];
+
+						// non-xml :nth-child(...) stores cache data on `parent`
+						if ( forward && useCache ) {
+
+							// Seek `elem` from a previously-cached index
+
+							// ...in a gzip-friendly way
+							node = parent;
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+							// Support: IE <9 only
+							// Defend against cloned attroperties (jQuery gh-1709)
+							uniqueCache = outerCache[ node.uniqueID ] ||
+								( outerCache[ node.uniqueID ] = {} );
+
+							cache = uniqueCache[ type ] || [];
+							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+							diff = nodeIndex && cache[ 2 ];
+							node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+								// Fallback to seeking `elem` from the start
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+								// When found, cache indexes on `parent` and break
+								if ( node.nodeType === 1 && ++diff && node === elem ) {
+									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+									break;
+								}
+							}
+
+						} else {
+
+							// Use previously-cached element index if available
+							if ( useCache ) {
+
+								// ...in a gzip-friendly way
+								node = elem;
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+								// Support: IE <9 only
+								// Defend against cloned attroperties (jQuery gh-1709)
+								uniqueCache = outerCache[ node.uniqueID ] ||
+									( outerCache[ node.uniqueID ] = {} );
+
+								cache = uniqueCache[ type ] || [];
+								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+								diff = nodeIndex;
+							}
+
+							// xml :nth-child(...)
+							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
+							if ( diff === false ) {
+
+								// Use the same loop as above to seek `elem` from the start
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+									if ( ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) &&
+										++diff ) {
+
+										// Cache the index of each encountered element
+										if ( useCache ) {
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
+
+											// Support: IE <9 only
+											// Defend against cloned attroperties (jQuery gh-1709)
+											uniqueCache = outerCache[ node.uniqueID ] ||
+												( outerCache[ node.uniqueID ] = {} );
+
+											uniqueCache[ type ] = [ dirruns, diff ];
+										}
+
+										if ( node === elem ) {
+											break;
+										}
+									}
+								}
+							}
+						}
+
+						// Incorporate the offset, then check against cycle size
+						diff -= last;
+						return diff === first || ( diff % first === 0 && diff / first >= 0 );
+					}
+				};
+		},
+
+		"PSEUDO": function( pseudo, argument ) {
+
+			// pseudo-class names are case-insensitive
+			// http://www.w3.org/TR/selectors/#pseudo-classes
+			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+			// Remember that setFilters inherits from pseudos
+			var args,
+				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+					Sizzle.error( "unsupported pseudo: " + pseudo );
+
+			// The user may use createPseudo to indicate that
+			// arguments are needed to create the filter function
+			// just as Sizzle does
+			if ( fn[ expando ] ) {
+				return fn( argument );
+			}
+
+			// But maintain support for old signatures
+			if ( fn.length > 1 ) {
+				args = [ pseudo, pseudo, "", argument ];
+				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+					markFunction( function( seed, matches ) {
+						var idx,
+							matched = fn( seed, argument ),
+							i = matched.length;
+						while ( i-- ) {
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+						}
+					} ) :
+					function( elem ) {
+						return fn( elem, 0, args );
+					};
+			}
+
+			return fn;
+		}
+	},
+
+	pseudos: {
+
+		// Potentially complex pseudos
+		"not": markFunction( function( selector ) {
+
+			// Trim the selector passed to compile
+			// to avoid treating leading and trailing
+			// spaces as combinators
+			var input = [],
+				results = [],
+				matcher = compile( selector.replace( rtrim, "$1" ) );
+
+			return matcher[ expando ] ?
+				markFunction( function( seed, matches, _context, xml ) {
+					var elem,
+						unmatched = matcher( seed, null, xml, [] ),
+						i = seed.length;
+
+					// Match elements unmatched by `matcher`
+					while ( i-- ) {
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
+						}
+					}
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
+					matcher( input, null, xml, results );
+
+					// Don't keep the element (issue #299)
+					input[ 0 ] = null;
+					return !results.pop();
+				};
+		} ),
+
+		"has": markFunction( function( selector ) {
+			return function( elem ) {
+				return Sizzle( selector, elem ).length > 0;
+			};
+		} ),
+
+		"contains": markFunction( function( text ) {
+			text = text.replace( runescape, funescape );
+			return function( elem ) {
+				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+			};
+		} ),
+
+		// "Whether an element is represented by a :lang() selector
+		// is based solely on the element's language value
+		// being equal to the identifier C,
+		// or beginning with the identifier C immediately followed by "-".
+		// The matching of C against the element's language value is performed case-insensitively.
+		// The identifier C does not have to be a valid language name."
+		// http://www.w3.org/TR/selectors/#lang-pseudo
+		"lang": markFunction( function( lang ) {
+
+			// lang value must be a valid identifier
+			if ( !ridentifier.test( lang || "" ) ) {
+				Sizzle.error( "unsupported lang: " + lang );
+			}
+			lang = lang.replace( runescape, funescape ).toLowerCase();
+			return function( elem ) {
+				var elemLang;
+				do {
+					if ( ( elemLang = documentIsHTML ?
+						elem.lang :
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+						elemLang = elemLang.toLowerCase();
+						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+					}
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+				return false;
+			};
+		} ),
+
+		// Miscellaneous
+		"target": function( elem ) {
+			var hash = window.location && window.location.hash;
+			return hash && hash.slice( 1 ) === elem.id;
+		},
+
+		"root": function( elem ) {
+			return elem === docElem;
+		},
+
+		"focus": function( elem ) {
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
+		},
+
+		// Boolean properties
+		"enabled": createDisabledPseudo( false ),
+		"disabled": createDisabledPseudo( true ),
+
+		"checked": function( elem ) {
+
+			// In CSS3, :checked should return both checked and selected elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			var nodeName = elem.nodeName.toLowerCase();
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
+		},
+
+		"selected": function( elem ) {
+
+			// Accessing this property makes selected-by-default
+			// options in Safari work properly
+			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
+				elem.parentNode.selectedIndex;
+			}
+
+			return elem.selected === true;
+		},
+
+		// Contents
+		"empty": function( elem ) {
+
+			// http://www.w3.org/TR/selectors/#empty-pseudo
+			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+			//   but not by others (comment: 8; processing instruction: 7; etc.)
+			// nodeType < 6 works because attributes (2) do not appear as children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				if ( elem.nodeType < 6 ) {
+					return false;
+				}
+			}
+			return true;
+		},
+
+		"parent": function( elem ) {
+			return !Expr.pseudos[ "empty" ]( elem );
+		},
+
+		// Element/input types
+		"header": function( elem ) {
+			return rheader.test( elem.nodeName );
+		},
+
+		"input": function( elem ) {
+			return rinputs.test( elem.nodeName );
+		},
+
+		"button": function( elem ) {
+			var name = elem.nodeName.toLowerCase();
+			return name === "input" && elem.type === "button" || name === "button";
+		},
+
+		"text": function( elem ) {
+			var attr;
+			return elem.nodeName.toLowerCase() === "input" &&
+				elem.type === "text" &&
+
+				// Support: IE<8
+				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
+		},
+
+		// Position-in-collection
+		"first": createPositionalPseudo( function() {
+			return [ 0 ];
+		} ),
+
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
+			return [ length - 1 ];
+		} ),
+
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+			return [ argument < 0 ? argument + length : argument ];
+		} ),
+
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 0;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 1;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ?
+				argument + length :
+				argument > length ?
+					length :
+					argument;
+			for ( ; --i >= 0; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ? argument + length : argument;
+			for ( ; ++i < length; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} )
+	}
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+	Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+	Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+	var matched, match, tokens, type,
+		soFar, groups, preFilters,
+		cached = tokenCache[ selector + " " ];
+
+	if ( cached ) {
+		return parseOnly ? 0 : cached.slice( 0 );
+	}
+
+	soFar = selector;
+	groups = [];
+	preFilters = Expr.preFilter;
+
+	while ( soFar ) {
+
+		// Comma and first run
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+			if ( match ) {
+
+				// Don't consume trailing commas as valid
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
+			}
+			groups.push( ( tokens = [] ) );
+		}
+
+		matched = false;
+
+		// Combinators
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
+			matched = match.shift();
+			tokens.push( {
+				value: matched,
+
+				// Cast descendant combinators to space
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
+			soFar = soFar.slice( matched.length );
+		}
+
+		// Filters
+		for ( type in Expr.filter ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
+				matched = match.shift();
+				tokens.push( {
+					value: matched,
+					type: type,
+					matches: match
+				} );
+				soFar = soFar.slice( matched.length );
+			}
+		}
+
+		if ( !matched ) {
+			break;
+		}
+	}
+
+	// Return the length of the invalid excess
+	// if we're just parsing
+	// Otherwise, throw an error or return tokens
+	return parseOnly ?
+		soFar.length :
+		soFar ?
+			Sizzle.error( selector ) :
+
+			// Cache the tokens
+			tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+	var i = 0,
+		len = tokens.length,
+		selector = "";
+	for ( ; i < len; i++ ) {
+		selector += tokens[ i ].value;
+	}
+	return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+	var dir = combinator.dir,
+		skip = combinator.next,
+		key = skip || dir,
+		checkNonElements = base && key === "parentNode",
+		doneName = done++;
+
+	return combinator.first ?
+
+		// Check against closest ancestor/preceding element
+		function( elem, context, xml ) {
+			while ( ( elem = elem[ dir ] ) ) {
+				if ( elem.nodeType === 1 || checkNonElements ) {
+					return matcher( elem, context, xml );
+				}
+			}
+			return false;
+		} :
+
+		// Check against all ancestor/preceding elements
+		function( elem, context, xml ) {
+			var oldCache, uniqueCache, outerCache,
+				newCache = [ dirruns, doneName ];
+
+			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+			if ( xml ) {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						if ( matcher( elem, context, xml ) ) {
+							return true;
+						}
+					}
+				}
+			} else {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+						// Support: IE <9 only
+						// Defend against cloned attroperties (jQuery gh-1709)
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
+
+						if ( skip && skip === elem.nodeName.toLowerCase() ) {
+							elem = elem[ dir ] || elem;
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
+							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+							// Assign to newCache so results back-propagate to previous elements
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
+						} else {
+
+							// Reuse newcache so results back-propagate to previous elements
+							uniqueCache[ key ] = newCache;
+
+							// A match means we're done; a fail means we have to keep checking
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+								return true;
+							}
+						}
+					}
+				}
+			}
+			return false;
+		};
+}
+
+function elementMatcher( matchers ) {
+	return matchers.length > 1 ?
+		function( elem, context, xml ) {
+			var i = matchers.length;
+			while ( i-- ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
+					return false;
+				}
+			}
+			return true;
+		} :
+		matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+	var i = 0,
+		len = contexts.length;
+	for ( ; i < len; i++ ) {
+		Sizzle( selector, contexts[ i ], results );
+	}
+	return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+	var elem,
+		newUnmatched = [],
+		i = 0,
+		len = unmatched.length,
+		mapped = map != null;
+
+	for ( ; i < len; i++ ) {
+		if ( ( elem = unmatched[ i ] ) ) {
+			if ( !filter || filter( elem, context, xml ) ) {
+				newUnmatched.push( elem );
+				if ( mapped ) {
+					map.push( i );
+				}
+			}
+		}
+	}
+
+	return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+	if ( postFilter && !postFilter[ expando ] ) {
+		postFilter = setMatcher( postFilter );
+	}
+	if ( postFinder && !postFinder[ expando ] ) {
+		postFinder = setMatcher( postFinder, postSelector );
+	}
+	return markFunction( function( seed, results, context, xml ) {
+		var temp, i, elem,
+			preMap = [],
+			postMap = [],
+			preexisting = results.length,
+
+			// Get initial elements from seed or context
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
+
+			// Prefilter to get matcher input, preserving a map for seed-results synchronization
+			matcherIn = preFilter && ( seed || !selector ) ?
+				condense( elems, preMap, preFilter, context, xml ) :
+				elems,
+
+			matcherOut = matcher ?
+
+				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+					// ...intermediate processing is necessary
+					[] :
+
+					// ...otherwise use results directly
+					results :
+				matcherIn;
+
+		// Find primary matches
+		if ( matcher ) {
+			matcher( matcherIn, matcherOut, context, xml );
+		}
+
+		// Apply postFilter
+		if ( postFilter ) {
+			temp = condense( matcherOut, postMap );
+			postFilter( temp, [], context, xml );
+
+			// Un-match failing elements by moving them back to matcherIn
+			i = temp.length;
+			while ( i-- ) {
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+				}
+			}
+		}
+
+		if ( seed ) {
+			if ( postFinder || preFilter ) {
+				if ( postFinder ) {
+
+					// Get the final matcherOut by condensing this intermediate into postFinder contexts
+					temp = [];
+					i = matcherOut.length;
+					while ( i-- ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
+							// Restore matcherIn since elem is not yet a final match
+							temp.push( ( matcherIn[ i ] = elem ) );
+						}
+					}
+					postFinder( null, ( matcherOut = [] ), temp, xml );
+				}
+
+				// Move matched elements from seed to results to keep them synchronized
+				i = matcherOut.length;
+				while ( i-- ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+						seed[ temp ] = !( results[ temp ] = elem );
+					}
+				}
+			}
+
+		// Add elements to results, through postFinder if defined
+		} else {
+			matcherOut = condense(
+				matcherOut === results ?
+					matcherOut.splice( preexisting, matcherOut.length ) :
+					matcherOut
+			);
+			if ( postFinder ) {
+				postFinder( null, results, matcherOut, xml );
+			} else {
+				push.apply( results, matcherOut );
+			}
+		}
+	} );
+}
+
+function matcherFromTokens( tokens ) {
+	var checkContext, matcher, j,
+		len = tokens.length,
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
+		i = leadingRelative ? 1 : 0,
+
+		// The foundational matcher ensures that elements are reachable from top-level context(s)
+		matchContext = addCombinator( function( elem ) {
+			return elem === checkContext;
+		}, implicitRelative, true ),
+		matchAnyContext = addCombinator( function( elem ) {
+			return indexOf( checkContext, elem ) > -1;
+		}, implicitRelative, true ),
+		matchers = [ function( elem, context, xml ) {
+			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+				( checkContext = context ).nodeType ?
+					matchContext( elem, context, xml ) :
+					matchAnyContext( elem, context, xml ) );
+
+			// Avoid hanging onto element (issue #299)
+			checkContext = null;
+			return ret;
+		} ];
+
+	for ( ; i < len; i++ ) {
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+		} else {
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+			// Return special upon seeing a positional matcher
+			if ( matcher[ expando ] ) {
+
+				// Find the next relative operator (if any) for proper handling
+				j = ++i;
+				for ( ; j < len; j++ ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
+						break;
+					}
+				}
+				return setMatcher(
+					i > 1 && elementMatcher( matchers ),
+					i > 1 && toSelector(
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+					).replace( rtrim, "$1" ),
+					matcher,
+					i < j && matcherFromTokens( tokens.slice( i, j ) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+					j < len && toSelector( tokens )
+				);
+			}
+			matchers.push( matcher );
+		}
+	}
+
+	return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+	var bySet = setMatchers.length > 0,
+		byElement = elementMatchers.length > 0,
+		superMatcher = function( seed, context, xml, results, outermost ) {
+			var elem, j, matcher,
+				matchedCount = 0,
+				i = "0",
+				unmatched = seed && [],
+				setMatched = [],
+				contextBackup = outermostContext,
+
+				// We must always have either seed elements or outermost context
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+				// Use integer dirruns iff this is the outermost matcher
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+				len = elems.length;
+
+			if ( outermost ) {
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
+			}
+
+			// Add elements passing elementMatchers directly to results
+			// Support: IE<9, Safari
+			// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+				if ( byElement && elem ) {
+					j = 0;
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
+						setDocument( elem );
+						xml = !documentIsHTML;
+					}
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
+							results.push( elem );
+							break;
+						}
+					}
+					if ( outermost ) {
+						dirruns = dirrunsUnique;
+					}
+				}
+
+				// Track unmatched elements for set filters
+				if ( bySet ) {
+
+					// They will have gone through all possible matchers
+					if ( ( elem = !matcher && elem ) ) {
+						matchedCount--;
+					}
+
+					// Lengthen the array for every element, matched or not
+					if ( seed ) {
+						unmatched.push( elem );
+					}
+				}
+			}
+
+			// `i` is now the count of elements visited above, and adding it to `matchedCount`
+			// makes the latter nonnegative.
+			matchedCount += i;
+
+			// Apply set filters to unmatched elements
+			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+			// no element matchers and no seed.
+			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
+			// numerically zero.
+			if ( bySet && i !== matchedCount ) {
+				j = 0;
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
+					matcher( unmatched, setMatched, context, xml );
+				}
+
+				if ( seed ) {
+
+					// Reintegrate element matches to eliminate the need for sorting
+					if ( matchedCount > 0 ) {
+						while ( i-- ) {
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
+							}
+						}
+					}
+
+					// Discard index placeholder values to get only actual matches
+					setMatched = condense( setMatched );
+				}
+
+				// Add matches to results
+				push.apply( results, setMatched );
+
+				// Seedless set matches succeeding multiple successful matchers stipulate sorting
+				if ( outermost && !seed && setMatched.length > 0 &&
+					( matchedCount + setMatchers.length ) > 1 ) {
+
+					Sizzle.uniqueSort( results );
+				}
+			}
+
+			// Override manipulation of globals by nested matchers
+			if ( outermost ) {
+				dirruns = dirrunsUnique;
+				outermostContext = contextBackup;
+			}
+
+			return unmatched;
+		};
+
+	return bySet ?
+		markFunction( superMatcher ) :
+		superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+	var i,
+		setMatchers = [],
+		elementMatchers = [],
+		cached = compilerCache[ selector + " " ];
+
+	if ( !cached ) {
+
+		// Generate a function of recursive functions that can be used to check each element
+		if ( !match ) {
+			match = tokenize( selector );
+		}
+		i = match.length;
+		while ( i-- ) {
+			cached = matcherFromTokens( match[ i ] );
+			if ( cached[ expando ] ) {
+				setMatchers.push( cached );
+			} else {
+				elementMatchers.push( cached );
+			}
+		}
+
+		// Cache the compiled function
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
+
+		// Save selector and tokenization
+		cached.selector = selector;
+	}
+	return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ *  selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ *  selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+	var i, tokens, token, type, find,
+		compiled = typeof selector === "function" && selector,
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+	results = results || [];
+
+	// Try to minimize operations if there is only one selector in the list and no seed
+	// (the latter of which guarantees us context)
+	if ( match.length === 1 ) {
+
+		// Reduce context if the leading compound selector is an ID
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
+			if ( !context ) {
+				return results;
+
+			// Precompiled matchers will still verify ancestry, so step up a level
+			} else if ( compiled ) {
+				context = context.parentNode;
+			}
+
+			selector = selector.slice( tokens.shift().value.length );
+		}
+
+		// Fetch a seed set for right-to-left matching
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+		while ( i-- ) {
+			token = tokens[ i ];
+
+			// Abort if we hit a combinator
+			if ( Expr.relative[ ( type = token.type ) ] ) {
+				break;
+			}
+			if ( ( find = Expr.find[ type ] ) ) {
+
+				// Search, expanding context for leading sibling combinators
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
+
+					// If seed is empty or no tokens remain, we can return early
+					tokens.splice( i, 1 );
+					selector = seed.length && toSelector( tokens );
+					if ( !selector ) {
+						push.apply( results, seed );
+						return results;
+					}
+
+					break;
+				}
+			}
+		}
+	}
+
+	// Compile and execute a filtering function if one is not provided
+	// Provide `match` to avoid retokenization if we modified the selector above
+	( compiled || compile( selector, match ) )(
+		seed,
+		context,
+		!documentIsHTML,
+		results,
+		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+	);
+	return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+	// Should return 1, but returns 4 (following)
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+	el.innerHTML = "<a href='#'></a>";
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+	addHandle( "type|href|height|width", function( elem, name, isXML ) {
+		if ( !isXML ) {
+			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+		}
+	} );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+	el.innerHTML = "<input/>";
+	el.firstChild.setAttribute( "value", "" );
+	return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
+		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+			return elem.defaultValue;
+		}
+	} );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
+	addHandle( booleans, function( elem, name, isXML ) {
+		var val;
+		if ( !isXML ) {
+			return elem[ name ] === true ? name.toLowerCase() :
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
+					val.value :
+					null;
+		}
+	} );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+	var matched = [],
+		truncate = until !== undefined;
+
+	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+		if ( elem.nodeType === 1 ) {
+			if ( truncate && jQuery( elem ).is( until ) ) {
+				break;
+			}
+			matched.push( elem );
+		}
+	}
+	return matched;
+};
+
+
+var siblings = function( n, elem ) {
+	var matched = [];
+
+	for ( ; n; n = n.nextSibling ) {
+		if ( n.nodeType === 1 && n !== elem ) {
+			matched.push( n );
+		}
+	}
+
+	return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+  return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+};
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+	if ( isFunction( qualifier ) ) {
+		return jQuery.grep( elements, function( elem, i ) {
+			return !!qualifier.call( elem, i, elem ) !== not;
+		} );
+	}
+
+	// Single element
+	if ( qualifier.nodeType ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( elem === qualifier ) !== not;
+		} );
+	}
+
+	// Arraylike of elements (jQuery, arguments, Array)
+	if ( typeof qualifier !== "string" ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+		} );
+	}
+
+	// Filtered directly for both simple and complex selectors
+	return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+	var elem = elems[ 0 ];
+
+	if ( not ) {
+		expr = ":not(" + expr + ")";
+	}
+
+	if ( elems.length === 1 && elem.nodeType === 1 ) {
+		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+	}
+
+	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+		return elem.nodeType === 1;
+	} ) );
+};
+
+jQuery.fn.extend( {
+	find: function( selector ) {
+		var i, ret,
+			len = this.length,
+			self = this;
+
+		if ( typeof selector !== "string" ) {
+			return this.pushStack( jQuery( selector ).filter( function() {
+				for ( i = 0; i < len; i++ ) {
+					if ( jQuery.contains( self[ i ], this ) ) {
+						return true;
+					}
+				}
+			} ) );
+		}
+
+		ret = this.pushStack( [] );
+
+		for ( i = 0; i < len; i++ ) {
+			jQuery.find( selector, self[ i ], ret );
+		}
+
+		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+	},
+	filter: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], false ) );
+	},
+	not: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], true ) );
+	},
+	is: function( selector ) {
+		return !!winnow(
+			this,
+
+			// If this is a positional/relative selector, check membership in the returned set
+			// so $("p:first").is("p:last") won't return true for a doc with two "p".
+			typeof selector === "string" && rneedsContext.test( selector ) ?
+				jQuery( selector ) :
+				selector || [],
+			false
+		).length;
+	}
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+	// A simple way to check for HTML strings
+	// Prioritize #id over <tag> to avoid XSS via location.hash (#9521)
+	// Strict HTML recognition (#11290: must start with <)
+	// Shortcut simple #id case for speed
+	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+	init = jQuery.fn.init = function( selector, context, root ) {
+		var match, elem;
+
+		// HANDLE: $(""), $(null), $(undefined), $(false)
+		if ( !selector ) {
+			return this;
+		}
+
+		// Method init() accepts an alternate rootjQuery
+		// so migrate can support jQuery.sub (gh-2101)
+		root = root || rootjQuery;
+
+		// Handle HTML strings
+		if ( typeof selector === "string" ) {
+			if ( selector[ 0 ] === "<" &&
+				selector[ selector.length - 1 ] === ">" &&
+				selector.length >= 3 ) {
+
+				// Assume that strings that start and end with <> are HTML and skip the regex check
+				match = [ null, selector, null ];
+
+			} else {
+				match = rquickExpr.exec( selector );
+			}
+
+			// Match html or make sure no context is specified for #id
+			if ( match && ( match[ 1 ] || !context ) ) {
+
+				// HANDLE: $(html) -> $(array)
+				if ( match[ 1 ] ) {
+					context = context instanceof jQuery ? context[ 0 ] : context;
+
+					// Option to run scripts is true for back-compat
+					// Intentionally let the error be thrown if parseHTML is not present
+					jQuery.merge( this, jQuery.parseHTML(
+						match[ 1 ],
+						context && context.nodeType ? context.ownerDocument || context : document,
+						true
+					) );
+
+					// HANDLE: $(html, props)
+					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+						for ( match in context ) {
+
+							// Properties of context are called as methods if possible
+							if ( isFunction( this[ match ] ) ) {
+								this[ match ]( context[ match ] );
+
+							// ...and otherwise set as attributes
+							} else {
+								this.attr( match, context[ match ] );
+							}
+						}
+					}
+
+					return this;
+
+				// HANDLE: $(#id)
+				} else {
+					elem = document.getElementById( match[ 2 ] );
+
+					if ( elem ) {
+
+						// Inject the element directly into the jQuery object
+						this[ 0 ] = elem;
+						this.length = 1;
+					}
+					return this;
+				}
+
+			// HANDLE: $(expr, $(...))
+			} else if ( !context || context.jquery ) {
+				return ( context || root ).find( selector );
+
+			// HANDLE: $(expr, context)
+			// (which is just equivalent to: $(context).find(expr)
+			} else {
+				return this.constructor( context ).find( selector );
+			}
+
+		// HANDLE: $(DOMElement)
+		} else if ( selector.nodeType ) {
+			this[ 0 ] = selector;
+			this.length = 1;
+			return this;
+
+		// HANDLE: $(function)
+		// Shortcut for document ready
+		} else if ( isFunction( selector ) ) {
+			return root.ready !== undefined ?
+				root.ready( selector ) :
+
+				// Execute immediately if ready is not present
+				selector( jQuery );
+		}
+
+		return jQuery.makeArray( selector, this );
+	};
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+	// Methods guaranteed to produce a unique set when starting from a unique set
+	guaranteedUnique = {
+		children: true,
+		contents: true,
+		next: true,
+		prev: true
+	};
+
+jQuery.fn.extend( {
+	has: function( target ) {
+		var targets = jQuery( target, this ),
+			l = targets.length;
+
+		return this.filter( function() {
+			var i = 0;
+			for ( ; i < l; i++ ) {
+				if ( jQuery.contains( this, targets[ i ] ) ) {
+					return true;
+				}
+			}
+		} );
+	},
+
+	closest: function( selectors, context ) {
+		var cur,
+			i = 0,
+			l = this.length,
+			matched = [],
+			targets = typeof selectors !== "string" && jQuery( selectors );
+
+		// Positional selectors never match, since there's no _selection_ context
+		if ( !rneedsContext.test( selectors ) ) {
+			for ( ; i < l; i++ ) {
+				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+					// Always skip document fragments
+					if ( cur.nodeType < 11 && ( targets ?
+						targets.index( cur ) > -1 :
+
+						// Don't pass non-elements to Sizzle
+						cur.nodeType === 1 &&
+							jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+						matched.push( cur );
+						break;
+					}
+				}
+			}
+		}
+
+		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+	},
+
+	// Determine the position of an element within the set
+	index: function( elem ) {
+
+		// No argument, return index in parent
+		if ( !elem ) {
+			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+		}
+
+		// Index in selector
+		if ( typeof elem === "string" ) {
+			return indexOf.call( jQuery( elem ), this[ 0 ] );
+		}
+
+		// Locate the position of the desired element
+		return indexOf.call( this,
+
+			// If it receives a jQuery object, the first element is used
+			elem.jquery ? elem[ 0 ] : elem
+		);
+	},
+
+	add: function( selector, context ) {
+		return this.pushStack(
+			jQuery.uniqueSort(
+				jQuery.merge( this.get(), jQuery( selector, context ) )
+			)
+		);
+	},
+
+	addBack: function( selector ) {
+		return this.add( selector == null ?
+			this.prevObject : this.prevObject.filter( selector )
+		);
+	}
+} );
+
+function sibling( cur, dir ) {
+	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+	return cur;
+}
+
+jQuery.each( {
+	parent: function( elem ) {
+		var parent = elem.parentNode;
+		return parent && parent.nodeType !== 11 ? parent : null;
+	},
+	parents: function( elem ) {
+		return dir( elem, "parentNode" );
+	},
+	parentsUntil: function( elem, _i, until ) {
+		return dir( elem, "parentNode", until );
+	},
+	next: function( elem ) {
+		return sibling( elem, "nextSibling" );
+	},
+	prev: function( elem ) {
+		return sibling( elem, "previousSibling" );
+	},
+	nextAll: function( elem ) {
+		return dir( elem, "nextSibling" );
+	},
+	prevAll: function( elem ) {
+		return dir( elem, "previousSibling" );
+	},
+	nextUntil: function( elem, _i, until ) {
+		return dir( elem, "nextSibling", until );
+	},
+	prevUntil: function( elem, _i, until ) {
+		return dir( elem, "previousSibling", until );
+	},
+	siblings: function( elem ) {
+		return siblings( ( elem.parentNode || {} ).firstChild, elem );
+	},
+	children: function( elem ) {
+		return siblings( elem.firstChild );
+	},
+	contents: function( elem ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			// <object> elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
+			return elem.contentDocument;
+		}
+
+		// Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+		// Treat the template element as a regular one in browsers that
+		// don't support it.
+		if ( nodeName( elem, "template" ) ) {
+			elem = elem.content || elem;
+		}
+
+		return jQuery.merge( [], elem.childNodes );
+	}
+}, function( name, fn ) {
+	jQuery.fn[ name ] = function( until, selector ) {
+		var matched = jQuery.map( this, fn, until );
+
+		if ( name.slice( -5 ) !== "Until" ) {
+			selector = until;
+		}
+
+		if ( selector && typeof selector === "string" ) {
+			matched = jQuery.filter( selector, matched );
+		}
+
+		if ( this.length > 1 ) {
+
+			// Remove duplicates
+			if ( !guaranteedUnique[ name ] ) {
+				jQuery.uniqueSort( matched );
+			}
+
+			// Reverse order for parents* and prev-derivatives
+			if ( rparentsprev.test( name ) ) {
+				matched.reverse();
+			}
+		}
+
+		return this.pushStack( matched );
+	};
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+	var object = {};
+	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+		object[ flag ] = true;
+	} );
+	return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ *	options: an optional list of space-separated options that will change how
+ *			the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ *	once:			will ensure the callback list can only be fired once (like a Deferred)
+ *
+ *	memory:			will keep track of previous values and will call any callback added
+ *					after the list has been fired right away with the latest "memorized"
+ *					values (like a Deferred)
+ *
+ *	unique:			will ensure a callback can only be added once (no duplicate in the list)
+ *
+ *	stopOnFalse:	interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+	// Convert options from String-formatted to Object-formatted if needed
+	// (we check in cache first)
+	options = typeof options === "string" ?
+		createOptions( options ) :
+		jQuery.extend( {}, options );
+
+	var // Flag to know if list is currently firing
+		firing,
+
+		// Last fire value for non-forgettable lists
+		memory,
+
+		// Flag to know if list was already fired
+		fired,
+
+		// Flag to prevent firing
+		locked,
+
+		// Actual callback list
+		list = [],
+
+		// Queue of execution data for repeatable lists
+		queue = [],
+
+		// Index of currently firing callback (modified by add/remove as needed)
+		firingIndex = -1,
+
+		// Fire callbacks
+		fire = function() {
+
+			// Enforce single-firing
+			locked = locked || options.once;
+
+			// Execute callbacks for all pending executions,
+			// respecting firingIndex overrides and runtime changes
+			fired = firing = true;
+			for ( ; queue.length; firingIndex = -1 ) {
+				memory = queue.shift();
+				while ( ++firingIndex < list.length ) {
+
+					// Run callback and check for early termination
+					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+						options.stopOnFalse ) {
+
+						// Jump to end and forget the data so .add doesn't re-fire
+						firingIndex = list.length;
+						memory = false;
+					}
+				}
+			}
+
+			// Forget the data if we're done with it
+			if ( !options.memory ) {
+				memory = false;
+			}
+
+			firing = false;
+
+			// Clean up if we're done firing for good
+			if ( locked ) {
+
+				// Keep an empty list if we have data for future add calls
+				if ( memory ) {
+					list = [];
+
+				// Otherwise, this object is spent
+				} else {
+					list = "";
+				}
+			}
+		},
+
+		// Actual Callbacks object
+		self = {
+
+			// Add a callback or a collection of callbacks to the list
+			add: function() {
+				if ( list ) {
+
+					// If we have memory from a past run, we should fire after adding
+					if ( memory && !firing ) {
+						firingIndex = list.length - 1;
+						queue.push( memory );
+					}
+
+					( function add( args ) {
+						jQuery.each( args, function( _, arg ) {
+							if ( isFunction( arg ) ) {
+								if ( !options.unique || !self.has( arg ) ) {
+									list.push( arg );
+								}
+							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+								// Inspect recursively
+								add( arg );
+							}
+						} );
+					} )( arguments );
+
+					if ( memory && !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Remove a callback from the list
+			remove: function() {
+				jQuery.each( arguments, function( _, arg ) {
+					var index;
+					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+						list.splice( index, 1 );
+
+						// Handle firing indexes
+						if ( index <= firingIndex ) {
+							firingIndex--;
+						}
+					}
+				} );
+				return this;
+			},
+
+			// Check if a given callback is in the list.
+			// If no argument is given, return whether or not list has callbacks attached.
+			has: function( fn ) {
+				return fn ?
+					jQuery.inArray( fn, list ) > -1 :
+					list.length > 0;
+			},
+
+			// Remove all callbacks from the list
+			empty: function() {
+				if ( list ) {
+					list = [];
+				}
+				return this;
+			},
+
+			// Disable .fire and .add
+			// Abort any current/pending executions
+			// Clear all callbacks and values
+			disable: function() {
+				locked = queue = [];
+				list = memory = "";
+				return this;
+			},
+			disabled: function() {
+				return !list;
+			},
+
+			// Disable .fire
+			// Also disable .add unless we have memory (since it would have no effect)
+			// Abort any pending executions
+			lock: function() {
+				locked = queue = [];
+				if ( !memory && !firing ) {
+					list = memory = "";
+				}
+				return this;
+			},
+			locked: function() {
+				return !!locked;
+			},
+
+			// Call all callbacks with the given context and arguments
+			fireWith: function( context, args ) {
+				if ( !locked ) {
+					args = args || [];
+					args = [ context, args.slice ? args.slice() : args ];
+					queue.push( args );
+					if ( !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Call all the callbacks with the given arguments
+			fire: function() {
+				self.fireWith( this, arguments );
+				return this;
+			},
+
+			// To know if the callbacks have already been called at least once
+			fired: function() {
+				return !!fired;
+			}
+		};
+
+	return self;
+};
+
+
+function Identity( v ) {
+	return v;
+}
+function Thrower( ex ) {
+	throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+	var method;
+
+	try {
+
+		// Check for promise aspect first to privilege synchronous behavior
+		if ( value && isFunction( ( method = value.promise ) ) ) {
+			method.call( value ).done( resolve ).fail( reject );
+
+		// Other thenables
+		} else if ( value && isFunction( ( method = value.then ) ) ) {
+			method.call( value, resolve, reject );
+
+		// Other non-thenables
+		} else {
+
+			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+			// * false: [ value ].slice( 0 ) => resolve( value )
+			// * true: [ value ].slice( 1 ) => resolve()
+			resolve.apply( undefined, [ value ].slice( noValue ) );
+		}
+
+	// For Promises/A+, convert exceptions into rejections
+	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+	// Deferred#then to conditionally suppress rejection.
+	} catch ( value ) {
+
+		// Support: Android 4.0 only
+		// Strict mode functions invoked without .call/.apply get global-object context
+		reject.apply( undefined, [ value ] );
+	}
+}
+
+jQuery.extend( {
+
+	Deferred: function( func ) {
+		var tuples = [
+
+				// action, add listener, callbacks,
+				// ... .then handlers, argument index, [final state]
+				[ "notify", "progress", jQuery.Callbacks( "memory" ),
+					jQuery.Callbacks( "memory" ), 2 ],
+				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+			],
+			state = "pending",
+			promise = {
+				state: function() {
+					return state;
+				},
+				always: function() {
+					deferred.done( arguments ).fail( arguments );
+					return this;
+				},
+				"catch": function( fn ) {
+					return promise.then( null, fn );
+				},
+
+				// Keep pipe for back-compat
+				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+					var fns = arguments;
+
+					return jQuery.Deferred( function( newDefer ) {
+						jQuery.each( tuples, function( _i, tuple ) {
+
+							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
+							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+							// deferred.progress(function() { bind to newDefer or newDefer.notify })
+							// deferred.done(function() { bind to newDefer or newDefer.resolve })
+							// deferred.fail(function() { bind to newDefer or newDefer.reject })
+							deferred[ tuple[ 1 ] ]( function() {
+								var returned = fn && fn.apply( this, arguments );
+								if ( returned && isFunction( returned.promise ) ) {
+									returned.promise()
+										.progress( newDefer.notify )
+										.done( newDefer.resolve )
+										.fail( newDefer.reject );
+								} else {
+									newDefer[ tuple[ 0 ] + "With" ](
+										this,
+										fn ? [ returned ] : arguments
+									);
+								}
+							} );
+						} );
+						fns = null;
+					} ).promise();
+				},
+				then: function( onFulfilled, onRejected, onProgress ) {
+					var maxDepth = 0;
+					function resolve( depth, deferred, handler, special ) {
+						return function() {
+							var that = this,
+								args = arguments,
+								mightThrow = function() {
+									var returned, then;
+
+									// Support: Promises/A+ section 2.3.3.3.3
+									// https://promisesaplus.com/#point-59
+									// Ignore double-resolution attempts
+									if ( depth < maxDepth ) {
+										return;
+									}
+
+									returned = handler.apply( that, args );
+
+									// Support: Promises/A+ section 2.3.1
+									// https://promisesaplus.com/#point-48
+									if ( returned === deferred.promise() ) {
+										throw new TypeError( "Thenable self-resolution" );
+									}
+
+									// Support: Promises/A+ sections 2.3.3.1, 3.5
+									// https://promisesaplus.com/#point-54
+									// https://promisesaplus.com/#point-75
+									// Retrieve `then` only once
+									then = returned &&
+
+										// Support: Promises/A+ section 2.3.4
+										// https://promisesaplus.com/#point-64
+										// Only check objects and functions for thenability
+										( typeof returned === "object" ||
+											typeof returned === "function" ) &&
+										returned.then;
+
+									// Handle a returned thenable
+									if ( isFunction( then ) ) {
+
+										// Special processors (notify) just wait for resolution
+										if ( special ) {
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special )
+											);
+
+										// Normal processors (resolve) also hook into progress
+										} else {
+
+											// ...and disregard older resolution values
+											maxDepth++;
+
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special ),
+												resolve( maxDepth, deferred, Identity,
+													deferred.notifyWith )
+											);
+										}
+
+									// Handle all other returned values
+									} else {
+
+										// Only substitute handlers pass on context
+										// and multiple values (non-spec behavior)
+										if ( handler !== Identity ) {
+											that = undefined;
+											args = [ returned ];
+										}
+
+										// Process the value(s)
+										// Default process is resolve
+										( special || deferred.resolveWith )( that, args );
+									}
+								},
+
+								// Only normal processors (resolve) catch and reject exceptions
+								process = special ?
+									mightThrow :
+									function() {
+										try {
+											mightThrow();
+										} catch ( e ) {
+
+											if ( jQuery.Deferred.exceptionHook ) {
+												jQuery.Deferred.exceptionHook( e,
+													process.stackTrace );
+											}
+
+											// Support: Promises/A+ section 2.3.3.3.4.1
+											// https://promisesaplus.com/#point-61
+											// Ignore post-resolution exceptions
+											if ( depth + 1 >= maxDepth ) {
+
+												// Only substitute handlers pass on context
+												// and multiple values (non-spec behavior)
+												if ( handler !== Thrower ) {
+													that = undefined;
+													args = [ e ];
+												}
+
+												deferred.rejectWith( that, args );
+											}
+										}
+									};
+
+							// Support: Promises/A+ section 2.3.3.3.1
+							// https://promisesaplus.com/#point-57
+							// Re-resolve promises immediately to dodge false rejection from
+							// subsequent errors
+							if ( depth ) {
+								process();
+							} else {
+
+								// Call an optional hook to record the stack, in case of exception
+								// since it's otherwise lost when execution goes async
+								if ( jQuery.Deferred.getStackHook ) {
+									process.stackTrace = jQuery.Deferred.getStackHook();
+								}
+								window.setTimeout( process );
+							}
+						};
+					}
+
+					return jQuery.Deferred( function( newDefer ) {
+
+						// progress_handlers.add( ... )
+						tuples[ 0 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onProgress ) ?
+									onProgress :
+									Identity,
+								newDefer.notifyWith
+							)
+						);
+
+						// fulfilled_handlers.add( ... )
+						tuples[ 1 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onFulfilled ) ?
+									onFulfilled :
+									Identity
+							)
+						);
+
+						// rejected_handlers.add( ... )
+						tuples[ 2 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onRejected ) ?
+									onRejected :
+									Thrower
+							)
+						);
+					} ).promise();
+				},
+
+				// Get a promise for this deferred
+				// If obj is provided, the promise aspect is added to the object
+				promise: function( obj ) {
+					return obj != null ? jQuery.extend( obj, promise ) : promise;
+				}
+			},
+			deferred = {};
+
+		// Add list-specific methods
+		jQuery.each( tuples, function( i, tuple ) {
+			var list = tuple[ 2 ],
+				stateString = tuple[ 5 ];
+
+			// promise.progress = list.add
+			// promise.done = list.add
+			// promise.fail = list.add
+			promise[ tuple[ 1 ] ] = list.add;
+
+			// Handle state
+			if ( stateString ) {
+				list.add(
+					function() {
+
+						// state = "resolved" (i.e., fulfilled)
+						// state = "rejected"
+						state = stateString;
+					},
+
+					// rejected_callbacks.disable
+					// fulfilled_callbacks.disable
+					tuples[ 3 - i ][ 2 ].disable,
+
+					// rejected_handlers.disable
+					// fulfilled_handlers.disable
+					tuples[ 3 - i ][ 3 ].disable,
+
+					// progress_callbacks.lock
+					tuples[ 0 ][ 2 ].lock,
+
+					// progress_handlers.lock
+					tuples[ 0 ][ 3 ].lock
+				);
+			}
+
+			// progress_handlers.fire
+			// fulfilled_handlers.fire
+			// rejected_handlers.fire
+			list.add( tuple[ 3 ].fire );
+
+			// deferred.notify = function() { deferred.notifyWith(...) }
+			// deferred.resolve = function() { deferred.resolveWith(...) }
+			// deferred.reject = function() { deferred.rejectWith(...) }
+			deferred[ tuple[ 0 ] ] = function() {
+				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+				return this;
+			};
+
+			// deferred.notifyWith = list.fireWith
+			// deferred.resolveWith = list.fireWith
+			// deferred.rejectWith = list.fireWith
+			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+		} );
+
+		// Make the deferred a promise
+		promise.promise( deferred );
+
+		// Call given func if any
+		if ( func ) {
+			func.call( deferred, deferred );
+		}
+
+		// All done!
+		return deferred;
+	},
+
+	// Deferred helper
+	when: function( singleValue ) {
+		var
+
+			// count of uncompleted subordinates
+			remaining = arguments.length,
+
+			// count of unprocessed arguments
+			i = remaining,
+
+			// subordinate fulfillment data
+			resolveContexts = Array( i ),
+			resolveValues = slice.call( arguments ),
+
+			// the master Deferred
+			master = jQuery.Deferred(),
+
+			// subordinate callback factory
+			updateFunc = function( i ) {
+				return function( value ) {
+					resolveContexts[ i ] = this;
+					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+					if ( !( --remaining ) ) {
+						master.resolveWith( resolveContexts, resolveValues );
+					}
+				};
+			};
+
+		// Single- and empty arguments are adopted like Promise.resolve
+		if ( remaining <= 1 ) {
+			adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject,
+				!remaining );
+
+			// Use .then() to unwrap secondary thenables (cf. gh-3000)
+			if ( master.state() === "pending" ||
+				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+				return master.then();
+			}
+		}
+
+		// Multiple arguments are aggregated like Promise.all array elements
+		while ( i-- ) {
+			adoptValue( resolveValues[ i ], updateFunc( i ), master.reject );
+		}
+
+		return master.promise();
+	}
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+	// Support: IE 8 - 9 only
+	// Console exists when dev tools are open, which can happen at any time
+	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+	}
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+	window.setTimeout( function() {
+		throw error;
+	} );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+	readyList
+		.then( fn )
+
+		// Wrap jQuery.readyException in a function so that the lookup
+		// happens at the time of error handling instead of callback
+		// registration.
+		.catch( function( error ) {
+			jQuery.readyException( error );
+		} );
+
+	return this;
+};
+
+jQuery.extend( {
+
+	// Is the DOM ready to be used? Set to true once it occurs.
+	isReady: false,
+
+	// A counter to track how many items to wait for before
+	// the ready event fires. See #6781
+	readyWait: 1,
+
+	// Handle when the DOM is ready
+	ready: function( wait ) {
+
+		// Abort if there are pending holds or we're already ready
+		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+			return;
+		}
+
+		// Remember that the DOM is ready
+		jQuery.isReady = true;
+
+		// If a normal DOM Ready event fired, decrement, and wait if need be
+		if ( wait !== true && --jQuery.readyWait > 0 ) {
+			return;
+		}
+
+		// If there are functions bound, to execute
+		readyList.resolveWith( document, [ jQuery ] );
+	}
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+	document.removeEventListener( "DOMContentLoaded", completed );
+	window.removeEventListener( "load", completed );
+	jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+	// Handle it asynchronously to allow scripts the opportunity to delay ready
+	window.setTimeout( jQuery.ready );
+
+} else {
+
+	// Use the handy event callback
+	document.addEventListener( "DOMContentLoaded", completed );
+
+	// A fallback to window.onload, that will always work
+	window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+	var i = 0,
+		len = elems.length,
+		bulk = key == null;
+
+	// Sets many values
+	if ( toType( key ) === "object" ) {
+		chainable = true;
+		for ( i in key ) {
+			access( elems, fn, i, key[ i ], true, emptyGet, raw );
+		}
+
+	// Sets one value
+	} else if ( value !== undefined ) {
+		chainable = true;
+
+		if ( !isFunction( value ) ) {
+			raw = true;
+		}
+
+		if ( bulk ) {
+
+			// Bulk operations run against the entire set
+			if ( raw ) {
+				fn.call( elems, value );
+				fn = null;
+
+			// ...except when executing function values
+			} else {
+				bulk = fn;
+				fn = function( elem, _key, value ) {
+					return bulk.call( jQuery( elem ), value );
+				};
+			}
+		}
+
+		if ( fn ) {
+			for ( ; i < len; i++ ) {
+				fn(
+					elems[ i ], key, raw ?
+					value :
+					value.call( elems[ i ], i, fn( elems[ i ], key ) )
+				);
+			}
+		}
+	}
+
+	if ( chainable ) {
+		return elems;
+	}
+
+	// Gets
+	if ( bulk ) {
+		return fn.call( elems );
+	}
+
+	return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+	rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+	return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+	// Accepts only:
+	//  - Node
+	//    - Node.ELEMENT_NODE
+	//    - Node.DOCUMENT_NODE
+	//  - Object
+	//    - Any
+	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+	this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+	cache: function( owner ) {
+
+		// Check if the owner object already has a cache
+		var value = owner[ this.expando ];
+
+		// If not, create one
+		if ( !value ) {
+			value = {};
+
+			// We can accept data for non-element nodes in modern browsers,
+			// but we should not, see #8335.
+			// Always return an empty object.
+			if ( acceptData( owner ) ) {
+
+				// If it is a node unlikely to be stringify-ed or looped over
+				// use plain assignment
+				if ( owner.nodeType ) {
+					owner[ this.expando ] = value;
+
+				// Otherwise secure it in a non-enumerable property
+				// configurable must be true to allow the property to be
+				// deleted when data is removed
+				} else {
+					Object.defineProperty( owner, this.expando, {
+						value: value,
+						configurable: true
+					} );
+				}
+			}
+		}
+
+		return value;
+	},
+	set: function( owner, data, value ) {
+		var prop,
+			cache = this.cache( owner );
+
+		// Handle: [ owner, key, value ] args
+		// Always use camelCase key (gh-2257)
+		if ( typeof data === "string" ) {
+			cache[ camelCase( data ) ] = value;
+
+		// Handle: [ owner, { properties } ] args
+		} else {
+
+			// Copy the properties one-by-one to the cache object
+			for ( prop in data ) {
+				cache[ camelCase( prop ) ] = data[ prop ];
+			}
+		}
+		return cache;
+	},
+	get: function( owner, key ) {
+		return key === undefined ?
+			this.cache( owner ) :
+
+			// Always use camelCase key (gh-2257)
+			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+	},
+	access: function( owner, key, value ) {
+
+		// In cases where either:
+		//
+		//   1. No key was specified
+		//   2. A string key was specified, but no value provided
+		//
+		// Take the "read" path and allow the get method to determine
+		// which value to return, respectively either:
+		//
+		//   1. The entire cache object
+		//   2. The data stored at the key
+		//
+		if ( key === undefined ||
+				( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+			return this.get( owner, key );
+		}
+
+		// When the key is not a string, or both a key and value
+		// are specified, set or extend (existing objects) with either:
+		//
+		//   1. An object of properties
+		//   2. A key and value
+		//
+		this.set( owner, key, value );
+
+		// Since the "set" path can have two possible entry points
+		// return the expected data based on which path was taken[*]
+		return value !== undefined ? value : key;
+	},
+	remove: function( owner, key ) {
+		var i,
+			cache = owner[ this.expando ];
+
+		if ( cache === undefined ) {
+			return;
+		}
+
+		if ( key !== undefined ) {
+
+			// Support array or space separated string of keys
+			if ( Array.isArray( key ) ) {
+
+				// If key is an array of keys...
+				// We always set camelCase keys, so remove that.
+				key = key.map( camelCase );
+			} else {
+				key = camelCase( key );
+
+				// If a key with the spaces exists, use it.
+				// Otherwise, create an array by matching non-whitespace
+				key = key in cache ?
+					[ key ] :
+					( key.match( rnothtmlwhite ) || [] );
+			}
+
+			i = key.length;
+
+			while ( i-- ) {
+				delete cache[ key[ i ] ];
+			}
+		}
+
+		// Remove the expando if there's no more data
+		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+			// Support: Chrome <=35 - 45
+			// Webkit & Blink performance suffers when deleting properties
+			// from DOM nodes, so set to undefined instead
+			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+			if ( owner.nodeType ) {
+				owner[ this.expando ] = undefined;
+			} else {
+				delete owner[ this.expando ];
+			}
+		}
+	},
+	hasData: function( owner ) {
+		var cache = owner[ this.expando ];
+		return cache !== undefined && !jQuery.isEmptyObject( cache );
+	}
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+//	Implementation Summary
+//
+//	1. Enforce API surface and semantic compatibility with 1.9.x branch
+//	2. Improve the module's maintainability by reducing the storage
+//		paths to a single mechanism.
+//	3. Use the same single mechanism to support "private" and "user" data.
+//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+//	5. Avoid exposing implementation details on user objects (eg. expando properties)
+//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+	rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+	if ( data === "true" ) {
+		return true;
+	}
+
+	if ( data === "false" ) {
+		return false;
+	}
+
+	if ( data === "null" ) {
+		return null;
+	}
+
+	// Only convert to a number if it doesn't change the string
+	if ( data === +data + "" ) {
+		return +data;
+	}
+
+	if ( rbrace.test( data ) ) {
+		return JSON.parse( data );
+	}
+
+	return data;
+}
+
+function dataAttr( elem, key, data ) {
+	var name;
+
+	// If nothing was found internally, try to fetch any
+	// data from the HTML5 data-* attribute
+	if ( data === undefined && elem.nodeType === 1 ) {
+		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+		data = elem.getAttribute( name );
+
+		if ( typeof data === "string" ) {
+			try {
+				data = getData( data );
+			} catch ( e ) {}
+
+			// Make sure we set the data so it isn't changed later
+			dataUser.set( elem, key, data );
+		} else {
+			data = undefined;
+		}
+	}
+	return data;
+}
+
+jQuery.extend( {
+	hasData: function( elem ) {
+		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+	},
+
+	data: function( elem, name, data ) {
+		return dataUser.access( elem, name, data );
+	},
+
+	removeData: function( elem, name ) {
+		dataUser.remove( elem, name );
+	},
+
+	// TODO: Now that all calls to _data and _removeData have been replaced
+	// with direct calls to dataPriv methods, these can be deprecated.
+	_data: function( elem, name, data ) {
+		return dataPriv.access( elem, name, data );
+	},
+
+	_removeData: function( elem, name ) {
+		dataPriv.remove( elem, name );
+	}
+} );
+
+jQuery.fn.extend( {
+	data: function( key, value ) {
+		var i, name, data,
+			elem = this[ 0 ],
+			attrs = elem && elem.attributes;
+
+		// Gets all values
+		if ( key === undefined ) {
+			if ( this.length ) {
+				data = dataUser.get( elem );
+
+				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+					i = attrs.length;
+					while ( i-- ) {
+
+						// Support: IE 11 only
+						// The attrs elements can be null (#14894)
+						if ( attrs[ i ] ) {
+							name = attrs[ i ].name;
+							if ( name.indexOf( "data-" ) === 0 ) {
+								name = camelCase( name.slice( 5 ) );
+								dataAttr( elem, name, data[ name ] );
+							}
+						}
+					}
+					dataPriv.set( elem, "hasDataAttrs", true );
+				}
+			}
+
+			return data;
+		}
+
+		// Sets multiple values
+		if ( typeof key === "object" ) {
+			return this.each( function() {
+				dataUser.set( this, key );
+			} );
+		}
+
+		return access( this, function( value ) {
+			var data;
+
+			// The calling jQuery object (element matches) is not empty
+			// (and therefore has an element appears at this[ 0 ]) and the
+			// `value` parameter was not undefined. An empty jQuery object
+			// will result in `undefined` for elem = this[ 0 ] which will
+			// throw an exception if an attempt to read a data cache is made.
+			if ( elem && value === undefined ) {
+
+				// Attempt to get data from the cache
+				// The key will always be camelCased in Data
+				data = dataUser.get( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// Attempt to "discover" the data in
+				// HTML5 custom data-* attrs
+				data = dataAttr( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// We tried really hard, but the data doesn't exist.
+				return;
+			}
+
+			// Set the data...
+			this.each( function() {
+
+				// We always store the camelCased key
+				dataUser.set( this, key, value );
+			} );
+		}, null, value, arguments.length > 1, null, true );
+	},
+
+	removeData: function( key ) {
+		return this.each( function() {
+			dataUser.remove( this, key );
+		} );
+	}
+} );
+
+
+jQuery.extend( {
+	queue: function( elem, type, data ) {
+		var queue;
+
+		if ( elem ) {
+			type = ( type || "fx" ) + "queue";
+			queue = dataPriv.get( elem, type );
+
+			// Speed up dequeue by getting out quickly if this is just a lookup
+			if ( data ) {
+				if ( !queue || Array.isArray( data ) ) {
+					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+				} else {
+					queue.push( data );
+				}
+			}
+			return queue || [];
+		}
+	},
+
+	dequeue: function( elem, type ) {
+		type = type || "fx";
+
+		var queue = jQuery.queue( elem, type ),
+			startLength = queue.length,
+			fn = queue.shift(),
+			hooks = jQuery._queueHooks( elem, type ),
+			next = function() {
+				jQuery.dequeue( elem, type );
+			};
+
+		// If the fx queue is dequeued, always remove the progress sentinel
+		if ( fn === "inprogress" ) {
+			fn = queue.shift();
+			startLength--;
+		}
+
+		if ( fn ) {
+
+			// Add a progress sentinel to prevent the fx queue from being
+			// automatically dequeued
+			if ( type === "fx" ) {
+				queue.unshift( "inprogress" );
+			}
+
+			// Clear up the last queue stop function
+			delete hooks.stop;
+			fn.call( elem, next, hooks );
+		}
+
+		if ( !startLength && hooks ) {
+			hooks.empty.fire();
+		}
+	},
+
+	// Not public - generate a queueHooks object, or return the current one
+	_queueHooks: function( elem, type ) {
+		var key = type + "queueHooks";
+		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+			empty: jQuery.Callbacks( "once memory" ).add( function() {
+				dataPriv.remove( elem, [ type + "queue", key ] );
+			} )
+		} );
+	}
+} );
+
+jQuery.fn.extend( {
+	queue: function( type, data ) {
+		var setter = 2;
+
+		if ( typeof type !== "string" ) {
+			data = type;
+			type = "fx";
+			setter--;
+		}
+
+		if ( arguments.length < setter ) {
+			return jQuery.queue( this[ 0 ], type );
+		}
+
+		return data === undefined ?
+			this :
+			this.each( function() {
+				var queue = jQuery.queue( this, type, data );
+
+				// Ensure a hooks for this queue
+				jQuery._queueHooks( this, type );
+
+				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+					jQuery.dequeue( this, type );
+				}
+			} );
+	},
+	dequeue: function( type ) {
+		return this.each( function() {
+			jQuery.dequeue( this, type );
+		} );
+	},
+	clearQueue: function( type ) {
+		return this.queue( type || "fx", [] );
+	},
+
+	// Get a promise resolved when queues of a certain type
+	// are emptied (fx is the type by default)
+	promise: function( type, obj ) {
+		var tmp,
+			count = 1,
+			defer = jQuery.Deferred(),
+			elements = this,
+			i = this.length,
+			resolve = function() {
+				if ( !( --count ) ) {
+					defer.resolveWith( elements, [ elements ] );
+				}
+			};
+
+		if ( typeof type !== "string" ) {
+			obj = type;
+			type = undefined;
+		}
+		type = type || "fx";
+
+		while ( i-- ) {
+			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+			if ( tmp && tmp.empty ) {
+				count++;
+				tmp.empty.add( resolve );
+			}
+		}
+		resolve();
+		return defer.promise( obj );
+	}
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+	var isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem );
+		},
+		composed = { composed: true };
+
+	// Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+	// Check attachment across shadow DOM boundaries when possible (gh-3504)
+	// Support: iOS 10.0-10.2 only
+	// Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+	// leading to errors. We need to check for `getRootNode`.
+	if ( documentElement.getRootNode ) {
+		isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem ) ||
+				elem.getRootNode( composed ) === elem.ownerDocument;
+		};
+	}
+var isHiddenWithinTree = function( elem, el ) {
+
+		// isHiddenWithinTree might be called from jQuery#filter function;
+		// in that case, element will be second argument
+		elem = el || elem;
+
+		// Inline style trumps all
+		return elem.style.display === "none" ||
+			elem.style.display === "" &&
+
+			// Otherwise, check computed style
+			// Support: Firefox <=43 - 45
+			// Disconnected elements can have computed display: none, so first confirm that elem is
+			// in the document.
+			isAttached( elem ) &&
+
+			jQuery.css( elem, "display" ) === "none";
+	};
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+	var adjusted, scale,
+		maxIterations = 20,
+		currentValue = tween ?
+			function() {
+				return tween.cur();
+			} :
+			function() {
+				return jQuery.css( elem, prop, "" );
+			},
+		initial = currentValue(),
+		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+		// Starting value computation is required for potential unit mismatches
+		initialInUnit = elem.nodeType &&
+			( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+			rcssNum.exec( jQuery.css( elem, prop ) );
+
+	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+		// Support: Firefox <=54
+		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+		initial = initial / 2;
+
+		// Trust units reported by jQuery.css
+		unit = unit || initialInUnit[ 3 ];
+
+		// Iteratively approximate from a nonzero starting point
+		initialInUnit = +initial || 1;
+
+		while ( maxIterations-- ) {
+
+			// Evaluate and update our best guess (doubling guesses that zero out).
+			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+			jQuery.style( elem, prop, initialInUnit + unit );
+			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+				maxIterations = 0;
+			}
+			initialInUnit = initialInUnit / scale;
+
+		}
+
+		initialInUnit = initialInUnit * 2;
+		jQuery.style( elem, prop, initialInUnit + unit );
+
+		// Make sure we update the tween properties later on
+		valueParts = valueParts || [];
+	}
+
+	if ( valueParts ) {
+		initialInUnit = +initialInUnit || +initial || 0;
+
+		// Apply relative offset (+=/-=) if specified
+		adjusted = valueParts[ 1 ] ?
+			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+			+valueParts[ 2 ];
+		if ( tween ) {
+			tween.unit = unit;
+			tween.start = initialInUnit;
+			tween.end = adjusted;
+		}
+	}
+	return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+	var temp,
+		doc = elem.ownerDocument,
+		nodeName = elem.nodeName,
+		display = defaultDisplayMap[ nodeName ];
+
+	if ( display ) {
+		return display;
+	}
+
+	temp = doc.body.appendChild( doc.createElement( nodeName ) );
+	display = jQuery.css( temp, "display" );
+
+	temp.parentNode.removeChild( temp );
+
+	if ( display === "none" ) {
+		display = "block";
+	}
+	defaultDisplayMap[ nodeName ] = display;
+
+	return display;
+}
+
+function showHide( elements, show ) {
+	var display, elem,
+		values = [],
+		index = 0,
+		length = elements.length;
+
+	// Determine new display value for elements that need to change
+	for ( ; index < length; index++ ) {
+		elem = elements[ index ];
+		if ( !elem.style ) {
+			continue;
+		}
+
+		display = elem.style.display;
+		if ( show ) {
+
+			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+			// check is required in this first loop unless we have a nonempty display value (either
+			// inline or about-to-be-restored)
+			if ( display === "none" ) {
+				values[ index ] = dataPriv.get( elem, "display" ) || null;
+				if ( !values[ index ] ) {
+					elem.style.display = "";
+				}
+			}
+			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+				values[ index ] = getDefaultDisplay( elem );
+			}
+		} else {
+			if ( display !== "none" ) {
+				values[ index ] = "none";
+
+				// Remember what we're overwriting
+				dataPriv.set( elem, "display", display );
+			}
+		}
+	}
+
+	// Set the display of the elements in a second loop to avoid constant reflow
+	for ( index = 0; index < length; index++ ) {
+		if ( values[ index ] != null ) {
+			elements[ index ].style.display = values[ index ];
+		}
+	}
+
+	return elements;
+}
+
+jQuery.fn.extend( {
+	show: function() {
+		return showHide( this, true );
+	},
+	hide: function() {
+		return showHide( this );
+	},
+	toggle: function( state ) {
+		if ( typeof state === "boolean" ) {
+			return state ? this.show() : this.hide();
+		}
+
+		return this.each( function() {
+			if ( isHiddenWithinTree( this ) ) {
+				jQuery( this ).show();
+			} else {
+				jQuery( this ).hide();
+			}
+		} );
+	}
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "<textarea>x</textarea>";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+	// Support: IE <=9 only
+	// IE <=9 replaces <option> tags with their contents when inserted outside of
+	// the select element.
+	div.innerHTML = "<option></option>";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+	// XHTML parsers do not magically insert elements in the
+	// same way that tag soup parsers do. So we cannot shorten
+	// this by omitting <tbody> or other required elements.
+	thead: [ 1, "<table>", "</table>" ],
+	col: [ 2, "<table><colgroup>", "</colgroup></table>" ],
+	tr: [ 2, "<table><tbody>", "</tbody></table>" ],
+	td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ],
+
+	_default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
+
+function getAll( context, tag ) {
+
+	// Support: IE <=9 - 11 only
+	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
+	var ret;
+
+	if ( typeof context.getElementsByTagName !== "undefined" ) {
+		ret = context.getElementsByTagName( tag || "*" );
+
+	} else if ( typeof context.querySelectorAll !== "undefined" ) {
+		ret = context.querySelectorAll( tag || "*" );
+
+	} else {
+		ret = [];
+	}
+
+	if ( tag === undefined || tag && nodeName( context, tag ) ) {
+		return jQuery.merge( [ context ], ret );
+	}
+
+	return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+	var i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		dataPriv.set(
+			elems[ i ],
+			"globalEval",
+			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
+		);
+	}
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+	var elem, tmp, tag, wrap, attached, j,
+		fragment = context.createDocumentFragment(),
+		nodes = [],
+		i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		elem = elems[ i ];
+
+		if ( elem || elem === 0 ) {
+
+			// Add nodes directly
+			if ( toType( elem ) === "object" ) {
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+			// Convert non-html into a text node
+			} else if ( !rhtml.test( elem ) ) {
+				nodes.push( context.createTextNode( elem ) );
+
+			// Convert html into DOM nodes
+			} else {
+				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+				// Deserialize a standard representation
+				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+				wrap = wrapMap[ tag ] || wrapMap._default;
+				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+				// Descend through wrappers to the right content
+				j = wrap[ 0 ];
+				while ( j-- ) {
+					tmp = tmp.lastChild;
+				}
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, tmp.childNodes );
+
+				// Remember the top-level container
+				tmp = fragment.firstChild;
+
+				// Ensure the created nodes are orphaned (#12392)
+				tmp.textContent = "";
+			}
+		}
+	}
+
+	// Remove wrapper from fragment
+	fragment.textContent = "";
+
+	i = 0;
+	while ( ( elem = nodes[ i++ ] ) ) {
+
+		// Skip elements already in the context collection (trac-4087)
+		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+			if ( ignored ) {
+				ignored.push( elem );
+			}
+			continue;
+		}
+
+		attached = isAttached( elem );
+
+		// Append to fragment
+		tmp = getAll( fragment.appendChild( elem ), "script" );
+
+		// Preserve script evaluation history
+		if ( attached ) {
+			setGlobalEval( tmp );
+		}
+
+		// Capture executables
+		if ( scripts ) {
+			j = 0;
+			while ( ( elem = tmp[ j++ ] ) ) {
+				if ( rscriptType.test( elem.type || "" ) ) {
+					scripts.push( elem );
+				}
+			}
+		}
+	}
+
+	return fragment;
+}
+
+
+var
+	rkeyEvent = /^key/,
+	rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/,
+	rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+	return true;
+}
+
+function returnFalse() {
+	return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+	return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+	try {
+		return document.activeElement;
+	} catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+	var origFn, type;
+
+	// Types can be a map of types/handlers
+	if ( typeof types === "object" ) {
+
+		// ( types-Object, selector, data )
+		if ( typeof selector !== "string" ) {
+
+			// ( types-Object, data )
+			data = data || selector;
+			selector = undefined;
+		}
+		for ( type in types ) {
+			on( elem, type, selector, data, types[ type ], one );
+		}
+		return elem;
+	}
+
+	if ( data == null && fn == null ) {
+
+		// ( types, fn )
+		fn = selector;
+		data = selector = undefined;
+	} else if ( fn == null ) {
+		if ( typeof selector === "string" ) {
+
+			// ( types, selector, fn )
+			fn = data;
+			data = undefined;
+		} else {
+
+			// ( types, data, fn )
+			fn = data;
+			data = selector;
+			selector = undefined;
+		}
+	}
+	if ( fn === false ) {
+		fn = returnFalse;
+	} else if ( !fn ) {
+		return elem;
+	}
+
+	if ( one === 1 ) {
+		origFn = fn;
+		fn = function( event ) {
+
+			// Can use an empty set, since event contains the info
+			jQuery().off( event );
+			return origFn.apply( this, arguments );
+		};
+
+		// Use same guid so caller can remove using origFn
+		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+	}
+	return elem.each( function() {
+		jQuery.event.add( this, types, fn, data, selector );
+	} );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+	global: {},
+
+	add: function( elem, types, handler, data, selector ) {
+
+		var handleObjIn, eventHandle, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.get( elem );
+
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
+			return;
+		}
+
+		// Caller can pass in an object of custom data in lieu of the handler
+		if ( handler.handler ) {
+			handleObjIn = handler;
+			handler = handleObjIn.handler;
+			selector = handleObjIn.selector;
+		}
+
+		// Ensure that invalid selectors throw exceptions at attach time
+		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
+		if ( selector ) {
+			jQuery.find.matchesSelector( documentElement, selector );
+		}
+
+		// Make sure that the handler has a unique ID, used to find/remove it later
+		if ( !handler.guid ) {
+			handler.guid = jQuery.guid++;
+		}
+
+		// Init the element's event structure and main handler, if this is the first
+		if ( !( events = elemData.events ) ) {
+			events = elemData.events = Object.create( null );
+		}
+		if ( !( eventHandle = elemData.handle ) ) {
+			eventHandle = elemData.handle = function( e ) {
+
+				// Discard the second event of a jQuery.event.trigger() and
+				// when an event is called after a page has unloaded
+				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+			};
+		}
+
+		// Handle multiple events separated by a space
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// There *must* be a type, no attaching namespace-only handlers
+			if ( !type ) {
+				continue;
+			}
+
+			// If event changes its type, use the special event handlers for the changed type
+			special = jQuery.event.special[ type ] || {};
+
+			// If selector defined, determine special event api type, otherwise given type
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+
+			// Update special based on newly reset type
+			special = jQuery.event.special[ type ] || {};
+
+			// handleObj is passed to all event handlers
+			handleObj = jQuery.extend( {
+				type: type,
+				origType: origType,
+				data: data,
+				handler: handler,
+				guid: handler.guid,
+				selector: selector,
+				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+				namespace: namespaces.join( "." )
+			}, handleObjIn );
+
+			// Init the event handler queue if we're the first
+			if ( !( handlers = events[ type ] ) ) {
+				handlers = events[ type ] = [];
+				handlers.delegateCount = 0;
+
+				// Only use addEventListener if the special events handler returns false
+				if ( !special.setup ||
+					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+					if ( elem.addEventListener ) {
+						elem.addEventListener( type, eventHandle );
+					}
+				}
+			}
+
+			if ( special.add ) {
+				special.add.call( elem, handleObj );
+
+				if ( !handleObj.handler.guid ) {
+					handleObj.handler.guid = handler.guid;
+				}
+			}
+
+			// Add to the element's handler list, delegates in front
+			if ( selector ) {
+				handlers.splice( handlers.delegateCount++, 0, handleObj );
+			} else {
+				handlers.push( handleObj );
+			}
+
+			// Keep track of which events have ever been used, for event optimization
+			jQuery.event.global[ type ] = true;
+		}
+
+	},
+
+	// Detach an event or set of events from an element
+	remove: function( elem, types, handler, selector, mappedTypes ) {
+
+		var j, origCount, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+		if ( !elemData || !( events = elemData.events ) ) {
+			return;
+		}
+
+		// Once for each type.namespace in types; type may be omitted
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// Unbind all events (on this namespace, if provided) for the element
+			if ( !type ) {
+				for ( type in events ) {
+					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+				}
+				continue;
+			}
+
+			special = jQuery.event.special[ type ] || {};
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+			handlers = events[ type ] || [];
+			tmp = tmp[ 2 ] &&
+				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+			// Remove matching events
+			origCount = j = handlers.length;
+			while ( j-- ) {
+				handleObj = handlers[ j ];
+
+				if ( ( mappedTypes || origType === handleObj.origType ) &&
+					( !handler || handler.guid === handleObj.guid ) &&
+					( !tmp || tmp.test( handleObj.namespace ) ) &&
+					( !selector || selector === handleObj.selector ||
+						selector === "**" && handleObj.selector ) ) {
+					handlers.splice( j, 1 );
+
+					if ( handleObj.selector ) {
+						handlers.delegateCount--;
+					}
+					if ( special.remove ) {
+						special.remove.call( elem, handleObj );
+					}
+				}
+			}
+
+			// Remove generic event handler if we removed something and no more handlers exist
+			// (avoids potential for endless recursion during removal of special event handlers)
+			if ( origCount && !handlers.length ) {
+				if ( !special.teardown ||
+					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+					jQuery.removeEvent( elem, type, elemData.handle );
+				}
+
+				delete events[ type ];
+			}
+		}
+
+		// Remove data and the expando if it's no longer used
+		if ( jQuery.isEmptyObject( events ) ) {
+			dataPriv.remove( elem, "handle events" );
+		}
+	},
+
+	dispatch: function( nativeEvent ) {
+
+		var i, j, ret, matched, handleObj, handlerQueue,
+			args = new Array( arguments.length ),
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+					dataPriv.get( this, "events" ) || Object.create( null )
+				)[ event.type ] || [],
+			special = jQuery.event.special[ event.type ] || {};
+
+		// Use the fix-ed jQuery.Event rather than the (read-only) native event
+		args[ 0 ] = event;
+
+		for ( i = 1; i < arguments.length; i++ ) {
+			args[ i ] = arguments[ i ];
+		}
+
+		event.delegateTarget = this;
+
+		// Call the preDispatch hook for the mapped type, and let it bail if desired
+		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+			return;
+		}
+
+		// Determine handlers
+		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+		// Run delegates first; they may want to stop propagation beneath us
+		i = 0;
+		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+			event.currentTarget = matched.elem;
+
+			j = 0;
+			while ( ( handleObj = matched.handlers[ j++ ] ) &&
+				!event.isImmediatePropagationStopped() ) {
+
+				// If the event is namespaced, then each handler is only invoked if it is
+				// specially universal or its namespaces are a superset of the event's.
+				if ( !event.rnamespace || handleObj.namespace === false ||
+					event.rnamespace.test( handleObj.namespace ) ) {
+
+					event.handleObj = handleObj;
+					event.data = handleObj.data;
+
+					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+						handleObj.handler ).apply( matched.elem, args );
+
+					if ( ret !== undefined ) {
+						if ( ( event.result = ret ) === false ) {
+							event.preventDefault();
+							event.stopPropagation();
+						}
+					}
+				}
+			}
+		}
+
+		// Call the postDispatch hook for the mapped type
+		if ( special.postDispatch ) {
+			special.postDispatch.call( this, event );
+		}
+
+		return event.result;
+	},
+
+	handlers: function( event, handlers ) {
+		var i, handleObj, sel, matchedHandlers, matchedSelectors,
+			handlerQueue = [],
+			delegateCount = handlers.delegateCount,
+			cur = event.target;
+
+		// Find delegate handlers
+		if ( delegateCount &&
+
+			// Support: IE <=9
+			// Black-hole SVG <use> instance trees (trac-13180)
+			cur.nodeType &&
+
+			// Support: Firefox <=42
+			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+			// Support: IE 11 only
+			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+			!( event.type === "click" && event.button >= 1 ) ) {
+
+			for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+				// Don't check non-elements (#13208)
+				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+					matchedHandlers = [];
+					matchedSelectors = {};
+					for ( i = 0; i < delegateCount; i++ ) {
+						handleObj = handlers[ i ];
+
+						// Don't conflict with Object.prototype properties (#13203)
+						sel = handleObj.selector + " ";
+
+						if ( matchedSelectors[ sel ] === undefined ) {
+							matchedSelectors[ sel ] = handleObj.needsContext ?
+								jQuery( sel, this ).index( cur ) > -1 :
+								jQuery.find( sel, this, null, [ cur ] ).length;
+						}
+						if ( matchedSelectors[ sel ] ) {
+							matchedHandlers.push( handleObj );
+						}
+					}
+					if ( matchedHandlers.length ) {
+						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+					}
+				}
+			}
+		}
+
+		// Add the remaining (directly-bound) handlers
+		cur = this;
+		if ( delegateCount < handlers.length ) {
+			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+		}
+
+		return handlerQueue;
+	},
+
+	addProp: function( name, hook ) {
+		Object.defineProperty( jQuery.Event.prototype, name, {
+			enumerable: true,
+			configurable: true,
+
+			get: isFunction( hook ) ?
+				function() {
+					if ( this.originalEvent ) {
+							return hook( this.originalEvent );
+					}
+				} :
+				function() {
+					if ( this.originalEvent ) {
+							return this.originalEvent[ name ];
+					}
+				},
+
+			set: function( value ) {
+				Object.defineProperty( this, name, {
+					enumerable: true,
+					configurable: true,
+					writable: true,
+					value: value
+				} );
+			}
+		} );
+	},
+
+	fix: function( originalEvent ) {
+		return originalEvent[ jQuery.expando ] ?
+			originalEvent :
+			new jQuery.Event( originalEvent );
+	},
+
+	special: {
+		load: {
+
+			// Prevent triggered image.load events from bubbling to window.load
+			noBubble: true
+		},
+		click: {
+
+			// Utilize native event to ensure correct state for checkable inputs
+			setup: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Claim the first handler
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					// dataPriv.set( el, "click", ... )
+					leverageNative( el, "click", returnTrue );
+				}
+
+				// Return false to allow normal processing in the caller
+				return false;
+			},
+			trigger: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Force setup before triggering a click
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					leverageNative( el, "click" );
+				}
+
+				// Return non-false to allow normal event-path propagation
+				return true;
+			},
+
+			// For cross-browser consistency, suppress native .click() on links
+			// Also prevent it if we're currently inside a leveraged native-event stack
+			_default: function( event ) {
+				var target = event.target;
+				return rcheckableType.test( target.type ) &&
+					target.click && nodeName( target, "input" ) &&
+					dataPriv.get( target, "click" ) ||
+					nodeName( target, "a" );
+			}
+		},
+
+		beforeunload: {
+			postDispatch: function( event ) {
+
+				// Support: Firefox 20+
+				// Firefox doesn't alert if the returnValue field is not set.
+				if ( event.result !== undefined && event.originalEvent ) {
+					event.originalEvent.returnValue = event.result;
+				}
+			}
+		}
+	}
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+	// Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+	if ( !expectSync ) {
+		if ( dataPriv.get( el, type ) === undefined ) {
+			jQuery.event.add( el, type, returnTrue );
+		}
+		return;
+	}
+
+	// Register the controller as a special universal handler for all event namespaces
+	dataPriv.set( el, type, false );
+	jQuery.event.add( el, type, {
+		namespace: false,
+		handler: function( event ) {
+			var notAsync, result,
+				saved = dataPriv.get( this, type );
+
+			if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+				// Interrupt processing of the outer synthetic .trigger()ed event
+				// Saved data should be false in such cases, but might be a leftover capture object
+				// from an async native handler (gh-4350)
+				if ( !saved.length ) {
+
+					// Store arguments for use when handling the inner native event
+					// There will always be at least one argument (an event object), so this array
+					// will not be confused with a leftover capture object.
+					saved = slice.call( arguments );
+					dataPriv.set( this, type, saved );
+
+					// Trigger the native event and capture its result
+					// Support: IE <=9 - 11+
+					// focus() and blur() are asynchronous
+					notAsync = expectSync( this, type );
+					this[ type ]();
+					result = dataPriv.get( this, type );
+					if ( saved !== result || notAsync ) {
+						dataPriv.set( this, type, false );
+					} else {
+						result = {};
+					}
+					if ( saved !== result ) {
+
+						// Cancel the outer synthetic event
+						event.stopImmediatePropagation();
+						event.preventDefault();
+						return result.value;
+					}
+
+				// If this is an inner synthetic event for an event with a bubbling surrogate
+				// (focus or blur), assume that the surrogate already propagated from triggering the
+				// native event and prevent that from happening again here.
+				// This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+				// bubbling surrogate propagates *after* the non-bubbling base), but that seems
+				// less bad than duplication.
+				} else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+					event.stopPropagation();
+				}
+
+			// If this is a native event triggered above, everything is now in order
+			// Fire an inner synthetic event with the original arguments
+			} else if ( saved.length ) {
+
+				// ...and capture the result
+				dataPriv.set( this, type, {
+					value: jQuery.event.trigger(
+
+						// Support: IE <=9 - 11+
+						// Extend with the prototype to reset the above stopImmediatePropagation()
+						jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+						saved.slice( 1 ),
+						this
+					)
+				} );
+
+				// Abort handling of the native event
+				event.stopImmediatePropagation();
+			}
+		}
+	} );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+	// This "if" is needed for plain objects
+	if ( elem.removeEventListener ) {
+		elem.removeEventListener( type, handle );
+	}
+};
+
+jQuery.Event = function( src, props ) {
+
+	// Allow instantiation without the 'new' keyword
+	if ( !( this instanceof jQuery.Event ) ) {
+		return new jQuery.Event( src, props );
+	}
+
+	// Event object
+	if ( src && src.type ) {
+		this.originalEvent = src;
+		this.type = src.type;
+
+		// Events bubbling up the document may have been marked as prevented
+		// by a handler lower down the tree; reflect the correct value.
+		this.isDefaultPrevented = src.defaultPrevented ||
+				src.defaultPrevented === undefined &&
+
+				// Support: Android <=2.3 only
+				src.returnValue === false ?
+			returnTrue :
+			returnFalse;
+
+		// Create target properties
+		// Support: Safari <=6 - 7 only
+		// Target should not be a text node (#504, #13143)
+		this.target = ( src.target && src.target.nodeType === 3 ) ?
+			src.target.parentNode :
+			src.target;
+
+		this.currentTarget = src.currentTarget;
+		this.relatedTarget = src.relatedTarget;
+
+	// Event type
+	} else {
+		this.type = src;
+	}
+
+	// Put explicitly provided properties onto the event object
+	if ( props ) {
+		jQuery.extend( this, props );
+	}
+
+	// Create a timestamp if incoming event doesn't have one
+	this.timeStamp = src && src.timeStamp || Date.now();
+
+	// Mark it as fixed
+	this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+	constructor: jQuery.Event,
+	isDefaultPrevented: returnFalse,
+	isPropagationStopped: returnFalse,
+	isImmediatePropagationStopped: returnFalse,
+	isSimulated: false,
+
+	preventDefault: function() {
+		var e = this.originalEvent;
+
+		this.isDefaultPrevented = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.preventDefault();
+		}
+	},
+	stopPropagation: function() {
+		var e = this.originalEvent;
+
+		this.isPropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopPropagation();
+		}
+	},
+	stopImmediatePropagation: function() {
+		var e = this.originalEvent;
+
+		this.isImmediatePropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopImmediatePropagation();
+		}
+
+		this.stopPropagation();
+	}
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+	altKey: true,
+	bubbles: true,
+	cancelable: true,
+	changedTouches: true,
+	ctrlKey: true,
+	detail: true,
+	eventPhase: true,
+	metaKey: true,
+	pageX: true,
+	pageY: true,
+	shiftKey: true,
+	view: true,
+	"char": true,
+	code: true,
+	charCode: true,
+	key: true,
+	keyCode: true,
+	button: true,
+	buttons: true,
+	clientX: true,
+	clientY: true,
+	offsetX: true,
+	offsetY: true,
+	pointerId: true,
+	pointerType: true,
+	screenX: true,
+	screenY: true,
+	targetTouches: true,
+	toElement: true,
+	touches: true,
+
+	which: function( event ) {
+		var button = event.button;
+
+		// Add which for key events
+		if ( event.which == null && rkeyEvent.test( event.type ) ) {
+			return event.charCode != null ? event.charCode : event.keyCode;
+		}
+
+		// Add which for click: 1 === left; 2 === middle; 3 === right
+		if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) {
+			if ( button & 1 ) {
+				return 1;
+			}
+
+			if ( button & 2 ) {
+				return 3;
+			}
+
+			if ( button & 4 ) {
+				return 2;
+			}
+
+			return 0;
+		}
+
+		return event.which;
+	}
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+	jQuery.event.special[ type ] = {
+
+		// Utilize native event if possible so blur/focus sequence is correct
+		setup: function() {
+
+			// Claim the first handler
+			// dataPriv.set( this, "focus", ... )
+			// dataPriv.set( this, "blur", ... )
+			leverageNative( this, type, expectSync );
+
+			// Return false to allow normal processing in the caller
+			return false;
+		},
+		trigger: function() {
+
+			// Force setup before trigger
+			leverageNative( this, type );
+
+			// Return non-false to allow normal event-path propagation
+			return true;
+		},
+
+		delegateType: delegateType
+	};
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+	mouseenter: "mouseover",
+	mouseleave: "mouseout",
+	pointerenter: "pointerover",
+	pointerleave: "pointerout"
+}, function( orig, fix ) {
+	jQuery.event.special[ orig ] = {
+		delegateType: fix,
+		bindType: fix,
+
+		handle: function( event ) {
+			var ret,
+				target = this,
+				related = event.relatedTarget,
+				handleObj = event.handleObj;
+
+			// For mouseenter/leave call the handler if related is outside the target.
+			// NB: No relatedTarget if the mouse left/entered the browser window
+			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+				event.type = handleObj.origType;
+				ret = handleObj.handler.apply( this, arguments );
+				event.type = fix;
+			}
+			return ret;
+		}
+	};
+} );
+
+jQuery.fn.extend( {
+
+	on: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn );
+	},
+	one: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn, 1 );
+	},
+	off: function( types, selector, fn ) {
+		var handleObj, type;
+		if ( types && types.preventDefault && types.handleObj ) {
+
+			// ( event )  dispatched jQuery.Event
+			handleObj = types.handleObj;
+			jQuery( types.delegateTarget ).off(
+				handleObj.namespace ?
+					handleObj.origType + "." + handleObj.namespace :
+					handleObj.origType,
+				handleObj.selector,
+				handleObj.handler
+			);
+			return this;
+		}
+		if ( typeof types === "object" ) {
+
+			// ( types-object [, selector] )
+			for ( type in types ) {
+				this.off( type, selector, types[ type ] );
+			}
+			return this;
+		}
+		if ( selector === false || typeof selector === "function" ) {
+
+			// ( types [, fn] )
+			fn = selector;
+			selector = undefined;
+		}
+		if ( fn === false ) {
+			fn = returnFalse;
+		}
+		return this.each( function() {
+			jQuery.event.remove( this, types, fn, selector );
+		} );
+	}
+} );
+
+
+var
+
+	// Support: IE <=10 - 11, Edge 12 - 13 only
+	// In IE/Edge using regex groups here causes severe slowdowns.
+	// See https://connect.microsoft.com/IE/feedback/details/1736512/
+	rnoInnerhtml = /<script|<style|<link/i,
+
+	// checked="checked" or checked
+	rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i,
+	rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+	if ( nodeName( elem, "table" ) &&
+		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+	}
+
+	return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+	return elem;
+}
+function restoreScript( elem ) {
+	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+		elem.type = elem.type.slice( 5 );
+	} else {
+		elem.removeAttribute( "type" );
+	}
+
+	return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+	var i, l, type, pdataOld, udataOld, udataCur, events;
+
+	if ( dest.nodeType !== 1 ) {
+		return;
+	}
+
+	// 1. Copy private data: events, handlers, etc.
+	if ( dataPriv.hasData( src ) ) {
+		pdataOld = dataPriv.get( src );
+		events = pdataOld.events;
+
+		if ( events ) {
+			dataPriv.remove( dest, "handle events" );
+
+			for ( type in events ) {
+				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+					jQuery.event.add( dest, type, events[ type ][ i ] );
+				}
+			}
+		}
+	}
+
+	// 2. Copy user data
+	if ( dataUser.hasData( src ) ) {
+		udataOld = dataUser.access( src );
+		udataCur = jQuery.extend( {}, udataOld );
+
+		dataUser.set( dest, udataCur );
+	}
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+	var nodeName = dest.nodeName.toLowerCase();
+
+	// Fails to persist the checked state of a cloned checkbox or radio button.
+	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+		dest.checked = src.checked;
+
+	// Fails to return the selected option to the default selected state when cloning options
+	} else if ( nodeName === "input" || nodeName === "textarea" ) {
+		dest.defaultValue = src.defaultValue;
+	}
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+	// Flatten any nested arrays
+	args = flat( args );
+
+	var fragment, first, scripts, hasScripts, node, doc,
+		i = 0,
+		l = collection.length,
+		iNoClone = l - 1,
+		value = args[ 0 ],
+		valueIsFunction = isFunction( value );
+
+	// We can't cloneNode fragments that contain checked, in WebKit
+	if ( valueIsFunction ||
+			( l > 1 && typeof value === "string" &&
+				!support.checkClone && rchecked.test( value ) ) ) {
+		return collection.each( function( index ) {
+			var self = collection.eq( index );
+			if ( valueIsFunction ) {
+				args[ 0 ] = value.call( this, index, self.html() );
+			}
+			domManip( self, args, callback, ignored );
+		} );
+	}
+
+	if ( l ) {
+		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+		first = fragment.firstChild;
+
+		if ( fragment.childNodes.length === 1 ) {
+			fragment = first;
+		}
+
+		// Require either new content or an interest in ignored elements to invoke the callback
+		if ( first || ignored ) {
+			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+			hasScripts = scripts.length;
+
+			// Use the original fragment for the last item
+			// instead of the first because it can end up
+			// being emptied incorrectly in certain situations (#8070).
+			for ( ; i < l; i++ ) {
+				node = fragment;
+
+				if ( i !== iNoClone ) {
+					node = jQuery.clone( node, true, true );
+
+					// Keep references to cloned scripts for later restoration
+					if ( hasScripts ) {
+
+						// Support: Android <=4.0 only, PhantomJS 1 only
+						// push.apply(_, arraylike) throws on ancient WebKit
+						jQuery.merge( scripts, getAll( node, "script" ) );
+					}
+				}
+
+				callback.call( collection[ i ], node, i );
+			}
+
+			if ( hasScripts ) {
+				doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+				// Reenable scripts
+				jQuery.map( scripts, restoreScript );
+
+				// Evaluate executable scripts on first document insertion
+				for ( i = 0; i < hasScripts; i++ ) {
+					node = scripts[ i ];
+					if ( rscriptType.test( node.type || "" ) &&
+						!dataPriv.access( node, "globalEval" ) &&
+						jQuery.contains( doc, node ) ) {
+
+						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
+
+							// Optional AJAX dependency, but won't run scripts if not present
+							if ( jQuery._evalUrl && !node.noModule ) {
+								jQuery._evalUrl( node.src, {
+									nonce: node.nonce || node.getAttribute( "nonce" )
+								}, doc );
+							}
+						} else {
+							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return collection;
+}
+
+function remove( elem, selector, keepData ) {
+	var node,
+		nodes = selector ? jQuery.filter( selector, elem ) : elem,
+		i = 0;
+
+	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+		if ( !keepData && node.nodeType === 1 ) {
+			jQuery.cleanData( getAll( node ) );
+		}
+
+		if ( node.parentNode ) {
+			if ( keepData && isAttached( node ) ) {
+				setGlobalEval( getAll( node, "script" ) );
+			}
+			node.parentNode.removeChild( node );
+		}
+	}
+
+	return elem;
+}
+
+jQuery.extend( {
+	htmlPrefilter: function( html ) {
+		return html;
+	},
+
+	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+		var i, l, srcElements, destElements,
+			clone = elem.cloneNode( true ),
+			inPage = isAttached( elem );
+
+		// Fix IE cloning issues
+		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+				!jQuery.isXMLDoc( elem ) ) {
+
+			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+			destElements = getAll( clone );
+			srcElements = getAll( elem );
+
+			for ( i = 0, l = srcElements.length; i < l; i++ ) {
+				fixInput( srcElements[ i ], destElements[ i ] );
+			}
+		}
+
+		// Copy the events from the original to the clone
+		if ( dataAndEvents ) {
+			if ( deepDataAndEvents ) {
+				srcElements = srcElements || getAll( elem );
+				destElements = destElements || getAll( clone );
+
+				for ( i = 0, l = srcElements.length; i < l; i++ ) {
+					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+				}
+			} else {
+				cloneCopyEvent( elem, clone );
+			}
+		}
+
+		// Preserve script evaluation history
+		destElements = getAll( clone, "script" );
+		if ( destElements.length > 0 ) {
+			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+		}
+
+		// Return the cloned set
+		return clone;
+	},
+
+	cleanData: function( elems ) {
+		var data, elem, type,
+			special = jQuery.event.special,
+			i = 0;
+
+		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+			if ( acceptData( elem ) ) {
+				if ( ( data = elem[ dataPriv.expando ] ) ) {
+					if ( data.events ) {
+						for ( type in data.events ) {
+							if ( special[ type ] ) {
+								jQuery.event.remove( elem, type );
+
+							// This is a shortcut to avoid jQuery.event.remove's overhead
+							} else {
+								jQuery.removeEvent( elem, type, data.handle );
+							}
+						}
+					}
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataPriv.expando ] = undefined;
+				}
+				if ( elem[ dataUser.expando ] ) {
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataUser.expando ] = undefined;
+				}
+			}
+		}
+	}
+} );
+
+jQuery.fn.extend( {
+	detach: function( selector ) {
+		return remove( this, selector, true );
+	},
+
+	remove: function( selector ) {
+		return remove( this, selector );
+	},
+
+	text: function( value ) {
+		return access( this, function( value ) {
+			return value === undefined ?
+				jQuery.text( this ) :
+				this.empty().each( function() {
+					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+						this.textContent = value;
+					}
+				} );
+		}, null, value, arguments.length );
+	},
+
+	append: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.appendChild( elem );
+			}
+		} );
+	},
+
+	prepend: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.insertBefore( elem, target.firstChild );
+			}
+		} );
+	},
+
+	before: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this );
+			}
+		} );
+	},
+
+	after: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this.nextSibling );
+			}
+		} );
+	},
+
+	empty: function() {
+		var elem,
+			i = 0;
+
+		for ( ; ( elem = this[ i ] ) != null; i++ ) {
+			if ( elem.nodeType === 1 ) {
+
+				// Prevent memory leaks
+				jQuery.cleanData( getAll( elem, false ) );
+
+				// Remove any remaining nodes
+				elem.textContent = "";
+			}
+		}
+
+		return this;
+	},
+
+	clone: function( dataAndEvents, deepDataAndEvents ) {
+		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+		return this.map( function() {
+			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+		} );
+	},
+
+	html: function( value ) {
+		return access( this, function( value ) {
+			var elem = this[ 0 ] || {},
+				i = 0,
+				l = this.length;
+
+			if ( value === undefined && elem.nodeType === 1 ) {
+				return elem.innerHTML;
+			}
+
+			// See if we can take a shortcut and just use innerHTML
+			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+				value = jQuery.htmlPrefilter( value );
+
+				try {
+					for ( ; i < l; i++ ) {
+						elem = this[ i ] || {};
+
+						// Remove element nodes and prevent memory leaks
+						if ( elem.nodeType === 1 ) {
+							jQuery.cleanData( getAll( elem, false ) );
+							elem.innerHTML = value;
+						}
+					}
+
+					elem = 0;
+
+				// If using innerHTML throws an exception, use the fallback method
+				} catch ( e ) {}
+			}
+
+			if ( elem ) {
+				this.empty().append( value );
+			}
+		}, null, value, arguments.length );
+	},
+
+	replaceWith: function() {
+		var ignored = [];
+
+		// Make the changes, replacing each non-ignored context element with the new content
+		return domManip( this, arguments, function( elem ) {
+			var parent = this.parentNode;
+
+			if ( jQuery.inArray( this, ignored ) < 0 ) {
+				jQuery.cleanData( getAll( this ) );
+				if ( parent ) {
+					parent.replaceChild( elem, this );
+				}
+			}
+
+		// Force callback invocation
+		}, ignored );
+	}
+} );
+
+jQuery.each( {
+	appendTo: "append",
+	prependTo: "prepend",
+	insertBefore: "before",
+	insertAfter: "after",
+	replaceAll: "replaceWith"
+}, function( name, original ) {
+	jQuery.fn[ name ] = function( selector ) {
+		var elems,
+			ret = [],
+			insert = jQuery( selector ),
+			last = insert.length - 1,
+			i = 0;
+
+		for ( ; i <= last; i++ ) {
+			elems = i === last ? this : this.clone( true );
+			jQuery( insert[ i ] )[ original ]( elems );
+
+			// Support: Android <=4.0 only, PhantomJS 1 only
+			// .get() because push.apply(_, arraylike) throws on ancient WebKit
+			push.apply( ret, elems.get() );
+		}
+
+		return this.pushStack( ret );
+	};
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+		// IE throws on elements created in popups
+		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+		var view = elem.ownerDocument.defaultView;
+
+		if ( !view || !view.opener ) {
+			view = window;
+		}
+
+		return view.getComputedStyle( elem );
+	};
+
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+	// Executing both pixelPosition & boxSizingReliable tests require only one layout
+	// so they're executed at the same time to save the second computation.
+	function computeStyleTests() {
+
+		// This is a singleton, we need to execute it only once
+		if ( !div ) {
+			return;
+		}
+
+		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+			"margin-top:1px;padding:0;border:0";
+		div.style.cssText =
+			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+			"margin:auto;border:1px;padding:1px;" +
+			"width:60%;top:1%";
+		documentElement.appendChild( container ).appendChild( div );
+
+		var divStyle = window.getComputedStyle( div );
+		pixelPositionVal = divStyle.top !== "1%";
+
+		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+		// Some styles come back with percentage values, even though they shouldn't
+		div.style.right = "60%";
+		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+		// Support: IE 9 - 11 only
+		// Detect misreporting of content dimensions for box-sizing:border-box elements
+		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+		// Support: IE 9 only
+		// Detect overflow:scroll screwiness (gh-3699)
+		// Support: Chrome <=64
+		// Don't get tricked when zoom affects offsetWidth (gh-4029)
+		div.style.position = "absolute";
+		scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+		documentElement.removeChild( container );
+
+		// Nullify the div so it wouldn't be stored in the memory and
+		// it will also be a sign that checks already performed
+		div = null;
+	}
+
+	function roundPixelMeasures( measure ) {
+		return Math.round( parseFloat( measure ) );
+	}
+
+	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
+		container = document.createElement( "div" ),
+		div = document.createElement( "div" );
+
+	// Finish early in limited (non-browser) environments
+	if ( !div.style ) {
+		return;
+	}
+
+	// Support: IE <=9 - 11 only
+	// Style of cloned element affects source element cloned (#8908)
+	div.style.backgroundClip = "content-box";
+	div.cloneNode( true ).style.backgroundClip = "";
+	support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+	jQuery.extend( support, {
+		boxSizingReliable: function() {
+			computeStyleTests();
+			return boxSizingReliableVal;
+		},
+		pixelBoxStyles: function() {
+			computeStyleTests();
+			return pixelBoxStylesVal;
+		},
+		pixelPosition: function() {
+			computeStyleTests();
+			return pixelPositionVal;
+		},
+		reliableMarginLeft: function() {
+			computeStyleTests();
+			return reliableMarginLeftVal;
+		},
+		scrollboxSize: function() {
+			computeStyleTests();
+			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px";
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = parseInt( trStyle.height ) > 3;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
+		}
+	} );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+	var width, minWidth, maxWidth, ret,
+
+		// Support: Firefox 51+
+		// Retrieving style before computed somehow
+		// fixes an issue with getting wrong values
+		// on detached elements
+		style = elem.style;
+
+	computed = computed || getStyles( elem );
+
+	// getPropertyValue is needed for:
+	//   .css('filter') (IE 9 only, #12537)
+	//   .css('--customProperty) (#3144)
+	if ( computed ) {
+		ret = computed.getPropertyValue( name ) || computed[ name ];
+
+		if ( ret === "" && !isAttached( elem ) ) {
+			ret = jQuery.style( elem, name );
+		}
+
+		// A tribute to the "awesome hack by Dean Edwards"
+		// Android Browser returns percentage for some values,
+		// but width seems to be reliably pixels.
+		// This is against the CSSOM draft spec:
+		// https://drafts.csswg.org/cssom/#resolved-values
+		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+			// Remember the original values
+			width = style.width;
+			minWidth = style.minWidth;
+			maxWidth = style.maxWidth;
+
+			// Put in the new values to get a computed value out
+			style.minWidth = style.maxWidth = style.width = ret;
+			ret = computed.width;
+
+			// Revert the changed values
+			style.width = width;
+			style.minWidth = minWidth;
+			style.maxWidth = maxWidth;
+		}
+	}
+
+	return ret !== undefined ?
+
+		// Support: IE <=9 - 11 only
+		// IE returns zIndex value as an integer.
+		ret + "" :
+		ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+	// Define the hook, we'll check on the first run if it's really needed.
+	return {
+		get: function() {
+			if ( conditionFn() ) {
+
+				// Hook not needed (or it's not possible to use it due
+				// to missing dependency), remove it.
+				delete this.get;
+				return;
+			}
+
+			// Hook needed; redefine it so that the support test is not executed again.
+			return ( this.get = hookFn ).apply( this, arguments );
+		}
+	};
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+	emptyStyle = document.createElement( "div" ).style,
+	vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+	// Check for vendor prefixed names
+	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+		i = cssPrefixes.length;
+
+	while ( i-- ) {
+		name = cssPrefixes[ i ] + capName;
+		if ( name in emptyStyle ) {
+			return name;
+		}
+	}
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+	var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+	if ( final ) {
+		return final;
+	}
+	if ( name in emptyStyle ) {
+		return name;
+	}
+	return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+	// Swappable if display is none or starts with table
+	// except "table", "table-cell", or "table-caption"
+	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+	rcustomProp = /^--/,
+	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+	cssNormalTransform = {
+		letterSpacing: "0",
+		fontWeight: "400"
+	};
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+	// Any relative (+/-) values have already been
+	// normalized at this point
+	var matches = rcssNum.exec( value );
+	return matches ?
+
+		// Guard against undefined "subtract", e.g., when used as in cssHooks
+		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+		value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+	var i = dimension === "width" ? 1 : 0,
+		extra = 0,
+		delta = 0;
+
+	// Adjustment may not be necessary
+	if ( box === ( isBorderBox ? "border" : "content" ) ) {
+		return 0;
+	}
+
+	for ( ; i < 4; i += 2 ) {
+
+		// Both box models exclude margin
+		if ( box === "margin" ) {
+			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+		}
+
+		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+		if ( !isBorderBox ) {
+
+			// Add padding
+			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+			// For "border" or "margin", add border
+			if ( box !== "padding" ) {
+				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+			// But still keep track of it otherwise
+			} else {
+				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+
+		// If we get here with a border-box (content + padding + border), we're seeking "content" or
+		// "padding" or "margin"
+		} else {
+
+			// For "content", subtract padding
+			if ( box === "content" ) {
+				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+			}
+
+			// For "content" or "padding", subtract border
+			if ( box !== "margin" ) {
+				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+		}
+	}
+
+	// Account for positive content-box scroll gutter when requested by providing computedVal
+	if ( !isBorderBox && computedVal >= 0 ) {
+
+		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+		// Assuming integer scroll gutter, subtract the rest and round down
+		delta += Math.max( 0, Math.ceil(
+			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+			computedVal -
+			delta -
+			extra -
+			0.5
+
+		// If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+		// Use an explicit zero to avoid NaN (gh-3964)
+		) ) || 0;
+	}
+
+	return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+	// Start with computed style
+	var styles = getStyles( elem ),
+
+		// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+		// Fake content-box until we know it's needed to know the true value.
+		boxSizingNeeded = !support.boxSizingReliable() || extra,
+		isBorderBox = boxSizingNeeded &&
+			jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+		valueIsBorderBox = isBorderBox,
+
+		val = curCSS( elem, dimension, styles ),
+		offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+	// Support: Firefox <=54
+	// Return a confounding non-pixel value or feign ignorance, as appropriate.
+	if ( rnumnonpx.test( val ) ) {
+		if ( !extra ) {
+			return val;
+		}
+		val = "auto";
+	}
+
+
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
+	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
+		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
+		elem.getClientRects().length ) {
+
+		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+		// Where available, offsetWidth/offsetHeight approximate border box dimensions.
+		// Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+		// retrieved value as a content box dimension.
+		valueIsBorderBox = offsetProp in elem;
+		if ( valueIsBorderBox ) {
+			val = elem[ offsetProp ];
+		}
+	}
+
+	// Normalize "" and auto
+	val = parseFloat( val ) || 0;
+
+	// Adjust for the element's box model
+	return ( val +
+		boxModelAdjustment(
+			elem,
+			dimension,
+			extra || ( isBorderBox ? "border" : "content" ),
+			valueIsBorderBox,
+			styles,
+
+			// Provide the current computed size to request scroll gutter calculation (gh-3589)
+			val
+		)
+	) + "px";
+}
+
+jQuery.extend( {
+
+	// Add in style property hooks for overriding the default
+	// behavior of getting and setting a style property
+	cssHooks: {
+		opacity: {
+			get: function( elem, computed ) {
+				if ( computed ) {
+
+					// We should always get a number back from opacity
+					var ret = curCSS( elem, "opacity" );
+					return ret === "" ? "1" : ret;
+				}
+			}
+		}
+	},
+
+	// Don't automatically add "px" to these possibly-unitless properties
+	cssNumber: {
+		"animationIterationCount": true,
+		"columnCount": true,
+		"fillOpacity": true,
+		"flexGrow": true,
+		"flexShrink": true,
+		"fontWeight": true,
+		"gridArea": true,
+		"gridColumn": true,
+		"gridColumnEnd": true,
+		"gridColumnStart": true,
+		"gridRow": true,
+		"gridRowEnd": true,
+		"gridRowStart": true,
+		"lineHeight": true,
+		"opacity": true,
+		"order": true,
+		"orphans": true,
+		"widows": true,
+		"zIndex": true,
+		"zoom": true
+	},
+
+	// Add in properties whose names you wish to fix before
+	// setting or getting the value
+	cssProps: {},
+
+	// Get and set the style property on a DOM Node
+	style: function( elem, name, value, extra ) {
+
+		// Don't set styles on text and comment nodes
+		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+			return;
+		}
+
+		// Make sure that we're working with the right name
+		var ret, type, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name ),
+			style = elem.style;
+
+		// Make sure that we're working with the right name. We don't
+		// want to query the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Gets hook for the prefixed version, then unprefixed version
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// Check if we're setting a value
+		if ( value !== undefined ) {
+			type = typeof value;
+
+			// Convert "+=" or "-=" to relative numbers (#7345)
+			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+				value = adjustCSS( elem, name, ret );
+
+				// Fixes bug #9237
+				type = "number";
+			}
+
+			// Make sure that null and NaN values aren't set (#7116)
+			if ( value == null || value !== value ) {
+				return;
+			}
+
+			// If a number was passed in, add the unit (except for certain CSS properties)
+			// The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+			// "px" to a few hardcoded values.
+			if ( type === "number" && !isCustomProp ) {
+				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+			}
+
+			// background-* props affect original clone's values
+			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+				style[ name ] = "inherit";
+			}
+
+			// If a hook was provided, use that value, otherwise just set the specified value
+			if ( !hooks || !( "set" in hooks ) ||
+				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+				if ( isCustomProp ) {
+					style.setProperty( name, value );
+				} else {
+					style[ name ] = value;
+				}
+			}
+
+		} else {
+
+			// If a hook was provided get the non-computed value from there
+			if ( hooks && "get" in hooks &&
+				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+				return ret;
+			}
+
+			// Otherwise just get the value from the style object
+			return style[ name ];
+		}
+	},
+
+	css: function( elem, name, extra, styles ) {
+		var val, num, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name );
+
+		// Make sure that we're working with the right name. We don't
+		// want to modify the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Try prefixed name followed by the unprefixed name
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// If a hook was provided get the computed value from there
+		if ( hooks && "get" in hooks ) {
+			val = hooks.get( elem, true, extra );
+		}
+
+		// Otherwise, if a way to get the computed value exists, use that
+		if ( val === undefined ) {
+			val = curCSS( elem, name, styles );
+		}
+
+		// Convert "normal" to computed value
+		if ( val === "normal" && name in cssNormalTransform ) {
+			val = cssNormalTransform[ name ];
+		}
+
+		// Make numeric if forced or a qualifier was provided and val looks numeric
+		if ( extra === "" || extra ) {
+			num = parseFloat( val );
+			return extra === true || isFinite( num ) ? num || 0 : val;
+		}
+
+		return val;
+	}
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+	jQuery.cssHooks[ dimension ] = {
+		get: function( elem, computed, extra ) {
+			if ( computed ) {
+
+				// Certain elements can have dimension info if we invisibly show them
+				// but it must have a current display style that would benefit
+				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+					// Support: Safari 8+
+					// Table columns in Safari have non-zero offsetWidth & zero
+					// getBoundingClientRect().width unless display is changed.
+					// Support: IE <=11 only
+					// Running getBoundingClientRect on a disconnected node
+					// in IE throws an error.
+					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+						swap( elem, cssShow, function() {
+							return getWidthOrHeight( elem, dimension, extra );
+						} ) :
+						getWidthOrHeight( elem, dimension, extra );
+			}
+		},
+
+		set: function( elem, value, extra ) {
+			var matches,
+				styles = getStyles( elem ),
+
+				// Only read styles.position if the test has a chance to fail
+				// to avoid forcing a reflow.
+				scrollboxSizeBuggy = !support.scrollboxSize() &&
+					styles.position === "absolute",
+
+				// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+				boxSizingNeeded = scrollboxSizeBuggy || extra,
+				isBorderBox = boxSizingNeeded &&
+					jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+				subtract = extra ?
+					boxModelAdjustment(
+						elem,
+						dimension,
+						extra,
+						isBorderBox,
+						styles
+					) :
+					0;
+
+			// Account for unreliable border-box dimensions by comparing offset* to computed and
+			// faking a content-box to get border and padding (gh-3699)
+			if ( isBorderBox && scrollboxSizeBuggy ) {
+				subtract -= Math.ceil(
+					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+					parseFloat( styles[ dimension ] ) -
+					boxModelAdjustment( elem, dimension, "border", false, styles ) -
+					0.5
+				);
+			}
+
+			// Convert to pixels if value adjustment is needed
+			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+				( matches[ 3 ] || "px" ) !== "px" ) {
+
+				elem.style[ dimension ] = value;
+				value = jQuery.css( elem, dimension );
+			}
+
+			return setPositiveNumber( elem, value, subtract );
+		}
+	};
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+	function( elem, computed ) {
+		if ( computed ) {
+			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+				elem.getBoundingClientRect().left -
+					swap( elem, { marginLeft: 0 }, function() {
+						return elem.getBoundingClientRect().left;
+					} )
+				) + "px";
+		}
+	}
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+	margin: "",
+	padding: "",
+	border: "Width"
+}, function( prefix, suffix ) {
+	jQuery.cssHooks[ prefix + suffix ] = {
+		expand: function( value ) {
+			var i = 0,
+				expanded = {},
+
+				// Assumes a single number if not a string
+				parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+			for ( ; i < 4; i++ ) {
+				expanded[ prefix + cssExpand[ i ] + suffix ] =
+					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+			}
+
+			return expanded;
+		}
+	};
+
+	if ( prefix !== "margin" ) {
+		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+	}
+} );
+
+jQuery.fn.extend( {
+	css: function( name, value ) {
+		return access( this, function( elem, name, value ) {
+			var styles, len,
+				map = {},
+				i = 0;
+
+			if ( Array.isArray( name ) ) {
+				styles = getStyles( elem );
+				len = name.length;
+
+				for ( ; i < len; i++ ) {
+					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+				}
+
+				return map;
+			}
+
+			return value !== undefined ?
+				jQuery.style( elem, name, value ) :
+				jQuery.css( elem, name );
+		}, name, value, arguments.length > 1 );
+	}
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+	return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+	constructor: Tween,
+	init: function( elem, options, prop, end, easing, unit ) {
+		this.elem = elem;
+		this.prop = prop;
+		this.easing = easing || jQuery.easing._default;
+		this.options = options;
+		this.start = this.now = this.cur();
+		this.end = end;
+		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+	},
+	cur: function() {
+		var hooks = Tween.propHooks[ this.prop ];
+
+		return hooks && hooks.get ?
+			hooks.get( this ) :
+			Tween.propHooks._default.get( this );
+	},
+	run: function( percent ) {
+		var eased,
+			hooks = Tween.propHooks[ this.prop ];
+
+		if ( this.options.duration ) {
+			this.pos = eased = jQuery.easing[ this.easing ](
+				percent, this.options.duration * percent, 0, 1, this.options.duration
+			);
+		} else {
+			this.pos = eased = percent;
+		}
+		this.now = ( this.end - this.start ) * eased + this.start;
+
+		if ( this.options.step ) {
+			this.options.step.call( this.elem, this.now, this );
+		}
+
+		if ( hooks && hooks.set ) {
+			hooks.set( this );
+		} else {
+			Tween.propHooks._default.set( this );
+		}
+		return this;
+	}
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+	_default: {
+		get: function( tween ) {
+			var result;
+
+			// Use a property on the element directly when it is not a DOM element,
+			// or when there is no matching style property that exists.
+			if ( tween.elem.nodeType !== 1 ||
+				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+				return tween.elem[ tween.prop ];
+			}
+
+			// Passing an empty string as a 3rd parameter to .css will automatically
+			// attempt a parseFloat and fallback to a string if the parse fails.
+			// Simple values such as "10px" are parsed to Float;
+			// complex values such as "rotate(1rad)" are returned as-is.
+			result = jQuery.css( tween.elem, tween.prop, "" );
+
+			// Empty strings, null, undefined and "auto" are converted to 0.
+			return !result || result === "auto" ? 0 : result;
+		},
+		set: function( tween ) {
+
+			// Use step hook for back compat.
+			// Use cssHook if its there.
+			// Use .style if available and use plain properties where available.
+			if ( jQuery.fx.step[ tween.prop ] ) {
+				jQuery.fx.step[ tween.prop ]( tween );
+			} else if ( tween.elem.nodeType === 1 && (
+					jQuery.cssHooks[ tween.prop ] ||
+					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+			} else {
+				tween.elem[ tween.prop ] = tween.now;
+			}
+		}
+	}
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+	set: function( tween ) {
+		if ( tween.elem.nodeType && tween.elem.parentNode ) {
+			tween.elem[ tween.prop ] = tween.now;
+		}
+	}
+};
+
+jQuery.easing = {
+	linear: function( p ) {
+		return p;
+	},
+	swing: function( p ) {
+		return 0.5 - Math.cos( p * Math.PI ) / 2;
+	},
+	_default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+	fxNow, inProgress,
+	rfxtypes = /^(?:toggle|show|hide)$/,
+	rrun = /queueHooks$/;
+
+function schedule() {
+	if ( inProgress ) {
+		if ( document.hidden === false && window.requestAnimationFrame ) {
+			window.requestAnimationFrame( schedule );
+		} else {
+			window.setTimeout( schedule, jQuery.fx.interval );
+		}
+
+		jQuery.fx.tick();
+	}
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+	window.setTimeout( function() {
+		fxNow = undefined;
+	} );
+	return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+	var which,
+		i = 0,
+		attrs = { height: type };
+
+	// If we include width, step value is 1 to do all cssExpand values,
+	// otherwise step value is 2 to skip over Left and Right
+	includeWidth = includeWidth ? 1 : 0;
+	for ( ; i < 4; i += 2 - includeWidth ) {
+		which = cssExpand[ i ];
+		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+	}
+
+	if ( includeWidth ) {
+		attrs.opacity = attrs.width = type;
+	}
+
+	return attrs;
+}
+
+function createTween( value, prop, animation ) {
+	var tween,
+		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+		index = 0,
+		length = collection.length;
+	for ( ; index < length; index++ ) {
+		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+			// We're done with this property
+			return tween;
+		}
+	}
+}
+
+function defaultPrefilter( elem, props, opts ) {
+	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+		isBox = "width" in props || "height" in props,
+		anim = this,
+		orig = {},
+		style = elem.style,
+		hidden = elem.nodeType && isHiddenWithinTree( elem ),
+		dataShow = dataPriv.get( elem, "fxshow" );
+
+	// Queue-skipping animations hijack the fx hooks
+	if ( !opts.queue ) {
+		hooks = jQuery._queueHooks( elem, "fx" );
+		if ( hooks.unqueued == null ) {
+			hooks.unqueued = 0;
+			oldfire = hooks.empty.fire;
+			hooks.empty.fire = function() {
+				if ( !hooks.unqueued ) {
+					oldfire();
+				}
+			};
+		}
+		hooks.unqueued++;
+
+		anim.always( function() {
+
+			// Ensure the complete handler is called before this completes
+			anim.always( function() {
+				hooks.unqueued--;
+				if ( !jQuery.queue( elem, "fx" ).length ) {
+					hooks.empty.fire();
+				}
+			} );
+		} );
+	}
+
+	// Detect show/hide animations
+	for ( prop in props ) {
+		value = props[ prop ];
+		if ( rfxtypes.test( value ) ) {
+			delete props[ prop ];
+			toggle = toggle || value === "toggle";
+			if ( value === ( hidden ? "hide" : "show" ) ) {
+
+				// Pretend to be hidden if this is a "show" and
+				// there is still data from a stopped show/hide
+				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+					hidden = true;
+
+				// Ignore all other no-op show/hide data
+				} else {
+					continue;
+				}
+			}
+			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+		}
+	}
+
+	// Bail out if this is a no-op like .hide().hide()
+	propTween = !jQuery.isEmptyObject( props );
+	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+		return;
+	}
+
+	// Restrict "overflow" and "display" styles during box animations
+	if ( isBox && elem.nodeType === 1 ) {
+
+		// Support: IE <=9 - 11, Edge 12 - 15
+		// Record all 3 overflow attributes because IE does not infer the shorthand
+		// from identically-valued overflowX and overflowY and Edge just mirrors
+		// the overflowX value there.
+		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+		// Identify a display type, preferring old show/hide data over the CSS cascade
+		restoreDisplay = dataShow && dataShow.display;
+		if ( restoreDisplay == null ) {
+			restoreDisplay = dataPriv.get( elem, "display" );
+		}
+		display = jQuery.css( elem, "display" );
+		if ( display === "none" ) {
+			if ( restoreDisplay ) {
+				display = restoreDisplay;
+			} else {
+
+				// Get nonempty value(s) by temporarily forcing visibility
+				showHide( [ elem ], true );
+				restoreDisplay = elem.style.display || restoreDisplay;
+				display = jQuery.css( elem, "display" );
+				showHide( [ elem ] );
+			}
+		}
+
+		// Animate inline elements as inline-block
+		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+			if ( jQuery.css( elem, "float" ) === "none" ) {
+
+				// Restore the original display value at the end of pure show/hide animations
+				if ( !propTween ) {
+					anim.done( function() {
+						style.display = restoreDisplay;
+					} );
+					if ( restoreDisplay == null ) {
+						display = style.display;
+						restoreDisplay = display === "none" ? "" : display;
+					}
+				}
+				style.display = "inline-block";
+			}
+		}
+	}
+
+	if ( opts.overflow ) {
+		style.overflow = "hidden";
+		anim.always( function() {
+			style.overflow = opts.overflow[ 0 ];
+			style.overflowX = opts.overflow[ 1 ];
+			style.overflowY = opts.overflow[ 2 ];
+		} );
+	}
+
+	// Implement show/hide animations
+	propTween = false;
+	for ( prop in orig ) {
+
+		// General show/hide setup for this element animation
+		if ( !propTween ) {
+			if ( dataShow ) {
+				if ( "hidden" in dataShow ) {
+					hidden = dataShow.hidden;
+				}
+			} else {
+				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+			}
+
+			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+			if ( toggle ) {
+				dataShow.hidden = !hidden;
+			}
+
+			// Show elements before animating them
+			if ( hidden ) {
+				showHide( [ elem ], true );
+			}
+
+			/* eslint-disable no-loop-func */
+
+			anim.done( function() {
+
+			/* eslint-enable no-loop-func */
+
+				// The final step of a "hide" animation is actually hiding the element
+				if ( !hidden ) {
+					showHide( [ elem ] );
+				}
+				dataPriv.remove( elem, "fxshow" );
+				for ( prop in orig ) {
+					jQuery.style( elem, prop, orig[ prop ] );
+				}
+			} );
+		}
+
+		// Per-property setup
+		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+		if ( !( prop in dataShow ) ) {
+			dataShow[ prop ] = propTween.start;
+			if ( hidden ) {
+				propTween.end = propTween.start;
+				propTween.start = 0;
+			}
+		}
+	}
+}
+
+function propFilter( props, specialEasing ) {
+	var index, name, easing, value, hooks;
+
+	// camelCase, specialEasing and expand cssHook pass
+	for ( index in props ) {
+		name = camelCase( index );
+		easing = specialEasing[ name ];
+		value = props[ index ];
+		if ( Array.isArray( value ) ) {
+			easing = value[ 1 ];
+			value = props[ index ] = value[ 0 ];
+		}
+
+		if ( index !== name ) {
+			props[ name ] = value;
+			delete props[ index ];
+		}
+
+		hooks = jQuery.cssHooks[ name ];
+		if ( hooks && "expand" in hooks ) {
+			value = hooks.expand( value );
+			delete props[ name ];
+
+			// Not quite $.extend, this won't overwrite existing keys.
+			// Reusing 'index' because we have the correct "name"
+			for ( index in value ) {
+				if ( !( index in props ) ) {
+					props[ index ] = value[ index ];
+					specialEasing[ index ] = easing;
+				}
+			}
+		} else {
+			specialEasing[ name ] = easing;
+		}
+	}
+}
+
+function Animation( elem, properties, options ) {
+	var result,
+		stopped,
+		index = 0,
+		length = Animation.prefilters.length,
+		deferred = jQuery.Deferred().always( function() {
+
+			// Don't match elem in the :animated selector
+			delete tick.elem;
+		} ),
+		tick = function() {
+			if ( stopped ) {
+				return false;
+			}
+			var currentTime = fxNow || createFxNow(),
+				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+				// Support: Android 2.3 only
+				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+				temp = remaining / animation.duration || 0,
+				percent = 1 - temp,
+				index = 0,
+				length = animation.tweens.length;
+
+			for ( ; index < length; index++ ) {
+				animation.tweens[ index ].run( percent );
+			}
+
+			deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+			// If there's more to do, yield
+			if ( percent < 1 && length ) {
+				return remaining;
+			}
+
+			// If this was an empty animation, synthesize a final progress notification
+			if ( !length ) {
+				deferred.notifyWith( elem, [ animation, 1, 0 ] );
+			}
+
+			// Resolve the animation and report its conclusion
+			deferred.resolveWith( elem, [ animation ] );
+			return false;
+		},
+		animation = deferred.promise( {
+			elem: elem,
+			props: jQuery.extend( {}, properties ),
+			opts: jQuery.extend( true, {
+				specialEasing: {},
+				easing: jQuery.easing._default
+			}, options ),
+			originalProperties: properties,
+			originalOptions: options,
+			startTime: fxNow || createFxNow(),
+			duration: options.duration,
+			tweens: [],
+			createTween: function( prop, end ) {
+				var tween = jQuery.Tween( elem, animation.opts, prop, end,
+						animation.opts.specialEasing[ prop ] || animation.opts.easing );
+				animation.tweens.push( tween );
+				return tween;
+			},
+			stop: function( gotoEnd ) {
+				var index = 0,
+
+					// If we are going to the end, we want to run all the tweens
+					// otherwise we skip this part
+					length = gotoEnd ? animation.tweens.length : 0;
+				if ( stopped ) {
+					return this;
+				}
+				stopped = true;
+				for ( ; index < length; index++ ) {
+					animation.tweens[ index ].run( 1 );
+				}
+
+				// Resolve when we played the last frame; otherwise, reject
+				if ( gotoEnd ) {
+					deferred.notifyWith( elem, [ animation, 1, 0 ] );
+					deferred.resolveWith( elem, [ animation, gotoEnd ] );
+				} else {
+					deferred.rejectWith( elem, [ animation, gotoEnd ] );
+				}
+				return this;
+			}
+		} ),
+		props = animation.props;
+
+	propFilter( props, animation.opts.specialEasing );
+
+	for ( ; index < length; index++ ) {
+		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+		if ( result ) {
+			if ( isFunction( result.stop ) ) {
+				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+					result.stop.bind( result );
+			}
+			return result;
+		}
+	}
+
+	jQuery.map( props, createTween, animation );
+
+	if ( isFunction( animation.opts.start ) ) {
+		animation.opts.start.call( elem, animation );
+	}
+
+	// Attach callbacks from options
+	animation
+		.progress( animation.opts.progress )
+		.done( animation.opts.done, animation.opts.complete )
+		.fail( animation.opts.fail )
+		.always( animation.opts.always );
+
+	jQuery.fx.timer(
+		jQuery.extend( tick, {
+			elem: elem,
+			anim: animation,
+			queue: animation.opts.queue
+		} )
+	);
+
+	return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+	tweeners: {
+		"*": [ function( prop, value ) {
+			var tween = this.createTween( prop, value );
+			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+			return tween;
+		} ]
+	},
+
+	tweener: function( props, callback ) {
+		if ( isFunction( props ) ) {
+			callback = props;
+			props = [ "*" ];
+		} else {
+			props = props.match( rnothtmlwhite );
+		}
+
+		var prop,
+			index = 0,
+			length = props.length;
+
+		for ( ; index < length; index++ ) {
+			prop = props[ index ];
+			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+			Animation.tweeners[ prop ].unshift( callback );
+		}
+	},
+
+	prefilters: [ defaultPrefilter ],
+
+	prefilter: function( callback, prepend ) {
+		if ( prepend ) {
+			Animation.prefilters.unshift( callback );
+		} else {
+			Animation.prefilters.push( callback );
+		}
+	}
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+		complete: fn || !fn && easing ||
+			isFunction( speed ) && speed,
+		duration: speed,
+		easing: fn && easing || easing && !isFunction( easing ) && easing
+	};
+
+	// Go to the end state if fx are off
+	if ( jQuery.fx.off ) {
+		opt.duration = 0;
+
+	} else {
+		if ( typeof opt.duration !== "number" ) {
+			if ( opt.duration in jQuery.fx.speeds ) {
+				opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+			} else {
+				opt.duration = jQuery.fx.speeds._default;
+			}
+		}
+	}
+
+	// Normalize opt.queue - true/undefined/null -> "fx"
+	if ( opt.queue == null || opt.queue === true ) {
+		opt.queue = "fx";
+	}
+
+	// Queueing
+	opt.old = opt.complete;
+
+	opt.complete = function() {
+		if ( isFunction( opt.old ) ) {
+			opt.old.call( this );
+		}
+
+		if ( opt.queue ) {
+			jQuery.dequeue( this, opt.queue );
+		}
+	};
+
+	return opt;
+};
+
+jQuery.fn.extend( {
+	fadeTo: function( speed, to, easing, callback ) {
+
+		// Show any hidden elements after setting opacity to 0
+		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+			// Animate to the value specified
+			.end().animate( { opacity: to }, speed, easing, callback );
+	},
+	animate: function( prop, speed, easing, callback ) {
+		var empty = jQuery.isEmptyObject( prop ),
+			optall = jQuery.speed( speed, easing, callback ),
+			doAnimation = function() {
+
+				// Operate on a copy of prop so per-property easing won't be lost
+				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+				// Empty animations, or finishing resolves immediately
+				if ( empty || dataPriv.get( this, "finish" ) ) {
+					anim.stop( true );
+				}
+			};
+			doAnimation.finish = doAnimation;
+
+		return empty || optall.queue === false ?
+			this.each( doAnimation ) :
+			this.queue( optall.queue, doAnimation );
+	},
+	stop: function( type, clearQueue, gotoEnd ) {
+		var stopQueue = function( hooks ) {
+			var stop = hooks.stop;
+			delete hooks.stop;
+			stop( gotoEnd );
+		};
+
+		if ( typeof type !== "string" ) {
+			gotoEnd = clearQueue;
+			clearQueue = type;
+			type = undefined;
+		}
+		if ( clearQueue ) {
+			this.queue( type || "fx", [] );
+		}
+
+		return this.each( function() {
+			var dequeue = true,
+				index = type != null && type + "queueHooks",
+				timers = jQuery.timers,
+				data = dataPriv.get( this );
+
+			if ( index ) {
+				if ( data[ index ] && data[ index ].stop ) {
+					stopQueue( data[ index ] );
+				}
+			} else {
+				for ( index in data ) {
+					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+						stopQueue( data[ index ] );
+					}
+				}
+			}
+
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this &&
+					( type == null || timers[ index ].queue === type ) ) {
+
+					timers[ index ].anim.stop( gotoEnd );
+					dequeue = false;
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Start the next in the queue if the last step wasn't forced.
+			// Timers currently will call their complete callbacks, which
+			// will dequeue but only if they were gotoEnd.
+			if ( dequeue || !gotoEnd ) {
+				jQuery.dequeue( this, type );
+			}
+		} );
+	},
+	finish: function( type ) {
+		if ( type !== false ) {
+			type = type || "fx";
+		}
+		return this.each( function() {
+			var index,
+				data = dataPriv.get( this ),
+				queue = data[ type + "queue" ],
+				hooks = data[ type + "queueHooks" ],
+				timers = jQuery.timers,
+				length = queue ? queue.length : 0;
+
+			// Enable finishing flag on private data
+			data.finish = true;
+
+			// Empty the queue first
+			jQuery.queue( this, type, [] );
+
+			if ( hooks && hooks.stop ) {
+				hooks.stop.call( this, true );
+			}
+
+			// Look for any active animations, and finish them
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+					timers[ index ].anim.stop( true );
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Look for any animations in the old queue and finish them
+			for ( index = 0; index < length; index++ ) {
+				if ( queue[ index ] && queue[ index ].finish ) {
+					queue[ index ].finish.call( this );
+				}
+			}
+
+			// Turn off finishing flag
+			delete data.finish;
+		} );
+	}
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+	var cssFn = jQuery.fn[ name ];
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return speed == null || typeof speed === "boolean" ?
+			cssFn.apply( this, arguments ) :
+			this.animate( genFx( name, true ), speed, easing, callback );
+	};
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+	slideDown: genFx( "show" ),
+	slideUp: genFx( "hide" ),
+	slideToggle: genFx( "toggle" ),
+	fadeIn: { opacity: "show" },
+	fadeOut: { opacity: "hide" },
+	fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return this.animate( props, speed, easing, callback );
+	};
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+	var timer,
+		i = 0,
+		timers = jQuery.timers;
+
+	fxNow = Date.now();
+
+	for ( ; i < timers.length; i++ ) {
+		timer = timers[ i ];
+
+		// Run the timer and safely remove it when done (allowing for external removal)
+		if ( !timer() && timers[ i ] === timer ) {
+			timers.splice( i--, 1 );
+		}
+	}
+
+	if ( !timers.length ) {
+		jQuery.fx.stop();
+	}
+	fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+	jQuery.timers.push( timer );
+	jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+	if ( inProgress ) {
+		return;
+	}
+
+	inProgress = true;
+	schedule();
+};
+
+jQuery.fx.stop = function() {
+	inProgress = null;
+};
+
+jQuery.fx.speeds = {
+	slow: 600,
+	fast: 200,
+
+	// Default speed
+	_default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+	type = type || "fx";
+
+	return this.queue( type, function( next, hooks ) {
+		var timeout = window.setTimeout( next, time );
+		hooks.stop = function() {
+			window.clearTimeout( timeout );
+		};
+	} );
+};
+
+
+( function() {
+	var input = document.createElement( "input" ),
+		select = document.createElement( "select" ),
+		opt = select.appendChild( document.createElement( "option" ) );
+
+	input.type = "checkbox";
+
+	// Support: Android <=4.3 only
+	// Default value for a checkbox should be "on"
+	support.checkOn = input.value !== "";
+
+	// Support: IE <=11 only
+	// Must access selectedIndex to make default options select
+	support.optSelected = opt.selected;
+
+	// Support: IE <=11 only
+	// An input loses its value after becoming a radio
+	input = document.createElement( "input" );
+	input.value = "t";
+	input.type = "radio";
+	support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+	attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+	attr: function( name, value ) {
+		return access( this, jQuery.attr, name, value, arguments.length > 1 );
+	},
+
+	removeAttr: function( name ) {
+		return this.each( function() {
+			jQuery.removeAttr( this, name );
+		} );
+	}
+} );
+
+jQuery.extend( {
+	attr: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set attributes on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		// Fallback to prop when attributes are not supported
+		if ( typeof elem.getAttribute === "undefined" ) {
+			return jQuery.prop( elem, name, value );
+		}
+
+		// Attribute hooks are determined by the lowercase version
+		// Grab necessary hook if one is defined
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+		}
+
+		if ( value !== undefined ) {
+			if ( value === null ) {
+				jQuery.removeAttr( elem, name );
+				return;
+			}
+
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			elem.setAttribute( name, value + "" );
+			return value;
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		ret = jQuery.find.attr( elem, name );
+
+		// Non-existent attributes return null, we normalize to undefined
+		return ret == null ? undefined : ret;
+	},
+
+	attrHooks: {
+		type: {
+			set: function( elem, value ) {
+				if ( !support.radioValue && value === "radio" &&
+					nodeName( elem, "input" ) ) {
+					var val = elem.value;
+					elem.setAttribute( "type", value );
+					if ( val ) {
+						elem.value = val;
+					}
+					return value;
+				}
+			}
+		}
+	},
+
+	removeAttr: function( elem, value ) {
+		var name,
+			i = 0,
+
+			// Attribute names can contain non-HTML whitespace characters
+			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+			attrNames = value && value.match( rnothtmlwhite );
+
+		if ( attrNames && elem.nodeType === 1 ) {
+			while ( ( name = attrNames[ i++ ] ) ) {
+				elem.removeAttribute( name );
+			}
+		}
+	}
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+	set: function( elem, value, name ) {
+		if ( value === false ) {
+
+			// Remove boolean attributes when set to false
+			jQuery.removeAttr( elem, name );
+		} else {
+			elem.setAttribute( name, name );
+		}
+		return name;
+	}
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+	var getter = attrHandle[ name ] || jQuery.find.attr;
+
+	attrHandle[ name ] = function( elem, name, isXML ) {
+		var ret, handle,
+			lowercaseName = name.toLowerCase();
+
+		if ( !isXML ) {
+
+			// Avoid an infinite loop by temporarily removing this function from the getter
+			handle = attrHandle[ lowercaseName ];
+			attrHandle[ lowercaseName ] = ret;
+			ret = getter( elem, name, isXML ) != null ?
+				lowercaseName :
+				null;
+			attrHandle[ lowercaseName ] = handle;
+		}
+		return ret;
+	};
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+	rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+	prop: function( name, value ) {
+		return access( this, jQuery.prop, name, value, arguments.length > 1 );
+	},
+
+	removeProp: function( name ) {
+		return this.each( function() {
+			delete this[ jQuery.propFix[ name ] || name ];
+		} );
+	}
+} );
+
+jQuery.extend( {
+	prop: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set properties on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+			// Fix name and attach hooks
+			name = jQuery.propFix[ name ] || name;
+			hooks = jQuery.propHooks[ name ];
+		}
+
+		if ( value !== undefined ) {
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			return ( elem[ name ] = value );
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		return elem[ name ];
+	},
+
+	propHooks: {
+		tabIndex: {
+			get: function( elem ) {
+
+				// Support: IE <=9 - 11 only
+				// elem.tabIndex doesn't always return the
+				// correct value when it hasn't been explicitly set
+				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+				// Use proper attribute retrieval(#12072)
+				var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+				if ( tabindex ) {
+					return parseInt( tabindex, 10 );
+				}
+
+				if (
+					rfocusable.test( elem.nodeName ) ||
+					rclickable.test( elem.nodeName ) &&
+					elem.href
+				) {
+					return 0;
+				}
+
+				return -1;
+			}
+		}
+	},
+
+	propFix: {
+		"for": "htmlFor",
+		"class": "className"
+	}
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+	jQuery.propHooks.selected = {
+		get: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent && parent.parentNode ) {
+				parent.parentNode.selectedIndex;
+			}
+			return null;
+		},
+		set: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent ) {
+				parent.selectedIndex;
+
+				if ( parent.parentNode ) {
+					parent.parentNode.selectedIndex;
+				}
+			}
+		}
+	};
+}
+
+jQuery.each( [
+	"tabIndex",
+	"readOnly",
+	"maxLength",
+	"cellSpacing",
+	"cellPadding",
+	"rowSpan",
+	"colSpan",
+	"useMap",
+	"frameBorder",
+	"contentEditable"
+], function() {
+	jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+	// Strip and collapse whitespace according to HTML spec
+	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+	function stripAndCollapse( value ) {
+		var tokens = value.match( rnothtmlwhite ) || [];
+		return tokens.join( " " );
+	}
+
+
+function getClass( elem ) {
+	return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+	if ( Array.isArray( value ) ) {
+		return value;
+	}
+	if ( typeof value === "string" ) {
+		return value.match( rnothtmlwhite ) || [];
+	}
+	return [];
+}
+
+jQuery.fn.extend( {
+	addClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+							cur += clazz + " ";
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	removeClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		if ( !arguments.length ) {
+			return this.attr( "class", "" );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+
+				// This expression is here for better compressibility (see addClass)
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+
+						// Remove *all* instances
+						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+							cur = cur.replace( " " + clazz + " ", " " );
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	toggleClass: function( value, stateVal ) {
+		var type = typeof value,
+			isValidValue = type === "string" || Array.isArray( value );
+
+		if ( typeof stateVal === "boolean" && isValidValue ) {
+			return stateVal ? this.addClass( value ) : this.removeClass( value );
+		}
+
+		if ( isFunction( value ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).toggleClass(
+					value.call( this, i, getClass( this ), stateVal ),
+					stateVal
+				);
+			} );
+		}
+
+		return this.each( function() {
+			var className, i, self, classNames;
+
+			if ( isValidValue ) {
+
+				// Toggle individual class names
+				i = 0;
+				self = jQuery( this );
+				classNames = classesToArray( value );
+
+				while ( ( className = classNames[ i++ ] ) ) {
+
+					// Check each className given, space separated list
+					if ( self.hasClass( className ) ) {
+						self.removeClass( className );
+					} else {
+						self.addClass( className );
+					}
+				}
+
+			// Toggle whole class name
+			} else if ( value === undefined || type === "boolean" ) {
+				className = getClass( this );
+				if ( className ) {
+
+					// Store className if set
+					dataPriv.set( this, "__className__", className );
+				}
+
+				// If the element has a class name or if we're passed `false`,
+				// then remove the whole classname (if there was one, the above saved it).
+				// Otherwise bring back whatever was previously saved (if anything),
+				// falling back to the empty string if nothing was stored.
+				if ( this.setAttribute ) {
+					this.setAttribute( "class",
+						className || value === false ?
+						"" :
+						dataPriv.get( this, "__className__" ) || ""
+					);
+				}
+			}
+		} );
+	},
+
+	hasClass: function( selector ) {
+		var className, elem,
+			i = 0;
+
+		className = " " + selector + " ";
+		while ( ( elem = this[ i++ ] ) ) {
+			if ( elem.nodeType === 1 &&
+				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+					return true;
+			}
+		}
+
+		return false;
+	}
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+	val: function( value ) {
+		var hooks, ret, valueIsFunction,
+			elem = this[ 0 ];
+
+		if ( !arguments.length ) {
+			if ( elem ) {
+				hooks = jQuery.valHooks[ elem.type ] ||
+					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+				if ( hooks &&
+					"get" in hooks &&
+					( ret = hooks.get( elem, "value" ) ) !== undefined
+				) {
+					return ret;
+				}
+
+				ret = elem.value;
+
+				// Handle most common string cases
+				if ( typeof ret === "string" ) {
+					return ret.replace( rreturn, "" );
+				}
+
+				// Handle cases where value is null/undef or number
+				return ret == null ? "" : ret;
+			}
+
+			return;
+		}
+
+		valueIsFunction = isFunction( value );
+
+		return this.each( function( i ) {
+			var val;
+
+			if ( this.nodeType !== 1 ) {
+				return;
+			}
+
+			if ( valueIsFunction ) {
+				val = value.call( this, i, jQuery( this ).val() );
+			} else {
+				val = value;
+			}
+
+			// Treat null/undefined as ""; convert numbers to string
+			if ( val == null ) {
+				val = "";
+
+			} else if ( typeof val === "number" ) {
+				val += "";
+
+			} else if ( Array.isArray( val ) ) {
+				val = jQuery.map( val, function( value ) {
+					return value == null ? "" : value + "";
+				} );
+			}
+
+			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+			// If set returns undefined, fall back to normal setting
+			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+				this.value = val;
+			}
+		} );
+	}
+} );
+
+jQuery.extend( {
+	valHooks: {
+		option: {
+			get: function( elem ) {
+
+				var val = jQuery.find.attr( elem, "value" );
+				return val != null ?
+					val :
+
+					// Support: IE <=10 - 11 only
+					// option.text throws exceptions (#14686, #14858)
+					// Strip and collapse whitespace
+					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+					stripAndCollapse( jQuery.text( elem ) );
+			}
+		},
+		select: {
+			get: function( elem ) {
+				var value, option, i,
+					options = elem.options,
+					index = elem.selectedIndex,
+					one = elem.type === "select-one",
+					values = one ? null : [],
+					max = one ? index + 1 : options.length;
+
+				if ( index < 0 ) {
+					i = max;
+
+				} else {
+					i = one ? index : 0;
+				}
+
+				// Loop through all the selected options
+				for ( ; i < max; i++ ) {
+					option = options[ i ];
+
+					// Support: IE <=9 only
+					// IE8-9 doesn't update selected after form reset (#2551)
+					if ( ( option.selected || i === index ) &&
+
+							// Don't return options that are disabled or in a disabled optgroup
+							!option.disabled &&
+							( !option.parentNode.disabled ||
+								!nodeName( option.parentNode, "optgroup" ) ) ) {
+
+						// Get the specific value for the option
+						value = jQuery( option ).val();
+
+						// We don't need an array for one selects
+						if ( one ) {
+							return value;
+						}
+
+						// Multi-Selects return an array
+						values.push( value );
+					}
+				}
+
+				return values;
+			},
+
+			set: function( elem, value ) {
+				var optionSet, option,
+					options = elem.options,
+					values = jQuery.makeArray( value ),
+					i = options.length;
+
+				while ( i-- ) {
+					option = options[ i ];
+
+					/* eslint-disable no-cond-assign */
+
+					if ( option.selected =
+						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+					) {
+						optionSet = true;
+					}
+
+					/* eslint-enable no-cond-assign */
+				}
+
+				// Force browsers to behave consistently when non-matching value is set
+				if ( !optionSet ) {
+					elem.selectedIndex = -1;
+				}
+				return values;
+			}
+		}
+	}
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+	jQuery.valHooks[ this ] = {
+		set: function( elem, value ) {
+			if ( Array.isArray( value ) ) {
+				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+			}
+		}
+	};
+	if ( !support.checkOn ) {
+		jQuery.valHooks[ this ].get = function( elem ) {
+			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+		};
+	}
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+	stopPropagationCallback = function( e ) {
+		e.stopPropagation();
+	};
+
+jQuery.extend( jQuery.event, {
+
+	trigger: function( event, data, elem, onlyHandlers ) {
+
+		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+			eventPath = [ elem || document ],
+			type = hasOwn.call( event, "type" ) ? event.type : event,
+			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+		cur = lastElement = tmp = elem = elem || document;
+
+		// Don't do events on text and comment nodes
+		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+			return;
+		}
+
+		// focus/blur morphs to focusin/out; ensure we're not firing them right now
+		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+			return;
+		}
+
+		if ( type.indexOf( "." ) > -1 ) {
+
+			// Namespaced trigger; create a regexp to match event type in handle()
+			namespaces = type.split( "." );
+			type = namespaces.shift();
+			namespaces.sort();
+		}
+		ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+		// Caller can pass in a jQuery.Event object, Object, or just an event type string
+		event = event[ jQuery.expando ] ?
+			event :
+			new jQuery.Event( type, typeof event === "object" && event );
+
+		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+		event.isTrigger = onlyHandlers ? 2 : 3;
+		event.namespace = namespaces.join( "." );
+		event.rnamespace = event.namespace ?
+			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+			null;
+
+		// Clean up the event in case it is being reused
+		event.result = undefined;
+		if ( !event.target ) {
+			event.target = elem;
+		}
+
+		// Clone any incoming data and prepend the event, creating the handler arg list
+		data = data == null ?
+			[ event ] :
+			jQuery.makeArray( data, [ event ] );
+
+		// Allow special events to draw outside the lines
+		special = jQuery.event.special[ type ] || {};
+		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+			return;
+		}
+
+		// Determine event propagation path in advance, per W3C events spec (#9951)
+		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+			bubbleType = special.delegateType || type;
+			if ( !rfocusMorph.test( bubbleType + type ) ) {
+				cur = cur.parentNode;
+			}
+			for ( ; cur; cur = cur.parentNode ) {
+				eventPath.push( cur );
+				tmp = cur;
+			}
+
+			// Only add window if we got to document (e.g., not plain obj or detached DOM)
+			if ( tmp === ( elem.ownerDocument || document ) ) {
+				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+			}
+		}
+
+		// Fire handlers on the event path
+		i = 0;
+		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+			lastElement = cur;
+			event.type = i > 1 ?
+				bubbleType :
+				special.bindType || type;
+
+			// jQuery handler
+			handle = (
+					dataPriv.get( cur, "events" ) || Object.create( null )
+				)[ event.type ] &&
+				dataPriv.get( cur, "handle" );
+			if ( handle ) {
+				handle.apply( cur, data );
+			}
+
+			// Native handler
+			handle = ontype && cur[ ontype ];
+			if ( handle && handle.apply && acceptData( cur ) ) {
+				event.result = handle.apply( cur, data );
+				if ( event.result === false ) {
+					event.preventDefault();
+				}
+			}
+		}
+		event.type = type;
+
+		// If nobody prevented the default action, do it now
+		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+			if ( ( !special._default ||
+				special._default.apply( eventPath.pop(), data ) === false ) &&
+				acceptData( elem ) ) {
+
+				// Call a native DOM method on the target with the same name as the event.
+				// Don't do default actions on window, that's where global variables be (#6170)
+				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+					// Don't re-trigger an onFOO event when we call its FOO() method
+					tmp = elem[ ontype ];
+
+					if ( tmp ) {
+						elem[ ontype ] = null;
+					}
+
+					// Prevent re-triggering of the same event, since we already bubbled it above
+					jQuery.event.triggered = type;
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.addEventListener( type, stopPropagationCallback );
+					}
+
+					elem[ type ]();
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.removeEventListener( type, stopPropagationCallback );
+					}
+
+					jQuery.event.triggered = undefined;
+
+					if ( tmp ) {
+						elem[ ontype ] = tmp;
+					}
+				}
+			}
+		}
+
+		return event.result;
+	},
+
+	// Piggyback on a donor event to simulate a different one
+	// Used only for `focus(in | out)` events
+	simulate: function( type, elem, event ) {
+		var e = jQuery.extend(
+			new jQuery.Event(),
+			event,
+			{
+				type: type,
+				isSimulated: true
+			}
+		);
+
+		jQuery.event.trigger( e, null, elem );
+	}
+
+} );
+
+jQuery.fn.extend( {
+
+	trigger: function( type, data ) {
+		return this.each( function() {
+			jQuery.event.trigger( type, data, this );
+		} );
+	},
+	triggerHandler: function( type, data ) {
+		var elem = this[ 0 ];
+		if ( elem ) {
+			return jQuery.event.trigger( type, data, elem, true );
+		}
+	}
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+		// Attach a single capturing handler on the document while someone wants focusin/focusout
+		var handler = function( event ) {
+			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+		};
+
+		jQuery.event.special[ fix ] = {
+			setup: function() {
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix );
+
+				if ( !attaches ) {
+					doc.addEventListener( orig, handler, true );
+				}
+				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+			},
+			teardown: function() {
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix ) - 1;
+
+				if ( !attaches ) {
+					doc.removeEventListener( orig, handler, true );
+					dataPriv.remove( doc, fix );
+
+				} else {
+					dataPriv.access( doc, fix, attaches );
+				}
+			}
+		};
+	} );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+	var xml;
+	if ( !data || typeof data !== "string" ) {
+		return null;
+	}
+
+	// Support: IE 9 - 11 only
+	// IE throws on parseFromString with invalid input.
+	try {
+		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+	} catch ( e ) {
+		xml = undefined;
+	}
+
+	if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) {
+		jQuery.error( "Invalid XML: " + data );
+	}
+	return xml;
+};
+
+
+var
+	rbracket = /\[\]$/,
+	rCRLF = /\r?\n/g,
+	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+	rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+	var name;
+
+	if ( Array.isArray( obj ) ) {
+
+		// Serialize array item.
+		jQuery.each( obj, function( i, v ) {
+			if ( traditional || rbracket.test( prefix ) ) {
+
+				// Treat each array item as a scalar.
+				add( prefix, v );
+
+			} else {
+
+				// Item is non-scalar (array or object), encode its numeric index.
+				buildParams(
+					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+					v,
+					traditional,
+					add
+				);
+			}
+		} );
+
+	} else if ( !traditional && toType( obj ) === "object" ) {
+
+		// Serialize object item.
+		for ( name in obj ) {
+			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+		}
+
+	} else {
+
+		// Serialize scalar item.
+		add( prefix, obj );
+	}
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+	var prefix,
+		s = [],
+		add = function( key, valueOrFunction ) {
+
+			// If value is a function, invoke it and use its return value
+			var value = isFunction( valueOrFunction ) ?
+				valueOrFunction() :
+				valueOrFunction;
+
+			s[ s.length ] = encodeURIComponent( key ) + "=" +
+				encodeURIComponent( value == null ? "" : value );
+		};
+
+	if ( a == null ) {
+		return "";
+	}
+
+	// If an array was passed in, assume that it is an array of form elements.
+	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+		// Serialize the form elements
+		jQuery.each( a, function() {
+			add( this.name, this.value );
+		} );
+
+	} else {
+
+		// If traditional, encode the "old" way (the way 1.3.2 or older
+		// did it), otherwise encode params recursively.
+		for ( prefix in a ) {
+			buildParams( prefix, a[ prefix ], traditional, add );
+		}
+	}
+
+	// Return the resulting serialization
+	return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+	serialize: function() {
+		return jQuery.param( this.serializeArray() );
+	},
+	serializeArray: function() {
+		return this.map( function() {
+
+			// Can add propHook for "elements" to filter or add form elements
+			var elements = jQuery.prop( this, "elements" );
+			return elements ? jQuery.makeArray( elements ) : this;
+		} )
+		.filter( function() {
+			var type = this.type;
+
+			// Use .is( ":disabled" ) so that fieldset[disabled] works
+			return this.name && !jQuery( this ).is( ":disabled" ) &&
+				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+				( this.checked || !rcheckableType.test( type ) );
+		} )
+		.map( function( _i, elem ) {
+			var val = jQuery( this ).val();
+
+			if ( val == null ) {
+				return null;
+			}
+
+			if ( Array.isArray( val ) ) {
+				return jQuery.map( val, function( val ) {
+					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+				} );
+			}
+
+			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+		} ).get();
+	}
+} );
+
+
+var
+	r20 = /%20/g,
+	rhash = /#.*$/,
+	rantiCache = /([?&])_=[^&]*/,
+	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+	// #7653, #8125, #8152: local protocol detection
+	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+	rnoContent = /^(?:GET|HEAD)$/,
+	rprotocol = /^\/\//,
+
+	/* Prefilters
+	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+	 * 2) These are called:
+	 *    - BEFORE asking for a transport
+	 *    - AFTER param serialization (s.data is a string if s.processData is true)
+	 * 3) key is the dataType
+	 * 4) the catchall symbol "*" can be used
+	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+	 */
+	prefilters = {},
+
+	/* Transports bindings
+	 * 1) key is the dataType
+	 * 2) the catchall symbol "*" can be used
+	 * 3) selection will start with transport dataType and THEN go to "*" if needed
+	 */
+	transports = {},
+
+	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+	allTypes = "*/".concat( "*" ),
+
+	// Anchor tag for parsing the document origin
+	originAnchor = document.createElement( "a" );
+	originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+	// dataTypeExpression is optional and defaults to "*"
+	return function( dataTypeExpression, func ) {
+
+		if ( typeof dataTypeExpression !== "string" ) {
+			func = dataTypeExpression;
+			dataTypeExpression = "*";
+		}
+
+		var dataType,
+			i = 0,
+			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+		if ( isFunction( func ) ) {
+
+			// For each dataType in the dataTypeExpression
+			while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+				// Prepend if requested
+				if ( dataType[ 0 ] === "+" ) {
+					dataType = dataType.slice( 1 ) || "*";
+					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+				// Otherwise append
+				} else {
+					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+				}
+			}
+		}
+	};
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+	var inspected = {},
+		seekingTransport = ( structure === transports );
+
+	function inspect( dataType ) {
+		var selected;
+		inspected[ dataType ] = true;
+		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+			if ( typeof dataTypeOrTransport === "string" &&
+				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+				options.dataTypes.unshift( dataTypeOrTransport );
+				inspect( dataTypeOrTransport );
+				return false;
+			} else if ( seekingTransport ) {
+				return !( selected = dataTypeOrTransport );
+			}
+		} );
+		return selected;
+	}
+
+	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+	var key, deep,
+		flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+	for ( key in src ) {
+		if ( src[ key ] !== undefined ) {
+			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+		}
+	}
+	if ( deep ) {
+		jQuery.extend( true, target, deep );
+	}
+
+	return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+	var ct, type, finalDataType, firstDataType,
+		contents = s.contents,
+		dataTypes = s.dataTypes;
+
+	// Remove auto dataType and get content-type in the process
+	while ( dataTypes[ 0 ] === "*" ) {
+		dataTypes.shift();
+		if ( ct === undefined ) {
+			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+		}
+	}
+
+	// Check if we're dealing with a known content-type
+	if ( ct ) {
+		for ( type in contents ) {
+			if ( contents[ type ] && contents[ type ].test( ct ) ) {
+				dataTypes.unshift( type );
+				break;
+			}
+		}
+	}
+
+	// Check to see if we have a response for the expected dataType
+	if ( dataTypes[ 0 ] in responses ) {
+		finalDataType = dataTypes[ 0 ];
+	} else {
+
+		// Try convertible dataTypes
+		for ( type in responses ) {
+			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+				finalDataType = type;
+				break;
+			}
+			if ( !firstDataType ) {
+				firstDataType = type;
+			}
+		}
+
+		// Or just use first one
+		finalDataType = finalDataType || firstDataType;
+	}
+
+	// If we found a dataType
+	// We add the dataType to the list if needed
+	// and return the corresponding response
+	if ( finalDataType ) {
+		if ( finalDataType !== dataTypes[ 0 ] ) {
+			dataTypes.unshift( finalDataType );
+		}
+		return responses[ finalDataType ];
+	}
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+	var conv2, current, conv, tmp, prev,
+		converters = {},
+
+		// Work with a copy of dataTypes in case we need to modify it for conversion
+		dataTypes = s.dataTypes.slice();
+
+	// Create converters map with lowercased keys
+	if ( dataTypes[ 1 ] ) {
+		for ( conv in s.converters ) {
+			converters[ conv.toLowerCase() ] = s.converters[ conv ];
+		}
+	}
+
+	current = dataTypes.shift();
+
+	// Convert to each sequential dataType
+	while ( current ) {
+
+		if ( s.responseFields[ current ] ) {
+			jqXHR[ s.responseFields[ current ] ] = response;
+		}
+
+		// Apply the dataFilter if provided
+		if ( !prev && isSuccess && s.dataFilter ) {
+			response = s.dataFilter( response, s.dataType );
+		}
+
+		prev = current;
+		current = dataTypes.shift();
+
+		if ( current ) {
+
+			// There's only work to do if current dataType is non-auto
+			if ( current === "*" ) {
+
+				current = prev;
+
+			// Convert response if prev dataType is non-auto and differs from current
+			} else if ( prev !== "*" && prev !== current ) {
+
+				// Seek a direct converter
+				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+				// If none found, seek a pair
+				if ( !conv ) {
+					for ( conv2 in converters ) {
+
+						// If conv2 outputs current
+						tmp = conv2.split( " " );
+						if ( tmp[ 1 ] === current ) {
+
+							// If prev can be converted to accepted input
+							conv = converters[ prev + " " + tmp[ 0 ] ] ||
+								converters[ "* " + tmp[ 0 ] ];
+							if ( conv ) {
+
+								// Condense equivalence converters
+								if ( conv === true ) {
+									conv = converters[ conv2 ];
+
+								// Otherwise, insert the intermediate dataType
+								} else if ( converters[ conv2 ] !== true ) {
+									current = tmp[ 0 ];
+									dataTypes.unshift( tmp[ 1 ] );
+								}
+								break;
+							}
+						}
+					}
+				}
+
+				// Apply converter (if not an equivalence)
+				if ( conv !== true ) {
+
+					// Unless errors are allowed to bubble, catch and return them
+					if ( conv && s.throws ) {
+						response = conv( response );
+					} else {
+						try {
+							response = conv( response );
+						} catch ( e ) {
+							return {
+								state: "parsererror",
+								error: conv ? e : "No conversion from " + prev + " to " + current
+							};
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+	// Counter for holding the number of active queries
+	active: 0,
+
+	// Last-Modified header cache for next request
+	lastModified: {},
+	etag: {},
+
+	ajaxSettings: {
+		url: location.href,
+		type: "GET",
+		isLocal: rlocalProtocol.test( location.protocol ),
+		global: true,
+		processData: true,
+		async: true,
+		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+		/*
+		timeout: 0,
+		data: null,
+		dataType: null,
+		username: null,
+		password: null,
+		cache: null,
+		throws: false,
+		traditional: false,
+		headers: {},
+		*/
+
+		accepts: {
+			"*": allTypes,
+			text: "text/plain",
+			html: "text/html",
+			xml: "application/xml, text/xml",
+			json: "application/json, text/javascript"
+		},
+
+		contents: {
+			xml: /\bxml\b/,
+			html: /\bhtml/,
+			json: /\bjson\b/
+		},
+
+		responseFields: {
+			xml: "responseXML",
+			text: "responseText",
+			json: "responseJSON"
+		},
+
+		// Data converters
+		// Keys separate source (or catchall "*") and destination types with a single space
+		converters: {
+
+			// Convert anything to text
+			"* text": String,
+
+			// Text to html (true = no transformation)
+			"text html": true,
+
+			// Evaluate text as a json expression
+			"text json": JSON.parse,
+
+			// Parse text as xml
+			"text xml": jQuery.parseXML
+		},
+
+		// For options that shouldn't be deep extended:
+		// you can add your own custom options here if
+		// and when you create one that shouldn't be
+		// deep extended (see ajaxExtend)
+		flatOptions: {
+			url: true,
+			context: true
+		}
+	},
+
+	// Creates a full fledged settings object into target
+	// with both ajaxSettings and settings fields.
+	// If target is omitted, writes into ajaxSettings.
+	ajaxSetup: function( target, settings ) {
+		return settings ?
+
+			// Building a settings object
+			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+			// Extending ajaxSettings
+			ajaxExtend( jQuery.ajaxSettings, target );
+	},
+
+	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+	ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+	// Main method
+	ajax: function( url, options ) {
+
+		// If url is an object, simulate pre-1.5 signature
+		if ( typeof url === "object" ) {
+			options = url;
+			url = undefined;
+		}
+
+		// Force options to be an object
+		options = options || {};
+
+		var transport,
+
+			// URL without anti-cache param
+			cacheURL,
+
+			// Response headers
+			responseHeadersString,
+			responseHeaders,
+
+			// timeout handle
+			timeoutTimer,
+
+			// Url cleanup var
+			urlAnchor,
+
+			// Request state (becomes false upon send and true upon completion)
+			completed,
+
+			// To know if global events are to be dispatched
+			fireGlobals,
+
+			// Loop variable
+			i,
+
+			// uncached part of the url
+			uncached,
+
+			// Create the final options object
+			s = jQuery.ajaxSetup( {}, options ),
+
+			// Callbacks context
+			callbackContext = s.context || s,
+
+			// Context for global events is callbackContext if it is a DOM node or jQuery collection
+			globalEventContext = s.context &&
+				( callbackContext.nodeType || callbackContext.jquery ) ?
+					jQuery( callbackContext ) :
+					jQuery.event,
+
+			// Deferreds
+			deferred = jQuery.Deferred(),
+			completeDeferred = jQuery.Callbacks( "once memory" ),
+
+			// Status-dependent callbacks
+			statusCode = s.statusCode || {},
+
+			// Headers (they are sent all at once)
+			requestHeaders = {},
+			requestHeadersNames = {},
+
+			// Default abort message
+			strAbort = "canceled",
+
+			// Fake xhr
+			jqXHR = {
+				readyState: 0,
+
+				// Builds headers hashtable if needed
+				getResponseHeader: function( key ) {
+					var match;
+					if ( completed ) {
+						if ( !responseHeaders ) {
+							responseHeaders = {};
+							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+								responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+									( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+										.concat( match[ 2 ] );
+							}
+						}
+						match = responseHeaders[ key.toLowerCase() + " " ];
+					}
+					return match == null ? null : match.join( ", " );
+				},
+
+				// Raw string
+				getAllResponseHeaders: function() {
+					return completed ? responseHeadersString : null;
+				},
+
+				// Caches the header
+				setRequestHeader: function( name, value ) {
+					if ( completed == null ) {
+						name = requestHeadersNames[ name.toLowerCase() ] =
+							requestHeadersNames[ name.toLowerCase() ] || name;
+						requestHeaders[ name ] = value;
+					}
+					return this;
+				},
+
+				// Overrides response content-type header
+				overrideMimeType: function( type ) {
+					if ( completed == null ) {
+						s.mimeType = type;
+					}
+					return this;
+				},
+
+				// Status-dependent callbacks
+				statusCode: function( map ) {
+					var code;
+					if ( map ) {
+						if ( completed ) {
+
+							// Execute the appropriate callbacks
+							jqXHR.always( map[ jqXHR.status ] );
+						} else {
+
+							// Lazy-add the new callbacks in a way that preserves old ones
+							for ( code in map ) {
+								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+							}
+						}
+					}
+					return this;
+				},
+
+				// Cancel the request
+				abort: function( statusText ) {
+					var finalText = statusText || strAbort;
+					if ( transport ) {
+						transport.abort( finalText );
+					}
+					done( 0, finalText );
+					return this;
+				}
+			};
+
+		// Attach deferreds
+		deferred.promise( jqXHR );
+
+		// Add protocol if not provided (prefilters might expect it)
+		// Handle falsy url in the settings object (#10093: consistency with old signature)
+		// We also use the url parameter if available
+		s.url = ( ( url || s.url || location.href ) + "" )
+			.replace( rprotocol, location.protocol + "//" );
+
+		// Alias method option to type as per ticket #12004
+		s.type = options.method || options.type || s.method || s.type;
+
+		// Extract dataTypes list
+		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+		// A cross-domain request is in order when the origin doesn't match the current origin.
+		if ( s.crossDomain == null ) {
+			urlAnchor = document.createElement( "a" );
+
+			// Support: IE <=8 - 11, Edge 12 - 15
+			// IE throws exception on accessing the href property if url is malformed,
+			// e.g. http://example.com:80x/
+			try {
+				urlAnchor.href = s.url;
+
+				// Support: IE <=8 - 11 only
+				// Anchor's host property isn't correctly set when s.url is relative
+				urlAnchor.href = urlAnchor.href;
+				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+					urlAnchor.protocol + "//" + urlAnchor.host;
+			} catch ( e ) {
+
+				// If there is an error parsing the URL, assume it is crossDomain,
+				// it can be rejected by the transport if it is invalid
+				s.crossDomain = true;
+			}
+		}
+
+		// Convert data if not already a string
+		if ( s.data && s.processData && typeof s.data !== "string" ) {
+			s.data = jQuery.param( s.data, s.traditional );
+		}
+
+		// Apply prefilters
+		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+		// If request was aborted inside a prefilter, stop there
+		if ( completed ) {
+			return jqXHR;
+		}
+
+		// We can fire global events as of now if asked to
+		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+		fireGlobals = jQuery.event && s.global;
+
+		// Watch for a new set of requests
+		if ( fireGlobals && jQuery.active++ === 0 ) {
+			jQuery.event.trigger( "ajaxStart" );
+		}
+
+		// Uppercase the type
+		s.type = s.type.toUpperCase();
+
+		// Determine if request has content
+		s.hasContent = !rnoContent.test( s.type );
+
+		// Save the URL in case we're toying with the If-Modified-Since
+		// and/or If-None-Match header later on
+		// Remove hash to simplify url manipulation
+		cacheURL = s.url.replace( rhash, "" );
+
+		// More options handling for requests with no content
+		if ( !s.hasContent ) {
+
+			// Remember the hash so we can put it back
+			uncached = s.url.slice( cacheURL.length );
+
+			// If data is available and should be processed, append data to url
+			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+				// #9682: remove data so that it's not used in an eventual retry
+				delete s.data;
+			}
+
+			// Add or update anti-cache param if needed
+			if ( s.cache === false ) {
+				cacheURL = cacheURL.replace( rantiCache, "$1" );
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
+			}
+
+			// Put hash and anti-cache on the URL that will be requested (gh-1732)
+			s.url = cacheURL + uncached;
+
+		// Change '%20' to '+' if this is encoded form body content (gh-2658)
+		} else if ( s.data && s.processData &&
+			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+			s.data = s.data.replace( r20, "+" );
+		}
+
+		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+		if ( s.ifModified ) {
+			if ( jQuery.lastModified[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+			}
+			if ( jQuery.etag[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+			}
+		}
+
+		// Set the correct header, if data is being sent
+		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+			jqXHR.setRequestHeader( "Content-Type", s.contentType );
+		}
+
+		// Set the Accepts header for the server, depending on the dataType
+		jqXHR.setRequestHeader(
+			"Accept",
+			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+				s.accepts[ s.dataTypes[ 0 ] ] +
+					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+				s.accepts[ "*" ]
+		);
+
+		// Check for headers option
+		for ( i in s.headers ) {
+			jqXHR.setRequestHeader( i, s.headers[ i ] );
+		}
+
+		// Allow custom headers/mimetypes and early abort
+		if ( s.beforeSend &&
+			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+			// Abort if not done already and return
+			return jqXHR.abort();
+		}
+
+		// Aborting is no longer a cancellation
+		strAbort = "abort";
+
+		// Install callbacks on deferreds
+		completeDeferred.add( s.complete );
+		jqXHR.done( s.success );
+		jqXHR.fail( s.error );
+
+		// Get transport
+		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+		// If no transport, we auto-abort
+		if ( !transport ) {
+			done( -1, "No Transport" );
+		} else {
+			jqXHR.readyState = 1;
+
+			// Send global event
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+			}
+
+			// If request was aborted inside ajaxSend, stop there
+			if ( completed ) {
+				return jqXHR;
+			}
+
+			// Timeout
+			if ( s.async && s.timeout > 0 ) {
+				timeoutTimer = window.setTimeout( function() {
+					jqXHR.abort( "timeout" );
+				}, s.timeout );
+			}
+
+			try {
+				completed = false;
+				transport.send( requestHeaders, done );
+			} catch ( e ) {
+
+				// Rethrow post-completion exceptions
+				if ( completed ) {
+					throw e;
+				}
+
+				// Propagate others as results
+				done( -1, e );
+			}
+		}
+
+		// Callback for when everything is done
+		function done( status, nativeStatusText, responses, headers ) {
+			var isSuccess, success, error, response, modified,
+				statusText = nativeStatusText;
+
+			// Ignore repeat invocations
+			if ( completed ) {
+				return;
+			}
+
+			completed = true;
+
+			// Clear timeout if it exists
+			if ( timeoutTimer ) {
+				window.clearTimeout( timeoutTimer );
+			}
+
+			// Dereference transport for early garbage collection
+			// (no matter how long the jqXHR object will be used)
+			transport = undefined;
+
+			// Cache response headers
+			responseHeadersString = headers || "";
+
+			// Set readyState
+			jqXHR.readyState = status > 0 ? 4 : 0;
+
+			// Determine if successful
+			isSuccess = status >= 200 && status < 300 || status === 304;
+
+			// Get response data
+			if ( responses ) {
+				response = ajaxHandleResponses( s, jqXHR, responses );
+			}
+
+			// Use a noop converter for missing script
+			if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
+			// Convert no matter what (that way responseXXX fields are always set)
+			response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+			// If successful, handle type chaining
+			if ( isSuccess ) {
+
+				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+				if ( s.ifModified ) {
+					modified = jqXHR.getResponseHeader( "Last-Modified" );
+					if ( modified ) {
+						jQuery.lastModified[ cacheURL ] = modified;
+					}
+					modified = jqXHR.getResponseHeader( "etag" );
+					if ( modified ) {
+						jQuery.etag[ cacheURL ] = modified;
+					}
+				}
+
+				// if no content
+				if ( status === 204 || s.type === "HEAD" ) {
+					statusText = "nocontent";
+
+				// if not modified
+				} else if ( status === 304 ) {
+					statusText = "notmodified";
+
+				// If we have data, let's convert it
+				} else {
+					statusText = response.state;
+					success = response.data;
+					error = response.error;
+					isSuccess = !error;
+				}
+			} else {
+
+				// Extract error from statusText and normalize for non-aborts
+				error = statusText;
+				if ( status || !statusText ) {
+					statusText = "error";
+					if ( status < 0 ) {
+						status = 0;
+					}
+				}
+			}
+
+			// Set data for the fake xhr object
+			jqXHR.status = status;
+			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+			// Success/Error
+			if ( isSuccess ) {
+				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+			} else {
+				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+			}
+
+			// Status-dependent callbacks
+			jqXHR.statusCode( statusCode );
+			statusCode = undefined;
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+					[ jqXHR, s, isSuccess ? success : error ] );
+			}
+
+			// Complete
+			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+				// Handle the global AJAX counter
+				if ( !( --jQuery.active ) ) {
+					jQuery.event.trigger( "ajaxStop" );
+				}
+			}
+		}
+
+		return jqXHR;
+	},
+
+	getJSON: function( url, data, callback ) {
+		return jQuery.get( url, data, callback, "json" );
+	},
+
+	getScript: function( url, callback ) {
+		return jQuery.get( url, undefined, callback, "script" );
+	}
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+	jQuery[ method ] = function( url, data, callback, type ) {
+
+		// Shift arguments if data argument was omitted
+		if ( isFunction( data ) ) {
+			type = type || callback;
+			callback = data;
+			data = undefined;
+		}
+
+		// The url can be an options object (which then must have .url)
+		return jQuery.ajax( jQuery.extend( {
+			url: url,
+			type: method,
+			dataType: type,
+			data: data,
+			success: callback
+		}, jQuery.isPlainObject( url ) && url ) );
+	};
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+	return jQuery.ajax( {
+		url: url,
+
+		// Make this explicit, since user can override this through ajaxSetup (#11264)
+		type: "GET",
+		dataType: "script",
+		cache: true,
+		async: false,
+		global: false,
+
+		// Only evaluate the response if it is successful (gh-4126)
+		// dataFilter is not invoked for failure responses, so using it instead
+		// of the default converter is kludgy but it works.
+		converters: {
+			"text script": function() {}
+		},
+		dataFilter: function( response ) {
+			jQuery.globalEval( response, options, doc );
+		}
+	} );
+};
+
+
+jQuery.fn.extend( {
+	wrapAll: function( html ) {
+		var wrap;
+
+		if ( this[ 0 ] ) {
+			if ( isFunction( html ) ) {
+				html = html.call( this[ 0 ] );
+			}
+
+			// The elements to wrap the target around
+			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+			if ( this[ 0 ].parentNode ) {
+				wrap.insertBefore( this[ 0 ] );
+			}
+
+			wrap.map( function() {
+				var elem = this;
+
+				while ( elem.firstElementChild ) {
+					elem = elem.firstElementChild;
+				}
+
+				return elem;
+			} ).append( this );
+		}
+
+		return this;
+	},
+
+	wrapInner: function( html ) {
+		if ( isFunction( html ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).wrapInner( html.call( this, i ) );
+			} );
+		}
+
+		return this.each( function() {
+			var self = jQuery( this ),
+				contents = self.contents();
+
+			if ( contents.length ) {
+				contents.wrapAll( html );
+
+			} else {
+				self.append( html );
+			}
+		} );
+	},
+
+	wrap: function( html ) {
+		var htmlIsFunction = isFunction( html );
+
+		return this.each( function( i ) {
+			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+		} );
+	},
+
+	unwrap: function( selector ) {
+		this.parent( selector ).not( "body" ).each( function() {
+			jQuery( this ).replaceWith( this.childNodes );
+		} );
+		return this;
+	}
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+	return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+	try {
+		return new window.XMLHttpRequest();
+	} catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+		// File protocol always yields status code 0, assume 200
+		0: 200,
+
+		// Support: IE <=9 only
+		// #1450: sometimes IE returns 1223 when it should be 204
+		1223: 204
+	},
+	xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+	var callback, errorCallback;
+
+	// Cross domain only allowed if supported through XMLHttpRequest
+	if ( support.cors || xhrSupported && !options.crossDomain ) {
+		return {
+			send: function( headers, complete ) {
+				var i,
+					xhr = options.xhr();
+
+				xhr.open(
+					options.type,
+					options.url,
+					options.async,
+					options.username,
+					options.password
+				);
+
+				// Apply custom fields if provided
+				if ( options.xhrFields ) {
+					for ( i in options.xhrFields ) {
+						xhr[ i ] = options.xhrFields[ i ];
+					}
+				}
+
+				// Override mime type if needed
+				if ( options.mimeType && xhr.overrideMimeType ) {
+					xhr.overrideMimeType( options.mimeType );
+				}
+
+				// X-Requested-With header
+				// For cross-domain requests, seeing as conditions for a preflight are
+				// akin to a jigsaw puzzle, we simply never set it to be sure.
+				// (it can always be set on a per-request basis or even using ajaxSetup)
+				// For same-domain requests, won't change header if already provided.
+				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+					headers[ "X-Requested-With" ] = "XMLHttpRequest";
+				}
+
+				// Set headers
+				for ( i in headers ) {
+					xhr.setRequestHeader( i, headers[ i ] );
+				}
+
+				// Callback
+				callback = function( type ) {
+					return function() {
+						if ( callback ) {
+							callback = errorCallback = xhr.onload =
+								xhr.onerror = xhr.onabort = xhr.ontimeout =
+									xhr.onreadystatechange = null;
+
+							if ( type === "abort" ) {
+								xhr.abort();
+							} else if ( type === "error" ) {
+
+								// Support: IE <=9 only
+								// On a manual native abort, IE9 throws
+								// errors on any property access that is not readyState
+								if ( typeof xhr.status !== "number" ) {
+									complete( 0, "error" );
+								} else {
+									complete(
+
+										// File: protocol always yields status 0; see #8605, #14207
+										xhr.status,
+										xhr.statusText
+									);
+								}
+							} else {
+								complete(
+									xhrSuccessStatus[ xhr.status ] || xhr.status,
+									xhr.statusText,
+
+									// Support: IE <=9 only
+									// IE9 has no XHR2 but throws on binary (trac-11426)
+									// For XHR2 non-text, let the caller handle it (gh-2498)
+									( xhr.responseType || "text" ) !== "text"  ||
+									typeof xhr.responseText !== "string" ?
+										{ binary: xhr.response } :
+										{ text: xhr.responseText },
+									xhr.getAllResponseHeaders()
+								);
+							}
+						}
+					};
+				};
+
+				// Listen to events
+				xhr.onload = callback();
+				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+				// Support: IE 9 only
+				// Use onreadystatechange to replace onabort
+				// to handle uncaught aborts
+				if ( xhr.onabort !== undefined ) {
+					xhr.onabort = errorCallback;
+				} else {
+					xhr.onreadystatechange = function() {
+
+						// Check readyState before timeout as it changes
+						if ( xhr.readyState === 4 ) {
+
+							// Allow onerror to be called first,
+							// but that will not handle a native abort
+							// Also, save errorCallback to a variable
+							// as xhr.onerror cannot be accessed
+							window.setTimeout( function() {
+								if ( callback ) {
+									errorCallback();
+								}
+							} );
+						}
+					};
+				}
+
+				// Create the abort callback
+				callback = callback( "abort" );
+
+				try {
+
+					// Do send the request (this may raise an exception)
+					xhr.send( options.hasContent && options.data || null );
+				} catch ( e ) {
+
+					// #14683: Only rethrow if this hasn't been notified as an error yet
+					if ( callback ) {
+						throw e;
+					}
+				}
+			},
+
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+	if ( s.crossDomain ) {
+		s.contents.script = false;
+	}
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+	accepts: {
+		script: "text/javascript, application/javascript, " +
+			"application/ecmascript, application/x-ecmascript"
+	},
+	contents: {
+		script: /\b(?:java|ecma)script\b/
+	},
+	converters: {
+		"text script": function( text ) {
+			jQuery.globalEval( text );
+			return text;
+		}
+	}
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+	if ( s.cache === undefined ) {
+		s.cache = false;
+	}
+	if ( s.crossDomain ) {
+		s.type = "GET";
+	}
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+	// This transport only deals with cross domain or forced-by-attrs requests
+	if ( s.crossDomain || s.scriptAttrs ) {
+		var script, callback;
+		return {
+			send: function( _, complete ) {
+				script = jQuery( "<script>" )
+					.attr( s.scriptAttrs || {} )
+					.prop( { charset: s.scriptCharset, src: s.url } )
+					.on( "load error", callback = function( evt ) {
+						script.remove();
+						callback = null;
+						if ( evt ) {
+							complete( evt.type === "error" ? 404 : 200, evt.type );
+						}
+					} );
+
+				// Use native DOM manipulation to avoid our domManip AJAX trickery
+				document.head.appendChild( script[ 0 ] );
+			},
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+var oldCallbacks = [],
+	rjsonp = /(=)\?(?=&|$)|\?\?/;
+
+// Default jsonp settings
+jQuery.ajaxSetup( {
+	jsonp: "callback",
+	jsonpCallback: function() {
+		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
+		this[ callback ] = true;
+		return callback;
+	}
+} );
+
+// Detect, normalize options and install callbacks for jsonp requests
+jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) {
+
+	var callbackName, overwritten, responseContainer,
+		jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ?
+			"url" :
+			typeof s.data === "string" &&
+				( s.contentType || "" )
+					.indexOf( "application/x-www-form-urlencoded" ) === 0 &&
+				rjsonp.test( s.data ) && "data"
+		);
+
+	// Handle iff the expected data type is "jsonp" or we have a parameter to set
+	if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) {
+
+		// Get callback name, remembering preexisting value associated with it
+		callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ?
+			s.jsonpCallback() :
+			s.jsonpCallback;
+
+		// Insert callback into url or form data
+		if ( jsonProp ) {
+			s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName );
+		} else if ( s.jsonp !== false ) {
+			s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName;
+		}
+
+		// Use data converter to retrieve json after script execution
+		s.converters[ "script json" ] = function() {
+			if ( !responseContainer ) {
+				jQuery.error( callbackName + " was not called" );
+			}
+			return responseContainer[ 0 ];
+		};
+
+		// Force json dataType
+		s.dataTypes[ 0 ] = "json";
+
+		// Install callback
+		overwritten = window[ callbackName ];
+		window[ callbackName ] = function() {
+			responseContainer = arguments;
+		};
+
+		// Clean-up function (fires after converters)
+		jqXHR.always( function() {
+
+			// If previous value didn't exist - remove it
+			if ( overwritten === undefined ) {
+				jQuery( window ).removeProp( callbackName );
+
+			// Otherwise restore preexisting value
+			} else {
+				window[ callbackName ] = overwritten;
+			}
+
+			// Save back as free
+			if ( s[ callbackName ] ) {
+
+				// Make sure that re-using the options doesn't screw things around
+				s.jsonpCallback = originalSettings.jsonpCallback;
+
+				// Save the callback name for future use
+				oldCallbacks.push( callbackName );
+			}
+
+			// Call if it was a function and we have a response
+			if ( responseContainer && isFunction( overwritten ) ) {
+				overwritten( responseContainer[ 0 ] );
+			}
+
+			responseContainer = overwritten = undefined;
+		} );
+
+		// Delegate to script
+		return "script";
+	}
+} );
+
+
+
+
+// Support: Safari 8 only
+// In Safari 8 documents created via document.implementation.createHTMLDocument
+// collapse sibling forms: the second one becomes a child of the first one.
+// Because of that, this security measure has to be disabled in Safari 8.
+// https://bugs.webkit.org/show_bug.cgi?id=137337
+support.createHTMLDocument = ( function() {
+	var body = document.implementation.createHTMLDocument( "" ).body;
+	body.innerHTML = "<form></form><form></form>";
+	return body.childNodes.length === 2;
+} )();
+
+
+// Argument "data" should be string of html
+// context (optional): If specified, the fragment will be created in this context,
+// defaults to document
+// keepScripts (optional): If true, will include scripts passed in the html string
+jQuery.parseHTML = function( data, context, keepScripts ) {
+	if ( typeof data !== "string" ) {
+		return [];
+	}
+	if ( typeof context === "boolean" ) {
+		keepScripts = context;
+		context = false;
+	}
+
+	var base, parsed, scripts;
+
+	if ( !context ) {
+
+		// Stop scripts or inline event handlers from being executed immediately
+		// by using document.implementation
+		if ( support.createHTMLDocument ) {
+			context = document.implementation.createHTMLDocument( "" );
+
+			// Set the base href for the created document
+			// so any parsed elements with URLs
+			// are based on the document's URL (gh-2965)
+			base = context.createElement( "base" );
+			base.href = document.location.href;
+			context.head.appendChild( base );
+		} else {
+			context = document;
+		}
+	}
+
+	parsed = rsingleTag.exec( data );
+	scripts = !keepScripts && [];
+
+	// Single tag
+	if ( parsed ) {
+		return [ context.createElement( parsed[ 1 ] ) ];
+	}
+
+	parsed = buildFragment( [ data ], context, scripts );
+
+	if ( scripts && scripts.length ) {
+		jQuery( scripts ).remove();
+	}
+
+	return jQuery.merge( [], parsed.childNodes );
+};
+
+
+/**
+ * Load a url into a page
+ */
+jQuery.fn.load = function( url, params, callback ) {
+	var selector, type, response,
+		self = this,
+		off = url.indexOf( " " );
+
+	if ( off > -1 ) {
+		selector = stripAndCollapse( url.slice( off ) );
+		url = url.slice( 0, off );
+	}
+
+	// If it's a function
+	if ( isFunction( params ) ) {
+
+		// We assume that it's the callback
+		callback = params;
+		params = undefined;
+
+	// Otherwise, build a param string
+	} else if ( params && typeof params === "object" ) {
+		type = "POST";
+	}
+
+	// If we have elements to modify, make the request
+	if ( self.length > 0 ) {
+		jQuery.ajax( {
+			url: url,
+
+			// If "type" variable is undefined, then "GET" method will be used.
+			// Make value of this field explicit since
+			// user can override it through ajaxSetup method
+			type: type || "GET",
+			dataType: "html",
+			data: params
+		} ).done( function( responseText ) {
+
+			// Save response for use in complete callback
+			response = arguments;
+
+			self.html( selector ?
+
+				// If a selector was specified, locate the right elements in a dummy div
+				// Exclude scripts to avoid IE 'Permission Denied' errors
+				jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+				// Otherwise use the full result
+				responseText );
+
+		// If the request succeeds, this function gets "data", "status", "jqXHR"
+		// but they are ignored because response was set above.
+		// If it fails, this function gets "jqXHR", "status", "error"
+		} ).always( callback && function( jqXHR, status ) {
+			self.each( function() {
+				callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] );
+			} );
+		} );
+	}
+
+	return this;
+};
+
+
+
+
+jQuery.expr.pseudos.animated = function( elem ) {
+	return jQuery.grep( jQuery.timers, function( fn ) {
+		return elem === fn.elem;
+	} ).length;
+};
+
+
+
+
+jQuery.offset = {
+	setOffset: function( elem, options, i ) {
+		var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+			position = jQuery.css( elem, "position" ),
+			curElem = jQuery( elem ),
+			props = {};
+
+		// Set position first, in-case top/left are set even on static elem
+		if ( position === "static" ) {
+			elem.style.position = "relative";
+		}
+
+		curOffset = curElem.offset();
+		curCSSTop = jQuery.css( elem, "top" );
+		curCSSLeft = jQuery.css( elem, "left" );
+		calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+			( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1;
+
+		// Need to be able to calculate position if either
+		// top or left is auto and position is either absolute or fixed
+		if ( calculatePosition ) {
+			curPosition = curElem.position();
+			curTop = curPosition.top;
+			curLeft = curPosition.left;
+
+		} else {
+			curTop = parseFloat( curCSSTop ) || 0;
+			curLeft = parseFloat( curCSSLeft ) || 0;
+		}
+
+		if ( isFunction( options ) ) {
+
+			// Use jQuery.extend here to allow modification of coordinates argument (gh-1848)
+			options = options.call( elem, i, jQuery.extend( {}, curOffset ) );
+		}
+
+		if ( options.top != null ) {
+			props.top = ( options.top - curOffset.top ) + curTop;
+		}
+		if ( options.left != null ) {
+			props.left = ( options.left - curOffset.left ) + curLeft;
+		}
+
+		if ( "using" in options ) {
+			options.using.call( elem, props );
+
+		} else {
+			if ( typeof props.top === "number" ) {
+				props.top += "px";
+			}
+			if ( typeof props.left === "number" ) {
+				props.left += "px";
+			}
+			curElem.css( props );
+		}
+	}
+};
+
+jQuery.fn.extend( {
+
+	// offset() relates an element's border box to the document origin
+	offset: function( options ) {
+
+		// Preserve chaining for setter
+		if ( arguments.length ) {
+			return options === undefined ?
+				this :
+				this.each( function( i ) {
+					jQuery.offset.setOffset( this, options, i );
+				} );
+		}
+
+		var rect, win,
+			elem = this[ 0 ];
+
+		if ( !elem ) {
+			return;
+		}
+
+		// Return zeros for disconnected and hidden (display: none) elements (gh-2310)
+		// Support: IE <=11 only
+		// Running getBoundingClientRect on a
+		// disconnected node in IE throws an error
+		if ( !elem.getClientRects().length ) {
+			return { top: 0, left: 0 };
+		}
+
+		// Get document-relative position by adding viewport scroll to viewport-relative gBCR
+		rect = elem.getBoundingClientRect();
+		win = elem.ownerDocument.defaultView;
+		return {
+			top: rect.top + win.pageYOffset,
+			left: rect.left + win.pageXOffset
+		};
+	},
+
+	// position() relates an element's margin box to its offset parent's padding box
+	// This corresponds to the behavior of CSS absolute positioning
+	position: function() {
+		if ( !this[ 0 ] ) {
+			return;
+		}
+
+		var offsetParent, offset, doc,
+			elem = this[ 0 ],
+			parentOffset = { top: 0, left: 0 };
+
+		// position:fixed elements are offset from the viewport, which itself always has zero offset
+		if ( jQuery.css( elem, "position" ) === "fixed" ) {
+
+			// Assume position:fixed implies availability of getBoundingClientRect
+			offset = elem.getBoundingClientRect();
+
+		} else {
+			offset = this.offset();
+
+			// Account for the *real* offset parent, which can be the document or its root element
+			// when a statically positioned element is identified
+			doc = elem.ownerDocument;
+			offsetParent = elem.offsetParent || doc.documentElement;
+			while ( offsetParent &&
+				( offsetParent === doc.body || offsetParent === doc.documentElement ) &&
+				jQuery.css( offsetParent, "position" ) === "static" ) {
+
+				offsetParent = offsetParent.parentNode;
+			}
+			if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) {
+
+				// Incorporate borders into its offset, since they are outside its content origin
+				parentOffset = jQuery( offsetParent ).offset();
+				parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true );
+				parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true );
+			}
+		}
+
+		// Subtract parent offsets and element margins
+		return {
+			top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+			left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true )
+		};
+	},
+
+	// This method will return documentElement in the following cases:
+	// 1) For the element inside the iframe without offsetParent, this method will return
+	//    documentElement of the parent window
+	// 2) For the hidden or detached element
+	// 3) For body or html element, i.e. in case of the html node - it will return itself
+	//
+	// but those exceptions were never presented as a real life use-cases
+	// and might be considered as more preferable results.
+	//
+	// This logic, however, is not guaranteed and can change at any point in the future
+	offsetParent: function() {
+		return this.map( function() {
+			var offsetParent = this.offsetParent;
+
+			while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) {
+				offsetParent = offsetParent.offsetParent;
+			}
+
+			return offsetParent || documentElement;
+		} );
+	}
+} );
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+	var top = "pageYOffset" === prop;
+
+	jQuery.fn[ method ] = function( val ) {
+		return access( this, function( elem, method, val ) {
+
+			// Coalesce documents and windows
+			var win;
+			if ( isWindow( elem ) ) {
+				win = elem;
+			} else if ( elem.nodeType === 9 ) {
+				win = elem.defaultView;
+			}
+
+			if ( val === undefined ) {
+				return win ? win[ prop ] : elem[ method ];
+			}
+
+			if ( win ) {
+				win.scrollTo(
+					!top ? val : win.pageXOffset,
+					top ? val : win.pageYOffset
+				);
+
+			} else {
+				elem[ method ] = val;
+			}
+		}, method, val, arguments.length );
+	};
+} );
+
+// Support: Safari <=7 - 9.1, Chrome <=37 - 49
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
+// getComputedStyle returns percent when specified for top/left/bottom/right;
+// rather than make the css module depend on the offset module, just check for it here
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
+	jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+		function( elem, computed ) {
+			if ( computed ) {
+				computed = curCSS( elem, prop );
+
+				// If curCSS returns percentage, fallback to offset
+				return rnumnonpx.test( computed ) ?
+					jQuery( elem ).position()[ prop ] + "px" :
+					computed;
+			}
+		}
+	);
+} );
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+	jQuery.each( { padding: "inner" + name, content: type, "": "outer" + name },
+		function( defaultExtra, funcName ) {
+
+		// Margin is only for outerHeight, outerWidth
+		jQuery.fn[ funcName ] = function( margin, value ) {
+			var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+				extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+			return access( this, function( elem, type, value ) {
+				var doc;
+
+				if ( isWindow( elem ) ) {
+
+					// $( window ).outerWidth/Height return w/h including scrollbars (gh-1729)
+					return funcName.indexOf( "outer" ) === 0 ?
+						elem[ "inner" + name ] :
+						elem.document.documentElement[ "client" + name ];
+				}
+
+				// Get document width or height
+				if ( elem.nodeType === 9 ) {
+					doc = elem.documentElement;
+
+					// Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height],
+					// whichever is greatest
+					return Math.max(
+						elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+						elem.body[ "offset" + name ], doc[ "offset" + name ],
+						doc[ "client" + name ]
+					);
+				}
+
+				return value === undefined ?
+
+					// Get width or height on the element, requesting but not forcing parseFloat
+					jQuery.css( elem, type, extra ) :
+
+					// Set width or height on the element
+					jQuery.style( elem, type, value, extra );
+			}, type, chainable ? margin : undefined, chainable );
+		};
+	} );
+} );
+
+
+jQuery.each( [
+	"ajaxStart",
+	"ajaxStop",
+	"ajaxComplete",
+	"ajaxError",
+	"ajaxSuccess",
+	"ajaxSend"
+], function( _i, type ) {
+	jQuery.fn[ type ] = function( fn ) {
+		return this.on( type, fn );
+	};
+} );
+
+
+
+
+jQuery.fn.extend( {
+
+	bind: function( types, data, fn ) {
+		return this.on( types, null, data, fn );
+	},
+	unbind: function( types, fn ) {
+		return this.off( types, null, fn );
+	},
+
+	delegate: function( selector, types, data, fn ) {
+		return this.on( types, selector, data, fn );
+	},
+	undelegate: function( selector, types, fn ) {
+
+		// ( namespace ) or ( selector, types [, fn] )
+		return arguments.length === 1 ?
+			this.off( selector, "**" ) :
+			this.off( types, selector || "**", fn );
+	},
+
+	hover: function( fnOver, fnOut ) {
+		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
+	}
+} );
+
+jQuery.each( ( "blur focus focusin focusout resize scroll click dblclick " +
+	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
+	function( _i, name ) {
+
+		// Handle event binding
+		jQuery.fn[ name ] = function( data, fn ) {
+			return arguments.length > 0 ?
+				this.on( name, null, data, fn ) :
+				this.trigger( name );
+		};
+	} );
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
+// Bind a function to a context, optionally partially applying any
+// arguments.
+// jQuery.proxy is deprecated to promote standards (specifically Function#bind)
+// However, it is not slated for removal any time soon
+jQuery.proxy = function( fn, context ) {
+	var tmp, args, proxy;
+
+	if ( typeof context === "string" ) {
+		tmp = fn[ context ];
+		context = fn;
+		fn = tmp;
+	}
+
+	// Quick check to determine if target is callable, in the spec
+	// this throws a TypeError, but we will just return undefined.
+	if ( !isFunction( fn ) ) {
+		return undefined;
+	}
+
+	// Simulated bind
+	args = slice.call( arguments, 2 );
+	proxy = function() {
+		return fn.apply( context || this, args.concat( slice.call( arguments ) ) );
+	};
+
+	// Set the guid of unique handler to the same of original handler, so it can be removed
+	proxy.guid = fn.guid = fn.guid || jQuery.guid++;
+
+	return proxy;
+};
+
+jQuery.holdReady = function( hold ) {
+	if ( hold ) {
+		jQuery.readyWait++;
+	} else {
+		jQuery.ready( true );
+	}
+};
+jQuery.isArray = Array.isArray;
+jQuery.parseJSON = JSON.parse;
+jQuery.nodeName = nodeName;
+jQuery.isFunction = isFunction;
+jQuery.isWindow = isWindow;
+jQuery.camelCase = camelCase;
+jQuery.type = toType;
+
+jQuery.now = Date.now;
+
+jQuery.isNumeric = function( obj ) {
+
+	// As of jQuery 3.0, isNumeric is limited to
+	// strings and numbers (primitives or objects)
+	// that can be coerced to finite numbers (gh-2662)
+	var type = jQuery.type( obj );
+	return ( type === "number" || type === "string" ) &&
+
+		// parseFloat NaNs numeric-cast false positives ("")
+		// ...but misinterprets leading-number strings, particularly hex literals ("0x...")
+		// subtraction forces infinities to NaN
+		!isNaN( obj - parseFloat( obj ) );
+};
+
+jQuery.trim = function( text ) {
+	return text == null ?
+		"" :
+		( text + "" ).replace( rtrim, "" );
+};
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+	define( "jquery", [], function() {
+		return jQuery;
+	} );
+}
+
+
+
+
+var
+
+	// Map over jQuery in case of overwrite
+	_jQuery = window.jQuery,
+
+	// Map over the $ in case of overwrite
+	_$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+	if ( window.$ === jQuery ) {
+		window.$ = _$;
+	}
+
+	if ( deep && window.jQuery === jQuery ) {
+		window.jQuery = _jQuery;
+	}
+
+	return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in AMD
+// (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === "undefined" ) {
+	window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+} );
diff --git a/build/_static/jquery.js b/build/_static/jquery.js
new file mode 100644
index 0000000000000000000000000000000000000000..b0614034ad3a95e4ae9f53c2b015eeb3e8d68bde
--- /dev/null
+++ b/build/_static/jquery.js
@@ -0,0 +1,2 @@
+/*! jQuery v3.5.1 | (c) JS Foundation and other contributors | jquery.org/license */
+!function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var 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index 0000000000000000000000000000000000000000..f2f97033da58372a837ab169351c6b8f34a109ad
--- /dev/null
+++ b/build/_static/js/tex-mml-chtml.js
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M.prototype.checkItem.call(this,t)},x.errors=Object.assign(Object.create(d.BaseItem.errors),{stop:["ExtraOpenMissingClose","Extra open brace or missing close brace"]}),x);function x(){return null!==M&&M.apply(this,arguments)||this}e.OpenItem=O;var S,E=(S=d.BaseItem,i(C,S),Object.defineProperty(C.prototype,"kind",{get:function(){return"close"},enumerable:!0,configurable:!0}),Object.defineProperty(C.prototype,"isClose",{get:function(){return!0},enumerable:!0,configurable:!0}),C);function C(){return null!==S&&S.apply(this,arguments)||this}e.CloseItem=E;var _,w=(_=d.BaseItem,i(A,_),Object.defineProperty(A.prototype,"kind",{get:function(){return"prime"},enumerable:!0,configurable:!0}),A.prototype.checkItem=function(t){var e=o(this.Peek(2),2),r=e[0],n=e[1];return!f.default.isType(r,"msubsup")||f.default.isType(r,"msup")?[[this.create("node","msup",[r,n]),t],!0]:(f.default.setChild(r,r.sup,n),[[r,t],!0])},A);function A(){return null!==_&&_.apply(this,arguments)||this}e.PrimeItem=w;var T,L=(T=d.BaseItem,i(N,T),Object.defineProperty(N.prototype,"kind",{get:function(){return"subsup"},enumerable:!0,configurable:!0}),N.prototype.checkItem=function(t){if(t.isKind("open")||t.isKind("left"))return d.BaseItem.success;var e=this.First,r=this.getProperty("position");if(t.isKind("mml")){if(this.getProperty("primes"))if(2!==r)f.default.setChild(e,2,this.getProperty("primes"));else{f.default.setProperty(this.getProperty("primes"),"variantForm",!0);var n=this.create("node","mrow",[this.getProperty("primes"),t.First]);t.First=n}return f.default.setChild(e,r,t.First),null!=this.getProperty("movesupsub")&&f.default.setProperty(e,"movesupsub",this.getProperty("movesupsub")),[[this.factory.create("mml",e)],!0]}if(T.prototype.checkItem.call(this,t)[1]){var i=this.getErrors(["","sub","sup"][r]);throw new(h.default.bind.apply(h.default,a([void 0,i[0],i[1]],i.splice(2))))}},N.errors=Object.assign(Object.create(d.BaseItem.errors),{stop:["MissingScript","Missing superscript or subscript 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null!=this.getProperty("thickness")&&f.default.setAttribute(e,"linethickness",this.getProperty("thickness")),(this.getProperty("open")||this.getProperty("close"))&&(f.default.setProperty(e,"withDelims",!0),e=p.default.fixedFence(this.factory.configuration,this.getProperty("open"),e,this.getProperty("close"))),[[this.factory.create("mml",e),t],!0]}return I.prototype.checkItem.call(this,t)},k.prototype.toString=function(){return"over["+this.getProperty("num")+" / "+this.nodes.join("; ")+"]"},k);function k(t){var e=I.call(this,t)||this;return e.setProperty("name","\\over"),e}e.OverItem=P;var R,j=(R=d.BaseItem,i(B,R),Object.defineProperty(B.prototype,"kind",{get:function(){return"left"},enumerable:!0,configurable:!0}),Object.defineProperty(B.prototype,"isOpen",{get:function(){return!0},enumerable:!0,configurable:!0}),B.prototype.checkItem=function(t){return 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it(){return null!==rt&&rt.apply(this,arguments)||this}e.MmlItem=nt;var ot,at=(ot=d.BaseItem,i(st,ot),Object.defineProperty(st.prototype,"kind",{get:function(){return"fn"},enumerable:!0,configurable:!0}),st.prototype.checkItem=function(t){var e=this.First;if(e){if(t.isOpen)return d.BaseItem.success;if(!t.isKind("fn")){var r=t.First;if(!t.isKind("mml")||!r)return[[e,t],!0];if(f.default.isType(r,"mstyle")&&r.childNodes.length&&f.default.isType(r.childNodes[0].childNodes[0],"mspace")||f.default.isType(r,"mspace"))return[[e,t],!0];f.default.isEmbellished(r)&&(r=f.default.getCoreMO(r));var n=f.default.getForm(r);if(null!=n&&[0,0,1,1,0,1,1,0,0,0][n[2]])return[[e,t],!0]}return[[e,this.create("token","mo",{texClass:u.TEXCLASS.NONE},c.entities.ApplyFunction),t],!0]}return ot.prototype.checkItem.apply(this,arguments)},st);function st(){return null!==ot&&ot.apply(this,arguments)||this}e.FnItem=at;var lt,ct=(lt=d.BaseItem,i(ut,lt),Object.defineProperty(ut.prototype,"kind",{get:function(){return"not"},enumerable:!0,configurable:!0}),ut.prototype.checkItem=function(t){var e,r,n;if(t.isKind("open")||t.isKind("left"))return d.BaseItem.success;if(t.isKind("mml")&&(f.default.isType(t.First,"mo")||f.default.isType(t.First,"mi")||f.default.isType(t.First,"mtext"))&&(e=t.First,1===(r=f.default.getText(e)).length&&!f.default.getProperty(e,"movesupsub")&&1===f.default.getChildren(e).length))return this.remap.contains(r)?(n=this.create("text",this.remap.lookup(r).char),f.default.setChild(e,0,n)):(n=this.create("text","\u0338"),f.default.appendChildren(e,[n])),[[t],!0];n=this.create("text","\u29f8");var i=this.create("node","mtext",[],{},n),o=this.create("node","mpadded",[i],{width:0});return[[e=this.create("node","TeXAtom",[o],{texClass:u.TEXCLASS.REL}),t],!0]},ut);function ut(){var t=null!==lt&&lt.apply(this,arguments)||this;return t.remap=l.MapHandler.getMap("not_remap"),t}e.NotItem=ct;var ht,pt=(ht=d.BaseItem,i(ft,ht),Object.defineProperty(ft.prototype,"kind",{get:function(){return"dots"},enumerable:!0,configurable:!0}),ft.prototype.checkItem=function(t){if(t.isKind("open")||t.isKind("left"))return d.BaseItem.success;var e=this.getProperty("ldots"),r=t.First;if(t.isKind("mml")&&f.default.isEmbellished(r)){var n=f.default.getTexClass(f.default.getCoreMO(r));n!==u.TEXCLASS.BIN&&n!==u.TEXCLASS.REL||(e=this.getProperty("cdots"))}return[[e,t],!0]},ft);function ft(){return null!==ht&&ht.apply(this,arguments)||this}e.DotsItem=pt;var dt,mt=(dt=d.BaseItem,i(yt,dt),Object.defineProperty(yt.prototype,"kind",{get:function(){return"array"},enumerable:!0,configurable:!0}),Object.defineProperty(yt.prototype,"isOpen",{get:function(){return!0},enumerable:!0,configurable:!0}),Object.defineProperty(yt.prototype,"copyEnv",{get:function(){return!1},enumerable:!0,configurable:!0}),yt.prototype.checkItem=function(t){if(!t.isClose||t.isKind("over"))return dt.prototype.checkItem.call(this,t);if(t.getProperty("isEntry"))return this.EndEntry(),this.clearEnv(),d.BaseItem.fail;if(t.getProperty("isCR"))return this.EndEntry(),this.EndRow(),this.clearEnv(),d.BaseItem.fail;this.EndTable(),this.clearEnv();var e=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var r=this.create("node","mtable",this.table,this.arraydef);4===this.frame.length?f.default.setAttribute(r,"frame",this.dashed?"dashed":"solid"):this.frame.length&&(this.arraydef.rowlines&&(this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")),r=this.create("node","menclose",[r],{notation:this.frame.join(" 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t;t=this.getProperty("isNumbered")&&3===this.row.length?(this.row.unshift(this.row.pop()),this.create("node","mlabeledtr",this.row)):this.create("node","mtr",this.row),this.table.push(t),this.row=[]},yt.prototype.EndTable=function(){(this.Size()||this.row.length)&&(this.EndEntry(),this.EndRow()),this.checkLines()},yt.prototype.checkLines=function(){if(this.arraydef.rowlines){var t=this.arraydef.rowlines.split(/ /);t.length===this.table.length?(this.frame.push("bottom"),t.pop(),this.arraydef.rowlines=t.join(" ")):t.length<this.table.length-1&&(this.arraydef.rowlines+=" none")}if(this.getProperty("rowspacing")){for(var e=this.arraydef.rowspacing.split(/ /);e.length<this.table.length;)e.push(this.getProperty("rowspacing")+"em");this.arraydef.rowspacing=e.join(" ")}},yt);function yt(){var t=null!==dt&&dt.apply(this,arguments)||this;return t.table=[],t.row=[],t.frame=[],t.hfill=[],t.arraydef={},t.dashed=!1,t}e.ArrayItem=mt;var vt,bt=(i(gt,vt=mt),Object.defineProperty(gt.prototype,"kind",{get:function(){return"eqnarray"},enumerable:!0,configurable:!0}),gt.prototype.EndEntry=function(){this.row.length&&p.default.fixInitialMO(this.factory.configuration,this.nodes);var t=this.create("node","mtd",this.nodes);this.row.push(t),this.Clear()},gt.prototype.EndRow=function(){var t="mtr",e=this.factory.configuration.tags.getTag();e&&(this.row=[e].concat(this.row),t="mlabeledtr"),this.factory.configuration.tags.clearTag();var r=this.create("node",t,this.row);this.table.push(r),this.row=[]},gt.prototype.EndTable=function(){vt.prototype.EndTable.call(this),this.factory.configuration.tags.end()},gt);function gt(t){for(var e=[],r=1;r<arguments.length;r++)e[r-1]=arguments[r];var n=vt.call(this,t)||this;return n.factory.configuration.tags.start(e[0],e[2],e[1]),n}e.EqnArrayItem=bt;var Mt,Ot=(Mt=d.BaseItem,i(xt,Mt),Object.defineProperty(xt.prototype,"kind",{get:function(){return"equation"},enumerable:!0,configurable:!0}),Object.defineProperty(xt.prototype,"isOpen",{get:function(){return!0},enumerable:!0,configurable:!0}),xt.prototype.checkItem=function(t){if(t.isKind("end")){var e=this.toMml(),r=this.factory.configuration.tags.getTag();return this.factory.configuration.tags.end(),[[r?this.factory.configuration.tags.enTag(e,r):e,t],!0]}if(t.isKind("stop"))throw new h.default("EnvMissingEnd","Missing \\end{%1}",this.getName());return Mt.prototype.checkItem.call(this,t)},xt);function xt(t){for(var e=[],r=1;r<arguments.length;r++)e[r-1]=arguments[r];var n=Mt.call(this,t)||this;return n.factory.configuration.tags.start("equation",!0,e[0]),n}e.EquationItem=Ot},function(t,e,r){"use strict";var f=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 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r,n,i;t.GetNext().match(/\d/)&&(t.string=t.string.substr(0,t.i+1)+" "+t.string.substr(t.i+1));var o=t.stack.Top();o.isKind("prime")?(i=(r=f(o.Peek(2),2))[0],n=r[1],t.stack.Pop()):i=(i=t.stack.Prev())||t.create("token","mi",{},"");var a=h.default.getProperty(i,"movesupsub"),s=h.default.isType(i,"msubsup")?i.sup:i.over;if(h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")&&h.default.getChildAt(i,i.sup)||h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&h.default.getChildAt(i,i.over)&&!h.default.getProperty(i,"subsupOK"))throw new m.default("DoubleExponent","Double exponent: use braces to clarify");h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")||(s=a?(h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&!h.default.getChildAt(i,i.over)||(i=t.create("node","munderover",[i],{movesupsub:!0})),i.over):(i=t.create("node","msubsup",[i])).sup),t.Push(t.itemFactory.create("subsup",i).setProperties({position:s,primes:n,movesupsub:a}))},i.Subscript=function(t,e){var r,n,i;t.GetNext().match(/\d/)&&(t.string=t.string.substr(0,t.i+1)+" "+t.string.substr(t.i+1));var o=t.stack.Top();o.isKind("prime")?(i=(r=f(o.Peek(2),2))[0],n=r[1],t.stack.Pop()):i=(i=t.stack.Prev())||t.create("token","mi",{},"");var a=h.default.getProperty(i,"movesupsub"),s=h.default.isType(i,"msubsup")?i.sub:i.under;if(h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")&&h.default.getChildAt(i,i.sub)||h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&h.default.getChildAt(i,i.under)&&!h.default.getProperty(i,"subsupOK"))throw new m.default("DoubleSubscripts","Double subscripts: use braces to clarify");h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")||(s=a?(h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&!h.default.getChildAt(i,i.under)||(i=t.create("node","munderover",[i],{movesupsub:!0})),i.under):(i=t.create("node","msubsup",[i])).sub),t.Push(t.itemFactory.create("subsup",i).setProperties({position:s,primes:n,movesupsub:a}))},i.Prime=function(t,e){var r=t.stack.Prev();if(r=r||t.create("node","mi"),h.default.isType(r,"msubsup")&&!h.default.isType(r,"msup")&&h.default.getChildAt(r,r.sup))throw new m.default("DoubleExponentPrime","Prime causes double exponent: use braces to clarify");var n="";for(t.i--;n+=o.entities.prime,t.i++,"'"===(e=t.GetNext())||e===o.entities.rquote;);n=["","\u2032","\u2033","\u2034","\u2057"][n.length]||n;var i=t.create("token","mo",{},n);t.Push(t.itemFactory.create("prime",r,i))},i.Comment=function(t,e){for(;t.i<t.string.length&&"\n"!==t.string.charAt(t.i);)t.i++},i.Hash=function(t,e){throw new m.default("CantUseHash1","You can't use 'macro parameter character #' in math mode")},i.SetFont=function(t,e,r){t.stack.env.font=r},i.SetStyle=function(t,e,r,n,i){t.stack.env.style=r,t.stack.env.level=i,t.Push(t.itemFactory.create("style").setProperty("styles",{displaystyle:n,scriptlevel:i}))},i.SetSize=function(t,e,r){t.stack.env.size=r,t.Push(t.itemFactory.create("style").setProperty("styles",{mathsize:r+"em"}))},i.Spacer=function(t,e,r){var n=t.create("node","mspace",[],{width:r}),i=t.create("node","mstyle",[n],{scriptlevel:0});t.Push(i)},i.LeftRight=function(t,e){var r=e.substr(1);t.Push(t.itemFactory.create(r).setProperty("delim",t.GetDelimiter(e)))},i.Middle=function(t,e){var r=t.GetDelimiter(e),n=t.create("node","TeXAtom",[],{texClass:p.TEXCLASS.CLOSE});if(t.Push(n),!t.stack.Top().isKind("left"))throw new m.default("MisplacedMiddle","%1 must be within \\left and \\right",t.currentCS);n=t.create("token","mo",{stretchy:!0},r),t.Push(n),n=t.create("node","TeXAtom",[],{texClass:p.TEXCLASS.OPEN}),t.Push(n)},i.NamedFn=function(t,e,r){r=r||e.substr(1);var n=t.create("token","mi",{texClass:p.TEXCLASS.OP},r);t.Push(t.itemFactory.create("fn",n))},i.NamedOp=function(t,e,r){r=(r=r||e.substr(1)).replace(/&thinsp;/,"\u2006");var n=t.create("token","mo",{movablelimits:!0,movesupsub:!0,form:y.TexConstant.Form.PREFIX,texClass:p.TEXCLASS.OP},r);t.Push(n)},i.Limits=function(t,e,r){var n=t.stack.Prev(!0);if(!n||h.default.getTexClass(h.default.getCoreMO(n))!==p.TEXCLASS.OP&&null==h.default.getProperty(n,"movesupsub"))throw new m.default("MisplacedLimits","%1 is allowed only on operators",t.currentCS);var i,o=t.stack.Top();h.default.isType(n,"munderover")&&!r?(i=t.create("node","msubsup"),h.default.copyChildren(n,i),n=o.Last=i):h.default.isType(n,"msubsup")&&r&&(i=t.create("node","munderover"),h.default.copyChildren(n,i),n=o.Last=i),h.default.setProperty(n,"movesupsub",!!r),h.default.setProperties(h.default.getCoreMO(n),{movablelimits:!1}),(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1})},i.Over=function(t,e,r,n){var i=t.itemFactory.create("over").setProperty("name",t.currentCS);r||n?(i.setProperty("open",r),i.setProperty("close",n)):e.match(/withdelims$/)&&(i.setProperty("open",t.GetDelimiter(e)),i.setProperty("close",t.GetDelimiter(e))),e.match(/^\\above/)?i.setProperty("thickness",t.GetDimen(e)):(e.match(/^\\atop/)||r||n)&&i.setProperty("thickness",0),t.Push(i)},i.Frac=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e),i=t.create("node","mfrac",[r,n]);t.Push(i)},i.Sqrt=function(t,e){var r=t.GetBrackets(e),n=t.GetArgument(e);"\\frac"===n&&(n+="{"+t.GetArgument(n)+"}{"+t.GetArgument(n)+"}");var i=new c.default(n,t.stack.env,t.configuration).mml();i=r?t.create("node","mroot",[i,a(t,r)]):t.create("node","msqrt",[i]),t.Push(i)},i.Root=function(t,e){var r=t.GetUpTo(e,"\\of"),n=t.ParseArg(e),i=t.create("node","mroot",[n,a(t,r)]);t.Push(i)},i.MoveRoot=function(t,e,r){if(!t.stack.env.inRoot)throw new m.default("MisplacedMoveRoot","%1 can appear only within a root",t.currentCS);if(t.stack.global[r])throw new m.default("MultipleMoveRoot","Multiple use of %1",t.currentCS);var n=t.GetArgument(e);if(!n.match(/-?[0-9]+/))throw new m.default("IntegerArg","The argument to %1 must be an integer",t.currentCS);"-"!==(n=parseInt(n,10)/15+"em").substr(0,1)&&(n="+"+n),t.stack.global[r]=n},i.Accent=function(t,e,r,n){var i=t.ParseArg(e),o=v.default.getFontDef(t);o.accent=!0;var a=h.default.createEntity(r),s=t.create("token","mo",o,a);h.default.setAttribute(s,"stretchy",!!n);var l=h.default.isEmbellished(i)?h.default.getCoreMO(i):i;h.default.isType(l,"mo")&&h.default.setProperties(l,{movablelimits:!1});var c=t.create("node","munderover");h.default.setChild(c,0,i),h.default.setChild(c,1,null),h.default.setChild(c,2,s);var u=t.create("node","TeXAtom",[c]);t.Push(u)},i.UnderOver=function(t,e,r,n,i){var o,a=t.ParseArg(e),s=h.default.getForm(a);(s&&s[3]&&s[3].movablelimits||h.default.getProperty(a,"movablelimits"))&&h.default.setProperties(a,{movablelimits:!1}),h.default.isType(a,"munderover")&&h.default.isEmbellished(a)&&(h.default.setProperties(h.default.getCoreMO(a),{lspace:0,rspace:0}),o=t.create("node","mo",[],{rspace:0}),a=t.create("node","mrow",[o,a]));var l=t.create("node","munderover",[a]),c=h.default.createEntity(r);o=t.create("token","mo",{stretchy:!0,accent:!i},c),h.default.setChild(l,"o"===e.charAt(1)?l.over:l.under,o);var u=l;n&&(u=t.create("node","TeXAtom",[l],{texClass:p.TEXCLASS.OP,movesupsub:!0})),h.default.setProperty(u,"subsupOK",!0),t.Push(u)},i.Overset=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e);(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1});var i=t.create("node","mover",[n,r]);t.Push(i)},i.Underset=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e);(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1});var i=t.create("node","munder",[n,r]);t.Push(i)},i.TeXAtom=function(t,e,r){var n,i,o,a={texClass:r};if(r===p.TEXCLASS.OP){a.movesupsub=a.movablelimits=!0;var s=t.GetArgument(e),l=s.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);i=l?(a.mathvariant=y.TexConstant.Variant.NORMAL,t.create("token","mi",a,l[1])):(o=new c.default(s,t.stack.env,t.configuration).mml(),t.create("node","TeXAtom",[o],a)),n=t.itemFactory.create("fn",i)}else o=t.ParseArg(e),n=t.create("node","TeXAtom",[o],a);t.Push(n)},i.MmlToken=function(t,e){var r,n=t.GetArgument(e),i=t.GetBrackets(e,"").replace(/^\s+/,""),o=t.GetArgument(e),a={};try{r=t.create("node",n)}catch(t){r=null}if(!r||!r.isToken)throw new m.default("NotMathMLToken","%1 is not a token element",n);for(;""!==i;){var s=i.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!s)throw new m.default("InvalidMathMLAttr","Invalid MathML attribute: %1",i);if(!r.attributes.hasDefault(s[1])&&!u[s[1]])throw new m.default("UnknownAttrForElement","%1 is not a recognized attribute for %2",s[1],n);var l=v.default.MmlFilterAttribute(t,s[1],s[2].replace(/^(['"])(.*)\1$/,"$2"));l&&("true"===l.toLowerCase()?l=!0:"false"===l.toLowerCase()&&(l=!1),a[s[1]]=l),i=i.substr(s[0].length)}var c=t.create("text",o);r.appendChild(c),h.default.setProperties(r,a),t.Push(r)},i.Strut=function(t,e){var r=t.create("node","mrow"),n=t.create("node","mpadded",[r],{height:"8.6pt",depth:"3pt",width:0});t.Push(n)},i.Phantom=function(t,e,r,n){var i=t.create("node","mphantom",[t.ParseArg(e)]);(r||n)&&(i=t.create("node","mpadded",[i]),n&&(h.default.setAttribute(i,"height",0),h.default.setAttribute(i,"depth",0)),r&&h.default.setAttribute(i,"width",0));var o=t.create("node","TeXAtom",[i]);t.Push(o)},i.Smash=function(t,e){var r=v.default.trimSpaces(t.GetBrackets(e,"")),n=t.create("node","mpadded",[t.ParseArg(e)]);switch(r){case"b":h.default.setAttribute(n,"depth",0);break;case"t":h.default.setAttribute(n,"height",0);break;default:h.default.setAttribute(n,"height",0),h.default.setAttribute(n,"depth",0)}var i=t.create("node","TeXAtom",[n]);t.Push(i)},i.Lap=function(t,e){var r=t.create("node","mpadded",[t.ParseArg(e)],{width:0});"\\llap"===e&&h.default.setAttribute(r,"lspace","-1width");var n=t.create("node","TeXAtom",[r]);t.Push(n)},i.RaiseLower=function(t,e){var r=t.GetDimen(e),n=t.itemFactory.create("position").setProperties({name:t.currentCS,move:"vertical"});"-"===r.charAt(0)&&(r=r.slice(1),e="raise"===e.substr(1)?"\\lower":"\\raise"),"\\lower"===e?(n.setProperty("dh","-"+r),n.setProperty("dd","+"+r)):(n.setProperty("dh","+"+r),n.setProperty("dd","-"+r)),t.Push(n)},i.MoveLeftRight=function(t,e){var r=t.GetDimen(e),n="-"===r.charAt(0)?r.slice(1):"-"+r;if("\\moveleft"===e){var i=r;r=n,n=i}t.Push(t.itemFactory.create("position").setProperties({name:t.currentCS,move:"horizontal",left:t.create("node","mspace",[],{width:r}),right:t.create("node","mspace",[],{width:n})}))},i.Hskip=function(t,e){var r=t.create("node","mspace",[],{width:t.GetDimen(e)});t.Push(r)},i.Rule=function(t,e,r){var n={width:t.GetDimen(e),height:t.GetDimen(e),depth:t.GetDimen(e)};"blank"!==r&&(n.mathbackground=t.stack.env.color||"black");var i=t.create("node","mspace",[],n);t.Push(i)},i.rule=function(t,e){var r=t.GetBrackets(e),n=t.GetDimen(e),i=t.GetDimen(e),o=t.create("node","mspace",[],{width:n,height:i,mathbackground:t.stack.env.color||"black"});r&&(o=t.create("node","mpadded",[o],{voffset:r}),r.match(/^\-/)?(h.default.setAttribute(o,"height",r),h.default.setAttribute(o,"depth","+"+r.substr(1))):h.default.setAttribute(o,"height","+"+r)),t.Push(o)},i.MakeBig=function(t,e,r,n){n*=1.2/.85;var i=String(n).replace(/(\.\d\d\d).+/,"$1")+"em",o=t.GetDelimiter(e,!0),a=t.create("token","mo",{minsize:i,maxsize:i,fence:!0,stretchy:!0,symmetric:!0},o),s=t.create("node","TeXAtom",[a],{texClass:r});t.Push(s)},i.BuildRel=function(t,e){var r=t.ParseUpTo(e,"\\over"),n=t.ParseArg(e),i=t.create("node","munderover");h.default.setChild(i,0,n),h.default.setChild(i,1,null),h.default.setChild(i,2,r);var o=t.create("node","TeXAtom",[i],{texClass:p.TEXCLASS.REL});t.Push(o)},i.HBox=function(t,e,r){t.PushAll(v.default.internalMath(t,t.GetArgument(e),r))},i.FBox=function(t,e){var r=v.default.internalMath(t,t.GetArgument(e)),n=t.create("node","menclose",r,{notation:"box"});t.Push(n)},i.Not=function(t,e){t.Push(t.itemFactory.create("not"))},i.Dots=function(t,e){var r=h.default.createEntity("2026"),n=h.default.createEntity("22EF"),i=t.create("token","mo",{stretchy:!1},r),o=t.create("token","mo",{stretchy:!1},n);t.Push(t.itemFactory.create("dots").setProperties({ldots:i,cdots:o}))},i.Matrix=function(t,e,r,n,i,o,a,s,l,c){var u=t.GetNext();if(""===u)throw new m.default("MissingArgFor","Missing argument for %1",t.currentCS);"{"===u?t.i++:(t.string=u+"}"+t.string.slice(t.i+1),t.i=0);var h=t.itemFactory.create("array").setProperty("requireClose",!0);h.arraydef={rowspacing:a||"4pt",columnspacing:o||"1em"},l&&h.setProperty("isCases",!0),c&&(h.setProperty("isNumbered",!0),h.arraydef.side=c),(r||n)&&(h.setProperty("open",r),h.setProperty("close",n)),"D"===s&&(h.arraydef.displaystyle=!0),null!=i&&(h.arraydef.columnalign=i),t.Push(h)},i.Entry=function(t,e){if(t.Push(t.itemFactory.create("cell").setProperties({isEntry:!0,name:e})),t.stack.Top().getProperty("isCases")){for(var r=t.string,n=0,i=-1,o=t.i,a=r.length;o<a;){var s=r.charAt(o);if("{"===s)n++,o++;else if("}"===s)0===n?a=0:(0===--n&&i<0&&(i=o-t.i),o++);else{if("&"===s&&0===n)throw new m.default("ExtraAlignTab","Extra alignment tab in \\cases text");"\\"===s?r.substr(o).match(/^((\\cr)[^a-zA-Z]|\\\\)/)?a=0:o+=2:o++}}var l=r.substr(t.i,o-t.i);if(!l.match(/^\s*\\text[^a-zA-Z]/)||i!==l.replace(/\s+$/,"").length-1){var 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e=this.standardCHTMLnode(t),r=this.getScriptData(),n=this.combinePrePost(r.sub,r.psub),i=this.combinePrePost(r.sup,r.psup),o=l(this.getUVQ(r.base,n,i),3),a=o[0],s=o[1];o[2],r.numPrescripts&&this.addScripts(a,-s,!0,r.psub,r.psup,this.firstPrescript,r.numPrescripts),this.childNodes[0].toCHTML(e),r.numScripts&&this.addScripts(a,-s,!1,r.sub,r.sup,1,r.numScripts)},h.prototype.addScripts=function(t,e,r,n,i,o,a){var s=this.adaptor,l=t-i.d+(e-n.h),c=t<0&&0===e?n.h+t:t,u=0<l?{style:{height:this.em(l)}}:{},h=c?{style:{"vertical-align":this.em(c)}}:{},p=this.html("mjx-row"),f=this.html("mjx-row",u),d=this.html("mjx-row"),m="mjx-"+(r?"pre":"")+"scripts";s.append(this.chtml,this.html(m,h,[p,f,d]));for(var y=o+2*a;o<y;)this.childNodes[o++].toCHTML(s.append(d,this.html("mjx-cell"))),this.childNodes[o++].toCHTML(s.append(p,this.html("mjx-cell")))},h.kind=c.MmlMmultiscripts.prototype.kind,h.styles={"mjx-prescripts":{display:"inline-table","padding-left":".05em"},"mjx-scripts":{display:"inline-table","padding-right":".05em"},"mjx-prescripts > mjx-row > mjx-cell":{"text-align":"right"}},h);function h(){return null!==o&&o.apply(this,arguments)||this}e.CHTMLmmultiscripts=u},function(t,s,e){"use strict";var n,r=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])})(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),d=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 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r=this.font.params.scriptspace,n=this.getScriptData(),i=this.combinePrePost(n.sub,n.psub),o=this.combinePrePost(n.sup,n.psup),a=d(this.getUVQ(n.base,i,o),2),s=a[0],l=a[1];if(t.empty(),n.numPrescripts&&(t.combine(n.psup,r,s),t.combine(n.psub,r,l)),t.append(n.base),n.numScripts){var c=t.w;t.combine(n.sup,c,s),t.combine(n.sub,c,l),t.w+=r}t.clean(),this.setChildPWidths(e)},e.prototype.getScriptData=function(){if(this.scriptData)return this.scriptData;var t=this.scriptData={base:null,sub:i.BBox.empty(),sup:i.BBox.empty(),psub:i.BBox.empty(),psup:i.BBox.empty(),numPrescripts:0,numScripts:0},e=this.getScriptBBoxLists();return this.combineBBoxLists(t.sub,t.sup,e.subList,e.supList),this.combineBBoxLists(t.psub,t.psup,e.psubList,e.psupList),this.scriptData.base=e.base[0],this.scriptData.numPrescripts=e.psubList.length,this.scriptData.numScripts=e.subList.length,this.scriptData},e.prototype.getScriptBBoxLists=function(){var 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i=d([0,0,0],3),o=i[0],a=i[1],s=i[2];0===e.h&&0===e.d?o=this.getU(t,r):0===r.h&&0===r.d?o=-this.getV(t,e):(o=(n=d(l.prototype.getUVQ.call(this,t,e,r),3))[0],a=n[1],s=n[2]),this.UVQ=[o,a,s]}return this.UVQ},e;function e(){var t=null!==l&&l.apply(this,arguments)||this;return t.scriptData=null,t.firstPrescript=0,t}var l}},function(t,e,r){"use strict";var n,i=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])})(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),y=this&&this.__values||function(t){var e="function"==typeof Symbol&&Symbol.iterator,r=e&&t[e],n=0;if(r)return r.call(t);if(t&&"number"==typeof t.length)return{next:function(){return t&&n>=t.length&&(t=void 0),{value:t&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 0===e||0<e--)&&!(n=o.next()).done;)a.push(n.value)}catch(t){i={error:t}}finally{try{n&&!n.done&&(r=o.return)&&r.call(o)}finally{if(i)throw i.error}}return a};Object.defineProperty(e,"__esModule",{value:!0});var o,a=r(3),s=r(163),l=r(63),h=r(8),c=(o=s.CommonMtableMixin(a.CHTMLWrapper),i(p,o),p.prototype.getAlignShift=function(){var t=o.prototype.getAlignShift.call(this);return this.isTop||(t[1]=0),t},p.prototype.toCHTML=function(t){var e,r,n=this.standardCHTMLnode(t);this.adaptor.append(n,this.html("mjx-table",{},[this.itable]));try{for(var i=y(this.childNodes),o=i.next();!o.done;o=i.next())o.value.toCHTML(this.itable)}catch(t){e={error:t}}finally{try{o&&!o.done&&(r=i.return)&&r.call(i)}finally{if(e)throw 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l=s.value,c=0;try{for(var u=(r=void 0,y(l.tableCells)),h=u.next();!h.done;h=u.next()){var p=h.value,f=i[c++],d=i[c],m=p?p.chtml:this.adaptor.childNodes(l.chtml)[c];(1<c&&"0.4em"!==f||o&&1===c)&&this.adaptor.setStyle(m,"paddingLeft",f),(c<this.numCols&&"0.4em"!==d||o&&c===this.numCols)&&this.adaptor.setStyle(m,"paddingRight",d)}}catch(t){r={error:t}}finally{try{h&&!h.done&&(n=u.return)&&n.call(u)}finally{if(r)throw r.error}}}}catch(t){e={error:t}}finally{try{s&&!s.done&&(t=a.return)&&t.call(a)}finally{if(e)throw e.error}}},p.prototype.handleColumnLines=function(){var e,t,r,n;if("none"!==this.node.attributes.get("columnlines")){var i=this.getColumnAttributes("columnlines");try{for(var o=y(this.childNodes),a=o.next();!a.done;a=o.next()){var s=a.value,l=0;try{for(var c=(r=void 0,y(this.adaptor.childNodes(s.chtml).slice(1))),u=c.next();!u.done;u=c.next()){var h=u.value,p=i[l++];"none"!==p&&this.adaptor.setStyle(h,"borderLeft",".07em 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s=y(this.childNodes),l=s.next();!l.done;l=s.next()){var c=l.value,u=i[a++],h=i[a];try{for(var p=(r=void 0,y(c.childNodes)),f=p.next();!f.done;f=p.next()){var d=f.value;(1<a&&"0.215em"!==u||o&&1===a)&&this.adaptor.setStyle(d.chtml,"paddingTop",u),(a<this.numRows&&"0.215em"!==h||o&&a===this.numRows)&&this.adaptor.setStyle(d.chtml,"paddingBottom",h)}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=p.return)&&n.call(p)}finally{if(r)throw r.error}}}}catch(t){e={error:t}}finally{try{l&&!l.done&&(t=s.return)&&t.call(s)}finally{if(e)throw e.error}}},p.prototype.handleRowLines=function(){var e,t,r,n;if("none"!==this.node.attributes.get("rowlines")){var i=this.getRowAttributes("rowlines"),o=0;try{for(var a=y(this.childNodes.slice(1)),s=a.next();!s.done;s=a.next()){var l=s.value,c=i[o++];if("none"!==c)try{for(var u=(r=void 0,y(this.adaptor.childNodes(l.chtml))),h=u.next();!h.done;h=u.next()){var p=h.value;this.adaptor.setStyle(p,"borderTop",".07em 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i=t.node.attributes.get("rowalign");if("baseline"===i||"axis"===i){var o=this.adaptor,a=o.lastChild(t.chtml);o.setStyle(a,"height",this.em(r)),o.setStyle(a,"verticalAlign",this.em(-n));var s=t.parent;if(!(s.node.isKind("mlabeledtr")&&t===s.childNodes[0]||"baseline"!==e&&"axis"!==e))return!0}return!1},p.prototype.handleFrame=function(){this.frame&&this.adaptor.setStyle(this.itable,"border",".07em "+this.node.attributes.get("frame"))},p.prototype.handleWidth=function(){var t=this.adaptor,e=this.getBBox(),r=e.w,n=e.L,i=e.R;t.setStyle(this.chtml,"minWidth",this.em(n+r+i));var o=this.node.attributes.get("width");if(h.isPercent(o))t.setStyle(this.chtml,"width",""),t.setAttribute(this.chtml,"width","full");else if(!this.hasLabels){if("auto"===o)return;o=this.em(this.length2em(o)+2*this.fLine)}var a=t.firstChild(this.chtml);t.setStyle(a,"width",o),t.setStyle(a,"minWidth",this.em(r)),(n||i)&&(t.setStyle(this.chtml,"margin",""),n===i?t.setStyle(a,"margin","0 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e=u(this.getPadAlignShift(t),3),r=(e[0],e[1]),n=e[2],i={};if("right"===t){var o=this.node.attributes.get("width"),a=this.getBBox(),s=a.w,l=a.L,c=a.R;i.style={width:h.isPercent(o)?"calc("+o+" + "+this.em(l+c)+")":this.em(l+s+c)}}return this.adaptor.append(this.chtml,this.html("mjx-labels",i,[this.labels])),[r,n]},p.prototype.updateRowHeights=function(){if(!this.node.attributes.get("equalrows"))for(var t=this.getTableData(),e=t.H,r=t.D,n=t.NH,i=t.ND,o=this.getRowHalfSpacing(),a=0;a<this.numRows;a++){var s=this.childNodes[a];e[a]!==n[a]||r[a]!==i[a]?this.setRowHeight(s,e[a]+r[a],r[a],o[a]+o[a+1]):s.node.isKind("mlabeledtr")&&this.setCellBaseline(s.childNodes[0],"",e[a]+r[a],r[a])}},p.prototype.addLabelSpacing=function(){for(var t=this.adaptor,e=this.node.attributes.get("equalrows"),r=this.getTableData(),n=r.H,i=r.D,o=e?this.getEqualRowHeight():0,a=this.getRowHalfSpacing(),s=this.fLine,l=t.firstChild(this.labels),c=0;c<this.numRows;c++)this.childNodes[c].node.isKind("mlabeledtr")?(s&&t.insert(this.html("mjx-mtr",{style:{height:this.em(s)}}),l),t.setStyle(l,"height",this.em((e?o:n[c]+i[c])+a[c]+a[c+1])),l=t.next(l),s=this.rLines[c]):s+=a[c]+(e?o:n[c]+i[c])+a[c+1]+this.rLines[c]},p.kind=l.MmlMtable.prototype.kind,p.styles={"mjx-mtable":{"vertical-align":".25em","text-align":"center",position:"relative","box-sizing":"border-box"},"mjx-labels":{position:"absolute",left:0,top:0},"mjx-table":{display:"inline-block","vertical-align":"-.5ex"},"mjx-table > mjx-itable":{"vertical-align":"middle","text-align":"left","box-sizing":"border-box"},"mjx-labels > mjx-itable":{position:"absolute",top:0},'mjx-mtable[justify="left"]':{"text-align":"left"},'mjx-mtable[justify="right"]':{"text-align":"right"},'mjx-mtable[justify="left"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="left"][side="right"]':{"padding-left":"0 ! important"},'mjx-mtable[justify="right"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="right"][side="right"]':{"padding-left":"0 ! important"},"mjx-mtable[align]":{"vertical-align":"baseline"},'mjx-mtable[align="top"] > mjx-table':{"vertical-align":"top"},'mjx-mtable[align="bottom"] > mjx-table':{"vertical-align":"bottom"},'mjx-mtable[side="right"] mjx-labels':{"min-width":"100%"}},p);function p(t,e,r){void 0===r&&(r=null);var n=o.call(this,t,e,r)||this;return n.itable=n.html("mjx-itable"),n.labels=n.html("mjx-itable"),n}e.CHTMLmtable=c},function(t,e,r){"use strict";var n,o=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof 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e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return"number"==typeof e.cWidths[t]?e.cWidths[t]:r[t]});return this.node.attributes.get("equalcolumns")&&(t=Array(t.length).fill(b.max(t))),t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):v.isPercent(t)?this.getColumnWidthsPercent(e,t):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);if("auto"===t){var n=this.getTableData().W;e=b.max(n)}else if(v.isPercent(t))e=this.percent(1/r);else{var i=b.sum([].concat(this.cLines,this.cSpace))+2*this.fSpace[0];e=Math.max(0,this.length2em(t)-i)/r}return Array(this.numCols).fill(e)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return 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r=this.node.attributes.get("equalrows"),n=this.getTableData(),i=n.H,o=n.D,a=r?this.getEqualRowHeight():0,s=this.getRowHalfSpacing(),l=this.fLine,c=0;c<t;c++)l+=s[c]+(r?a:i[c]+o[c])+s[c+1]+this.rLines[c];var u=y(r?[(a+i[t]-o[t])/2,(a-i[t]+o[t])/2]:[i[t],o[t]],2),h=u[0],p=u[1];return l+={top:0,center:s[t]+(h+p)/2,bottom:s[t]+h+p+s[t+1],baseline:s[t]+h,axis:s[t]+h-.25}[e]||0},e.prototype.getEmHalfSpacing=function(t,e){var r=this.em(t),n=this.addEm(e,2);return n.unshift(r),n.push(r),n},e.prototype.getRowHalfSpacing=function(){var t=this.rSpace.map(function(t){return t/2});return t.unshift(this.fSpace[1]),t.push(this.fSpace[1]),t},e.prototype.getColumnHalfSpacing=function(){var t=this.cSpace.map(function(t){return t/2});return t.unshift(this.fSpace[0]),t.push(this.fSpace[0]),t},e.prototype.getAlignmentRow=function(){var t=y(v.split(this.node.attributes.get("align")),2),e=t[0],r=t[1];if(null==r)return[e,null];var n=parseInt(r);return 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n=u(Object.keys(this.settings)),i=n.next();!i.done;i=n.next()){var o=i.value;this.settings[o]!==this.defaultSettings[o]&&(r[o]=this.settings[o])}}catch(t){e={error:t}}finally{try{i&&!i.done&&(t=n.return)&&t.call(n)}finally{if(e)throw e.error}}try{Object.keys(r).length?localStorage.setItem(d.MENU_STORAGE,JSON.stringify(r)):localStorage.removeItem(d.MENU_STORAGE)}catch(t){console.log("MathJax localStorage error: "+t.message)}},d.prototype.setA11y=function(t){h._.a11y&&h._.a11y.explorer&&h._.a11y.explorer_ts.setA11yOptions(this.document,t)},d.prototype.getA11y=function(t){if(h._.a11y&&h._.a11y.explorer)return this.document.options.a11y[t]},d.prototype.setScale=function(t){this.document.outputJax.options.scale=parseFloat(t),this.document.rerender()},d.prototype.setRenderer=function(e){var r=this;if(this.jax[e])this.setOutputJax(e);else{var n=e.toLowerCase();this.loadComponent("output/"+n,function(){var t=h.startup;n in t.constructors&&(t.useOutput(n,!0),t.output=t.getOutputJax(),r.jax[e]=t.output,r.setOutputJax(e))})}},d.prototype.setOutputJax=function(t){this.jax[t].setAdaptor(this.document.adaptor),this.document.outputJax=this.jax[t],this.rerender()},d.prototype.setTabOrder=function(t){this.menu.getStore().inTaborder(t)},d.prototype.setAssistiveMml=function(t){!t||h._.a11y&&h._.a11y["assistive-mml"]?this.rerender():this.loadA11y("assistive-mml")},d.prototype.setExplorer=function(t){this.enableExplorerItems(t),!t||h._.a11y&&h._.a11y.explorer?this.rerender(this.settings.collapsible?c.STATE.RERENDER:c.STATE.COMPILED):this.loadA11y("explorer")},d.prototype.setCollapsible=function(t){!t||h._.a11y&&h._.a11y.complexity?this.rerender(c.STATE.COMPILED):this.loadA11y("complexity")},d.prototype.scaleAllMath=function(){var t=(100*parseFloat(this.settings.scale)).toFixed(1).replace(/.0$/,""),e=prompt("Scale all mathematics (compared to surrounding text) 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n=r.load(t).then(function(){d.loading--,d.loadingPromises.delete(t),e(),0===d.loading&&d._loadingPromise&&(d._loadingPromise=null,d._loadingOK())}).catch(function(t){d._loadingPromise?(d._loadingPromise=null,d._loadingFailed(t)):console.log(t)});d.loadingPromises.set(t,n)}}},d.prototype.loadA11y=function(r){var n=this,i=!c.STATE.ENRICHED;this.loadComponent("a11y/"+r,function(){var t=h.startup;o.mathjax.handlers.unregister(t.handler),t.handler=t.getHandler(),o.mathjax.handlers.register(t.handler);var e=n.document;n.document=t.document=t.getDocument(),(n.document.menu=n).transferMathList(e),n.document.processed=e.processed,d._loadingPromise||n.rerender("complexity"===r||i?c.STATE.COMPILED:c.STATE.TYPESET)})},d.prototype.transferMathList=function(t){var e,r,n=this.document.options.MathItem;try{for(var i=u(t.math),o=i.next();!o.done;o=i.next()){var a=o.value,s=new 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qt(t,e){var r=mt.call(this)||this;return r.title="",r.window=null,r.localSettings={left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},r.windowList=[],r.mobileFlag=!1,r.active=null,r.title=t,r.content=e||function(){return""},r}r=vt=vt||{},gt.prototype.getName=function(){return this.name},gt.prototype.getValue=function(t){try{return this.getter(t)}catch(t){r.MenuUtil.error(t,"Command of variable "+this.name+" failed.")}},gt.prototype.setValue=function(t,e){try{this.setter(t,e)}catch(t){r.MenuUtil.error(t,"Command of variable "+this.name+" failed.")}this.update()},gt.prototype.register=function(t){-1===this.items.indexOf(t)&&this.items.push(t)},gt.prototype.unregister=function(t){var e=this.items.indexOf(t);-1!==e&&this.items.splice(e,1)},gt.prototype.update=function(){this.items.forEach(function(t){return t.update()})},gt.prototype.registerCallback=function(e){this.items.forEach(function(t){return 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e in t)this.html.setAttribute(e,t[e])},Ct.prototype.getHtml=function(){return this.html||this.generateHtml(),this.html},Ct.prototype.setHtml=function(t){this.html=t,this.addEvents(t)},Ct.prototype.generateHtml=function(){var t=document.createElement("div");t.classList.add(this.className),t.setAttribute("role",this.role),this.setHtml(t)},Ct.prototype.focus=function(){var t=this.getHtml();t.setAttribute("tabindex","0"),t.focus()},Ct.prototype.unfocus=function(){var t=this.getHtml();t.hasAttribute("tabindex")&&t.setAttribute("tabindex","-1");try{t.blur()}catch(t){}},m=Ct,f.MenuElement=m,y=vt=vt||{},v=y.MenuElement,bt(_t,v),_t.prototype.getMenu=function(){return this.menu},_t.prototype.setMenu=function(t){this.menu=t},_t.prototype.getType=function(){return this.type},_t.prototype.hide=function(){this.hidden=!0,this.menu.generateMenu()},_t.prototype.show=function(){this.hidden=!1,this.menu.generateMenu()},_t.prototype.isHidden=function(){return this.hidden},b=_t,y.AbstractEntry=b,g=vt=vt||{},M=g.MenuElement,bt(wt,M),wt.prototype.isPosted=function(){return this.posted},wt.prototype.post=function(t,e){this.posted||(void 0!==t&&void 0!==e&&this.getHtml().setAttribute("style","left: "+t+"px; top: "+e+"px;"),this.display(),this.posted=!0)},wt.prototype.unpost=function(){if(this.posted){var t=this.getHtml();t.parentNode&&t.parentNode.removeChild(t),this.posted=!1}},O=wt,g.AbstractPostable=O,x=vt=vt||{},S=x.AbstractPostable,bt(At,S),At.prototype.getItems=function(){return this.items},At.prototype.getPool=function(){return this.variablePool},At.prototype.getFocused=function(){return this.focused},At.prototype.setFocused=function(t){if(this.focused!==t){this.focused||this.unfocus();var e=this.focused;this.focused=t,e&&e.unfocus()}},At.prototype.up=function(t){var e=this.getItems().filter(function(t){return t instanceof x.AbstractItem&&!t.isHidden()});if(0!==e.length)if(this.focused){var r=e.indexOf(this.focused);-1!==r&&e[r=r?--r:e.length-1].focus()}else e[e.length-1].focus()},At.prototype.down=function(t){var e=this.getItems().filter(function(t){return t instanceof x.AbstractItem&&!t.isHidden()});if(0!==e.length)if(this.focused){var r=e.indexOf(this.focused);-1!==r&&e[r=++r===e.length?0:r].focus()}else e[0].focus()},At.prototype.generateHtml=function(){S.prototype.generateHtml.call(this),this.generateMenu()},At.prototype.generateMenu=function(){var t=this.getHtml();t.classList.add(x.HtmlClasses.MENU);for(var e=0,r=this.items;e<r.length;e++){var n=r[e];if(n.isHidden()){var i=n.getHtml();i.parentNode&&i.parentNode.removeChild(i)}else t.appendChild(n.getHtml())}},At.prototype.post=function(t,e){this.variablePool.update(),S.prototype.post.call(this,t,e)},At.prototype.unpostSubmenus=function(){for(var t=0,e=this.items.filter(function(t){return t instanceof x.Submenu});t<e.length;t++){var r=e[t];r.getSubmenu().unpost(),r!==this.getFocused()&&r.unfocus()}},At.prototype.unpost=function(){S.prototype.unpost.call(this),this.unpostSubmenus(),this.setFocused(null)},At.prototype.find=function(t){for(var e=0,r=this.getItems();e<r.length;e++){var n=r[e];if("rule"!==n.getType()){if(n.getId()===t)return n;if("submenu"===n.getType()){var i=n.getSubmenu().find(t);if(i)return i}}}return null},At.prototype.parseItems=function(t){var e=this;t.map(function(t){return[e.parseItem.bind(e)(t),t.hidden]}).forEach(function(t){return t[1]&&t[0].hide()})},At.prototype.parseItem=function(t){var e={checkbox:x.Checkbox.parse,combo:x.Combo.parse,command:x.Command.parse,label:x.Label.parse,radio:x.Radio.parse,rule:x.Rule.parse,submenu:x.Submenu.parse}[t.type];if(e){var r=e(t,this);return this.getItems().push(r),t.disabled&&r.disable(),r}},E=At,x.AbstractMenu=E,C=vt=vt||{},Tt.prototype.setActive=function(t){do{if(-1!==this.store.indexOf(t)){this.active=t;break}t=t.parentNode}while(t)},Tt.prototype.getActive=function(){return this.active},Tt.prototype.next=function(){var t=this.store.length;if(0===t)return this.active=null;var e=this.store.indexOf(this.active);return e=-1!==e&&e<t-1?e+1:0,this.active=this.store[e],this.active},Tt.prototype.previous=function(){var t=this.store.length;if(0===t)return this.active=null;var e=t-1,r=this.store.indexOf(this.active);return r=-1===r||0===r?e:r-1,this.active=this.store[r],this.active},Tt.prototype.clear=function(){this.remove(this.store)},Tt.prototype.insert=function(t){for(var e=0,r=t instanceof HTMLElement?[t]:t;e<r.length;e++){var n=r[e];this.insertElement(n)}this.sort()},Tt.prototype.remove=function(t){for(var e=0,r=t instanceof HTMLElement?[t]:t;e<r.length;e++){var n=r[e];this.removeElement(n)}this.sort()},Tt.prototype.inTaborder=function(t){this.taborder&&!t&&this.removeTaborder(),!this.taborder&&t&&this.insertTaborder(),this.taborder=t},Tt.prototype.insertTaborder=function(){this.taborder&&this.insertTaborder_()},Tt.prototype.removeTaborder=function(){this.taborder&&this.removeTaborder_()},Tt.prototype.insertElement=function(t){t.classList.contains(this.attachedClass)||(t.classList.add(this.attachedClass),this.taborder&&this.addTabindex(t),this.addEvents(t))},Tt.prototype.removeElement=function(t){t.classList.contains(this.attachedClass)&&(t.classList.remove(this.attachedClass),this.taborder&&this.removeTabindex(t),this.removeEvents(t))},Tt.prototype.sort=function(){var t=document.getElementsByClassName(this.attachedClass);this.store=[].slice.call(t)},Tt.prototype.insertTaborder_=function(){this.store.forEach(function(t){return t.setAttribute("tabindex","0")})},Tt.prototype.removeTaborder_=function(){this.store.forEach(function(t){return t.setAttribute("tabindex","-1")})},Tt.prototype.addTabindex=function(t){t.hasAttribute("tabindex")&&t.setAttribute(C.HtmlAttrs.OLDTAB,t.getAttribute("tabindex")),t.setAttribute("tabindex","0")},Tt.prototype.removeTabindex=function(t){t.hasAttribute(C.HtmlAttrs.OLDTAB)?(t.setAttribute("tabindex",t.getAttribute(C.HtmlAttrs.OLDTAB)),t.removeAttribute(C.HtmlAttrs.OLDTAB)):t.removeAttribute("tabindex")},Tt.prototype.addEvents=function(t){t.hasAttribute(C.HtmlAttrs.COUNTER)||(this.addEvent(t,"contextmenu",this.menu.post.bind(this.menu)),this.addEvent(t,"keydown",this.keydown.bind(this)),t.setAttribute(C.HtmlAttrs.COUNTER,this.counter.toString()),this.counter++)},Tt.prototype.addEvent=function(t,e,r){var n=C.HtmlAttrs[e.toUpperCase()+"FUNC"];this.attrMap[n+this.counter]=r,t.addEventListener(e,r)},Tt.prototype.removeEvents=function(t){if(t.hasAttribute(C.HtmlAttrs.COUNTER)){var e=t.getAttribute(C.HtmlAttrs.COUNTER);this.removeEvent(t,"contextmenu",e),this.removeEvent(t,"keydown",e),t.removeAttribute(C.HtmlAttrs.COUNTER)}},Tt.prototype.removeEvent=function(t,e,r){var n=C.HtmlAttrs[e.toUpperCase()+"FUNC"],i=this.attrMap[n+r];t.removeEventListener(e,i)},Tt.prototype.keydown=function(t){t.keyCode===C.KEY.SPACE&&(this.menu.post(t),t.preventDefault(),t.stopImmediatePropagation())},_=Tt,C.MenuStore=_,w=vt=vt||{},A=w.AbstractMenu,bt(Lt,A),Lt.parse=function(t){var e=t.menu;if(e){var r=e.pool,n=e.items,i=(e.id,new this);return r.forEach(i.parseVariable.bind(i)),i.parseItems(n),i}w.MenuUtil.error(null,"Wrong JSON format for menu.")},Lt.prototype.generateHtml=function(){this.isPosted()&&this.unpost(),A.prototype.generateHtml.call(this),this.frame=document.createElement("div"),this.frame.classList.add(w.HtmlClasses.MENUFRAME);var t="left: 0px; top: 0px; z-index: 200; width: 100%; height: 100%; border: 0px; padding: 0px; margin: 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this.moving||this.getStore().removeTaborder(),void A.prototype.post.call(this,t,e);var r,n,i,o=t;if(o instanceof Event?(r=o.target,this.stop(o)):r=o,o instanceof MouseEvent&&(n=o.pageX,i=o.pageY,n||i||!o.clientX||(n=o.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,i=o.clientY+document.body.scrollTop+document.documentElement.scrollTop)),!n&&!i&&r){var a=window.pageXOffset||document.documentElement.scrollLeft,s=window.pageYOffset||document.documentElement.scrollTop,l=r.getBoundingClientRect();n=(l.right+l.left)/2+a,i=(l.bottom+l.top)/2+s}this.getStore().setActive(r),this.anchor=this.getStore().getActive();var c=this.getHtml();n+c.offsetWidth>document.body.offsetWidth-5&&(n=document.body.offsetWidth-c.offsetWidth-5),this.post(n,i)},Lt.prototype.registerWidget=function(t){this.widgets.push(t)},Lt.prototype.unregisterWidget=function(t){var e=this.widgets.indexOf(t);-1<e&&this.widgets.splice(e,1),0===this.widgets.length&&this.unpost()},Lt.prototype.unpostWidgets=function(){this.widgets.forEach(function(t){return t.unpost()})},Lt.prototype.move_=function(t){this.anchor&&t!==this.anchor&&(this.moving=!0,this.unpost(),this.post(t),this.moving=!1)},Lt.prototype.parseVariable=function(t){var e=t.name,r=t.getter,n=t.setter;this.getPool().insert(new w.Variable(e,r,n))},T=Lt,w.ContextMenu=T,"undefined"!=typeof window&&(window.ContextMenu=vt),L=vt=vt||{},N=L.AbstractMenu,bt(Nt,N),Nt.parse=function(t,e){var r=t.items,n=(t.id,new Nt(e));return n.parseItems(r),n},Nt.prototype.getAnchor=function(){return this.anchor},Nt.prototype.post=function(){if(this.anchor.getMenu().isPosted()){for(var t=this.anchor.getHtml(),e=this.getHtml(),r=this.baseMenu.getFrame(),n=t.offsetWidth,i=n-2,o=0;t&&t!==r;)i+=t.offsetLeft,o+=t.offsetTop,t=t.parentNode;i+e.offsetWidth>document.body.offsetWidth-5&&(i=Math.max(5,i-n-e.offsetWidth+6)),N.prototype.post.call(this,i,o)}},Nt.prototype.display=function(){this.baseMenu.getFrame().appendChild(this.getHtml())},Nt.prototype.setBaseMenu=function(){for(var t=this;(t=t.anchor.getMenu())instanceof Nt;);this.baseMenu=t},I=Nt,L.SubMenu=I,function(t){t.close=function(t){var e=t.getMenu();e instanceof P.SubMenu?e.baseMenu.unpost():e.unpost()},t.getActiveElement=function(t){var e=t.getMenu();return(e instanceof P.SubMenu?e.baseMenu:e).getStore().getActive()},t.error=function(t,e){console.log("ContextMenu Error: "+e)},t.counter=function(){return e++};var e=0}((P=vt=vt||{}).MenuUtil||(P.MenuUtil={})),k=vt=vt||{},R=k.AbstractEntry,bt(It,R),Object.defineProperty(It.prototype,"content",{get:function(){return 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t=this.getHtml();t.setAttribute("aria-disabled","false"),t.textContent=this.content},It.prototype.activate=function(){this.disabled||this.getHtml().classList.add(k.HtmlClasses.MENUACTIVE)},It.prototype.deactivate=function(){this.getHtml().classList.remove(k.HtmlClasses.MENUACTIVE)},It.prototype.focus=function(){this.getMenu().setFocused(this),R.prototype.focus.call(this),this.activate()},It.prototype.unfocus=function(){this.deactivate(),R.prototype.unfocus.call(this)},It.prototype.escape=function(t){k.MenuUtil.close(this)},It.prototype.up=function(t){this.getMenu().up(t)},It.prototype.down=function(t){this.getMenu().down(t)},It.prototype.left=function(t){if(this.getMenu()instanceof k.ContextMenu)this.getMenu().left(t);else{var e=this.getMenu();e.setFocused(null),e.getAnchor().focus()}},It.prototype.right=function(t){this.getMenu().right(t)},It.prototype.space=function(t){this.press()},It.prototype.disable=function(){this.disabled=!0;var t=this.getHtml();t.classList.add(k.HtmlClasses.MENUDISABLED),t.setAttribute("aria-disabled","true")},It.prototype.enable=function(){this.disabled=!1;var t=this.getHtml();t.classList.remove(k.HtmlClasses.MENUDISABLED),t.removeAttribute("aria-disabled")},It.prototype.executeCallbacks_=function(){k.MenuUtil.getActiveElement(this);for(var t=0,e=this.callbacks;t<e.length;t++){var r=e[t];try{r(this)}catch(t){k.MenuUtil.error(t,"Callback for menu entry "+this.getId()+" failed.")}}},j=It,k.AbstractItem=j,B=vt=vt||{},D=B.AbstractItem,bt(Pt,D),Pt.prototype.generateHtml=function(){D.prototype.generateHtml.call(this);var t=this.getHtml();this.span||this.generateSpan(),t.appendChild(this.span),this.update()},Pt.prototype.register=function(){this.variable.register(this)},Pt.prototype.unregister=function(){this.variable.unregister(this)},Pt.prototype.update=function(){this.updateAria(),this.span&&this.updateSpan()},H=Pt,B.AbstractVariableItem=H,function(t){function 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diff --git a/build/_static/language_data.js b/build/_static/language_data.js
new file mode 100644
index 0000000000000000000000000000000000000000..d2b4ee91b0da7308cf5693804779c7b18c26252a
--- /dev/null
+++ b/build/_static/language_data.js
@@ -0,0 +1,297 @@
+/*
+ * language_data.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ *
+ * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+
+
+/* Non-minified version JS is _stemmer.js if file is provided */ 
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+  var step2list = {
+    ational: 'ate',
+    tional: 'tion',
+    enci: 'ence',
+    anci: 'ance',
+    izer: 'ize',
+    bli: 'ble',
+    alli: 'al',
+    entli: 'ent',
+    eli: 'e',
+    ousli: 'ous',
+    ization: 'ize',
+    ation: 'ate',
+    ator: 'ate',
+    alism: 'al',
+    iveness: 'ive',
+    fulness: 'ful',
+    ousness: 'ous',
+    aliti: 'al',
+    iviti: 'ive',
+    biliti: 'ble',
+    logi: 'log'
+  };
+
+  var step3list = {
+    icate: 'ic',
+    ative: '',
+    alize: 'al',
+    iciti: 'ic',
+    ical: 'ic',
+    ful: '',
+    ness: ''
+  };
+
+  var c = "[^aeiou]";          // consonant
+  var v = "[aeiouy]";          // vowel
+  var C = c + "[^aeiouy]*";    // consonant sequence
+  var V = v + "[aeiou]*";      // vowel sequence
+
+  var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
+  var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
+  var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
+  var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
+
+  this.stemWord = function (w) {
+    var stem;
+    var suffix;
+    var firstch;
+    var origword = w;
+
+    if (w.length < 3)
+      return w;
+
+    var re;
+    var re2;
+    var re3;
+    var re4;
+
+    firstch = w.substr(0,1);
+    if (firstch == "y")
+      w = firstch.toUpperCase() + w.substr(1);
+
+    // Step 1a
+    re = /^(.+?)(ss|i)es$/;
+    re2 = /^(.+?)([^s])s$/;
+
+    if (re.test(w))
+      w = w.replace(re,"$1$2");
+    else if (re2.test(w))
+      w = w.replace(re2,"$1$2");
+
+    // Step 1b
+    re = /^(.+?)eed$/;
+    re2 = /^(.+?)(ed|ing)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      re = new RegExp(mgr0);
+      if (re.test(fp[1])) {
+        re = /.$/;
+        w = w.replace(re,"");
+      }
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1];
+      re2 = new RegExp(s_v);
+      if (re2.test(stem)) {
+        w = stem;
+        re2 = /(at|bl|iz)$/;
+        re3 = new RegExp("([^aeiouylsz])\\1$");
+        re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+        if (re2.test(w))
+          w = w + "e";
+        else if (re3.test(w)) {
+          re = /.$/;
+          w = w.replace(re,"");
+        }
+        else if (re4.test(w))
+          w = w + "e";
+      }
+    }
+
+    // Step 1c
+    re = /^(.+?)y$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(s_v);
+      if (re.test(stem))
+        w = stem + "i";
+    }
+
+    // Step 2
+    re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step2list[suffix];
+    }
+
+    // Step 3
+    re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step3list[suffix];
+    }
+
+    // Step 4
+    re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+    re2 = /^(.+?)(s|t)(ion)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      if (re.test(stem))
+        w = stem;
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1] + fp[2];
+      re2 = new RegExp(mgr1);
+      if (re2.test(stem))
+        w = stem;
+    }
+
+    // Step 5
+    re = /^(.+?)e$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      re2 = new RegExp(meq1);
+      re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+        w = stem;
+    }
+    re = /ll$/;
+    re2 = new RegExp(mgr1);
+    if (re.test(w) && re2.test(w)) {
+      re = /.$/;
+      w = w.replace(re,"");
+    }
+
+    // and turn initial Y back to y
+    if (firstch == "y")
+      w = firstch.toLowerCase() + w.substr(1);
+    return w;
+  }
+}
+
+
+
+
+
+var splitChars = (function() {
+    var result = {};
+    var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
+         1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
+         2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
+         2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
+         3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
+         3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
+         4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
+         8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
+         11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
+         43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
+    var i, j, start, end;
+    for (i = 0; i < singles.length; i++) {
+        result[singles[i]] = true;
+    }
+    var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
+         [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
+         [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
+         [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
+         [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
+         [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
+         [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
+         [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
+         [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
+         [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
+         [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
+         [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
+         [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
+         [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
+         [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
+         [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
+         [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
+         [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
+         [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
+         [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
+         [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
+         [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
+         [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
+         [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
+         [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
+         [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
+         [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
+         [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
+         [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
+         [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
+         [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
+         [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
+         [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
+         [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
+         [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
+         [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
+         [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
+         [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
+         [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
+         [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
+         [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
+         [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
+         [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
+         [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
+         [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
+         [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
+         [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
+         [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
+         [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
+    for (i = 0; i < ranges.length; i++) {
+        start = ranges[i][0];
+        end = ranges[i][1];
+        for (j = start; j <= end; j++) {
+            result[j] = true;
+        }
+    }
+    return result;
+})();
+
+function splitQuery(query) {
+    var result = [];
+    var start = -1;
+    for (var i = 0; i < query.length; i++) {
+        if (splitChars[query.charCodeAt(i)]) {
+            if (start !== -1) {
+                result.push(query.slice(start, i));
+                start = -1;
+            }
+        } else if (start === -1) {
+            start = i;
+        }
+    }
+    if (start !== -1) {
+        result.push(query.slice(start));
+    }
+    return result;
+}
+
+
diff --git a/build/_static/middlebg.png b/build/_static/middlebg.png
new file mode 100644
index 0000000000000000000000000000000000000000..5ee55db25adc9f8a36388f55dc0c58a6763c28de
Binary files /dev/null and b/build/_static/middlebg.png differ
diff --git a/build/_static/minus.png b/build/_static/minus.png
new file mode 100644
index 0000000000000000000000000000000000000000..d96755fdaf8bb2214971e0db9c1fd3077d7c419d
Binary files /dev/null and b/build/_static/minus.png differ
diff --git a/build/_static/plus.png b/build/_static/plus.png
new file mode 100644
index 0000000000000000000000000000000000000000..7107cec93a979b9a5f64843235a16651d563ce2d
Binary files /dev/null and b/build/_static/plus.png differ
diff --git a/build/_static/pygments.css b/build/_static/pygments.css
new file mode 100644
index 0000000000000000000000000000000000000000..dc166f7699eab1709f7aa0d11cb9ed0d16df2d98
--- /dev/null
+++ b/build/_static/pygments.css
@@ -0,0 +1,69 @@
+.highlight .hll { background-color: #ffffcc }
+.highlight  { background: #f8f8f8; }
+.highlight .c { color: #60a0b0; font-style: italic } /* Comment */
+.highlight .err { color: #a40000; background-color: #fbe3e4 } /* Error */
+.highlight .k { color: #007020; font-weight: bold } /* Keyword */
+.highlight .o { color: #666666 } /* Operator */
+.highlight .ch { color: #60a0b0; font-style: italic } /* Comment.Hashbang */
+.highlight .cm { color: #60a0b0; font-style: italic } /* Comment.Multiline */
+.highlight .cp { color: #007020 } /* Comment.Preproc */
+.highlight .cpf { color: #60a0b0; font-style: italic } /* Comment.PreprocFile */
+.highlight .c1 { color: #60a0b0; font-style: italic } /* Comment.Single */
+.highlight .cs { color: #60a0b0; background-color: #fff0f0 } /* Comment.Special */
+.highlight .gd { color: #A00000 } /* Generic.Deleted */
+.highlight .ge { font-style: italic } /* Generic.Emph */
+.highlight .gr { color: #FF0000 } /* Generic.Error */
+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
+.highlight .gi { color: #00A000 } /* Generic.Inserted */
+.highlight .go { color: #888888 } /* Generic.Output */
+.highlight .gp { color: #c65d09; font-weight: bold } /* Generic.Prompt */
+.highlight .gs { font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #0044DD } /* Generic.Traceback */
+.highlight .kc { color: #007020; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #007020; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #007020; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #007020 } /* Keyword.Pseudo */
+.highlight .kr { color: #007020; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #902000 } /* Keyword.Type */
+.highlight .m { color: #40a070 } /* Literal.Number */
+.highlight .s { color: #4070a0 } /* Literal.String */
+.highlight .na { color: #0e84b5 } /* Name.Attribute */
+.highlight .nb { color: #007020 } /* Name.Builtin */
+.highlight .nc { color: #0e84b5; font-weight: bold } /* Name.Class */
+.highlight .no { color: #60add5 } /* Name.Constant */
+.highlight .nd { color: #555555; font-weight: bold } /* Name.Decorator */
+.highlight .ni { color: #d55537; font-weight: bold } /* Name.Entity */
+.highlight .ne { color: #007020 } /* Name.Exception */
+.highlight .nf { color: #06287e } /* Name.Function */
+.highlight .nl { color: #002070; font-weight: bold } /* Name.Label */
+.highlight .nn { color: #0e84b5; font-weight: bold } /* Name.Namespace */
+.highlight .nt { color: #062873; font-weight: bold } /* Name.Tag */
+.highlight .nv { color: #bb60d5 } /* Name.Variable */
+.highlight .ow { color: #007020; font-weight: bold } /* Operator.Word */
+.highlight .w { color: #bbbbbb } /* Text.Whitespace */
+.highlight .mb { color: #40a070 } /* Literal.Number.Bin */
+.highlight .mf { color: #40a070 } /* Literal.Number.Float */
+.highlight .mh { color: #40a070 } /* Literal.Number.Hex */
+.highlight .mi { color: #40a070 } /* Literal.Number.Integer */
+.highlight .mo { color: #40a070 } /* Literal.Number.Oct */
+.highlight .sa { color: #4070a0 } /* Literal.String.Affix */
+.highlight .sb { color: #4070a0 } /* Literal.String.Backtick */
+.highlight .sc { color: #4070a0 } /* Literal.String.Char */
+.highlight .dl { color: #4070a0 } /* Literal.String.Delimiter */
+.highlight .sd { color: #4070a0; font-style: italic } /* Literal.String.Doc */
+.highlight .s2 { color: #4070a0 } /* Literal.String.Double */
+.highlight .se { color: #4070a0; font-weight: bold } /* Literal.String.Escape */
+.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */
+.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */
+.highlight .sx { color: #c65d09 } /* Literal.String.Other */
+.highlight .sr { color: #235388 } /* Literal.String.Regex */
+.highlight .s1 { color: #4070a0 } /* Literal.String.Single */
+.highlight .ss { color: #517918 } /* Literal.String.Symbol */
+.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */
+.highlight .fm { color: #06287e } /* Name.Function.Magic */
+.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */
+.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */
+.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */
+.highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */
+.highlight .il { color: #40a070 } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/build/_static/pyramid.css b/build/_static/pyramid.css
new file mode 100644
index 0000000000000000000000000000000000000000..dbc19d26e83e8421bcd339905fe8bf8d34796513
--- /dev/null
+++ b/build/_static/pyramid.css
@@ -0,0 +1,342 @@
+/*
+ * pyramid.css_t
+ * ~~~~~~~~~~~~
+ *
+ * Sphinx stylesheet -- pylons theme.
+ *
+ * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+ 
+@import url("basic.css");
+ 
+/* -- page layout ----------------------------------------------------------- */
+ 
+body {
+    font-family: "Nobile", sans-serif;
+    font-size: 100%;
+    background-color: #393939;
+    color: #ffffff;
+    margin: 0;
+    padding: 0;
+}
+
+div.documentwrapper {
+    float: left;
+    width: 100%;
+}
+
+div.bodywrapper {
+    margin: 0 0 0 230px;
+}
+
+hr {
+    border: 1px solid #B1B4B6;
+}
+ 
+div.document {
+    background-color: #eee;
+}
+
+div.header {
+    width:100%;
+    background: #f4ad32 url(headerbg.png) repeat-x 0 top;
+    border-bottom: 2px solid #ffffff;
+}
+
+div.logo {
+    text-align: center;
+    padding-top: 10px;
+}
+
+div.body {
+    background-color: #ffffff;
+    color: #3E4349;
+    padding: 0 30px 30px 30px;
+    font-size: 1em;
+    border: 2px solid #ddd;
+    border-right-style: none;
+    overflow: auto;
+}
+ 
+div.footer {
+    color: #ffffff;
+    width: 100%;
+    padding: 13px 0;
+    text-align: center;
+    font-size: 75%;
+    background: transparent;
+    clear:both;
+}
+ 
+div.footer a {
+    color: #ffffff;
+    text-decoration: none;
+}
+
+div.footer a:hover {
+    color: #e88f00;
+    text-decoration: underline;
+}
+ 
+div.related {
+    line-height: 30px;
+    color: #373839;
+    font-size: 0.8em;
+    background-color: #eee;
+}
+ 
+div.related a {
+    color: #1b61d6;
+}
+
+div.related ul {
+    padding-left: calc(230px + 10px);
+}
+ 
+div.sphinxsidebar {
+    font-size: 0.75em;
+    line-height: 1.5em;
+}
+
+div.sphinxsidebarwrapper{
+    padding: 10px 0;
+}
+ 
+div.sphinxsidebar h3,
+div.sphinxsidebar h4 {
+    font-family: "Neuton", sans-serif;
+    color: #373839;
+    font-size: 1.4em;
+    font-weight: normal;
+    margin: 0;
+    padding: 5px 10px;
+    border-bottom: 2px solid #ddd;
+}
+
+div.sphinxsidebar h4{
+    font-size: 1.3em;
+}
+ 
+div.sphinxsidebar h3 a {
+    color: #000000;
+}
+ 
+ 
+div.sphinxsidebar p {
+    color: #888;
+    padding: 5px 20px;
+}
+ 
+div.sphinxsidebar p.topless {
+}
+ 
+div.sphinxsidebar ul {
+    margin: 10px 20px;
+    padding: 0;
+    color: #373839;
+}
+ 
+div.sphinxsidebar a {
+    color: #444;
+}
+ 
+div.sphinxsidebar input {
+    border: 1px solid #ccc;
+    font-family: sans-serif;
+    font-size: 1em;
+}
+
+div.sphinxsidebar .searchformwrapper {
+    margin-left: 20px;
+    margin-right: 20px;
+}
+
+/* -- sidebars -------------------------------------------------------------- */
+
+div.sidebar {
+    margin: 0 0 0.5em 1em;
+    border: 2px solid #c6d880;
+    background-color: #e6efc2;
+    width: 40%;
+    float: right;
+    border-right-style: none;
+    border-left-style: none;
+    padding: 10px 20px;
+}
+
+p.sidebar-title {
+    font-weight: bold;
+}
+
+/* -- body styles ----------------------------------------------------------- */
+ 
+a, a .pre {
+    color: #1b61d6;
+    text-decoration: none;
+}
+ 
+a:hover, a:hover .pre {
+    text-decoration: underline;
+}
+ 
+div.body h1,
+div.body h2,
+div.body h3,
+div.body h4,
+div.body h5,
+div.body h6 {
+    font-family: "Neuton", sans-serif;
+    background-color: #ffffff;
+    font-weight: normal;
+    color: #373839;
+    margin: 30px 0px 10px 0px;
+    padding: 5px 0;
+}
+ 
+div.body h1 { border-top: 20px solid white; margin-top: 0; font-size: 200%; }
+div.body h2 { font-size: 150%; background-color: #ffffff; }
+div.body h3 { font-size: 120%; background-color: #ffffff; }
+div.body h4 { font-size: 110%; background-color: #ffffff; }
+div.body h5 { font-size: 100%; background-color: #ffffff; }
+div.body h6 { font-size: 100%; background-color: #ffffff; }
+ 
+a.headerlink {
+    color: #1b61d6;
+    font-size: 0.8em;
+    padding: 0 4px 0 4px;
+    text-decoration: none;
+}
+ 
+a.headerlink:hover {
+    text-decoration: underline;
+}
+ 
+div.body p, div.body dd, div.body li {
+    line-height: 1.5em;
+}
+ 
+div.admonition p.admonition-title + p {
+    display: inline;
+}
+
+div.admonition {
+    background: #eeeeec;
+    border: 2px solid #babdb6;
+    border-right-style: none;
+    border-left-style: none;
+    padding: 10px 20px 10px 60px;
+}
+
+div.note {
+    border: 2px solid #7a9eec;
+    border-right-style: none;
+    border-left-style: none;
+    padding: 10px 20px 10px 60px;
+    background: #e1ecfe url(dialog-note.png) no-repeat 10px 8px;
+}
+ 
+div.seealso {
+    background: #fff6bf url(dialog-seealso.png) no-repeat 10px 8px;
+    border: 2px solid #ffd324;
+    border-left-style: none;
+    border-right-style: none;
+    padding: 10px 20px 10px 60px;
+}
+ 
+div.topic {
+    background: #eeeeee;
+    border: 2px solid #C6C9CB;
+    padding: 10px 20px;
+    border-right-style: none;
+    border-left-style: none;
+}
+ 
+div.warning {
+    background: #fbe3e4 url(dialog-warning.png) no-repeat 10px 8px;
+    border: 2px solid #fbc2c4;
+    border-right-style: none;
+    border-left-style: none;
+    padding: 10px 20px 10px 60px;
+}
+
+div.admonition-todo {
+    background: #f2d9b4 url(dialog-todo.png) no-repeat 10px 8px;
+    border: 2px solid #e9b96e;
+    border-right-style: none;
+    border-left-style: none;
+    padding: 10px 20px 10px 60px;
+}
+ 
+div.note p.admonition-title,
+div.warning p.admonition-title,
+div.seealso p.admonition-title,
+div.admonition-todo p.admonition-title {
+    display: none;
+}
+ 
+p.admonition-title:after {
+    content: ":";
+}
+ 
+pre {
+    padding: 10px;
+    line-height: 1.2em;
+    border: 2px solid #C6C9CB;
+    font-size: 1.1em;
+    margin: 1.5em 0 1.5em 0;
+    border-right-style: none;
+    border-left-style: none;
+}
+ 
+code {
+    background-color: transparent;
+    color: #222;
+    font-size: 1.1em;
+    font-family: monospace;
+}
+
+.viewcode-back {
+    font-family: "Nobile", sans-serif;
+}
+
+div.viewcode-block:target {
+    background-color: #fff6bf;
+    border: 2px solid #ffd324;
+    border-left-style: none;
+    border-right-style: none;
+    padding: 10px 20px;
+}
+
+table.highlighttable {
+    width: 100%;
+}
+
+table.highlighttable td {
+    padding: 0;
+}
+
+a em.std-term {
+   color: #007f00;
+}
+
+a:hover em.std-term {
+    text-decoration: underline;
+}
+
+.download {
+    font-family: "Nobile", sans-serif;
+    font-weight: normal;
+    font-style: normal;
+}
+
+code.xref {
+    font-weight: normal;
+    font-style: normal;
+}
+
+div.code-block-caption {
+    background-color: #ddd;
+    color: #222;
+}
\ No newline at end of file
diff --git a/build/_static/searchtools.js b/build/_static/searchtools.js
new file mode 100644
index 0000000000000000000000000000000000000000..ab56499655111429619df63a1dc6687646d22a3e
--- /dev/null
+++ b/build/_static/searchtools.js
@@ -0,0 +1,515 @@
+/*
+ * searchtools.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for the full-text search.
+ *
+ * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+if (!Scorer) {
+  /**
+   * Simple result scoring code.
+   */
+  var Scorer = {
+    // Implement the following function to further tweak the score for each result
+    // The function takes a result array [filename, title, anchor, descr, score]
+    // and returns the new score.
+    /*
+    score: function(result) {
+      return result[4];
+    },
+    */
+
+    // query matches the full name of an object
+    objNameMatch: 11,
+    // or matches in the last dotted part of the object name
+    objPartialMatch: 6,
+    // Additive scores depending on the priority of the object
+    objPrio: {0:  15,   // used to be importantResults
+              1:  5,   // used to be objectResults
+              2: -5},  // used to be unimportantResults
+    //  Used when the priority is not in the mapping.
+    objPrioDefault: 0,
+
+    // query found in title
+    title: 15,
+    partialTitle: 7,
+    // query found in terms
+    term: 5,
+    partialTerm: 2
+  };
+}
+
+if (!splitQuery) {
+  function splitQuery(query) {
+    return query.split(/\s+/);
+  }
+}
+
+/**
+ * Search Module
+ */
+var Search = {
+
+  _index : null,
+  _queued_query : null,
+  _pulse_status : -1,
+
+  htmlToText : function(htmlString) {
+      var htmlElement = document.createElement('span');
+      htmlElement.innerHTML = htmlString;
+      $(htmlElement).find('.headerlink').remove();
+      docContent = $(htmlElement).find('[role=main]')[0];
+      if(docContent === undefined) {
+          console.warn("Content block not found. Sphinx search tries to obtain it " +
+                       "via '[role=main]'. Could you check your theme or template.");
+          return "";
+      }
+      return docContent.textContent || docContent.innerText;
+  },
+
+  init : function() {
+      var params = $.getQueryParameters();
+      if (params.q) {
+          var query = params.q[0];
+          $('input[name="q"]')[0].value = query;
+          this.performSearch(query);
+      }
+  },
+
+  loadIndex : function(url) {
+    $.ajax({type: "GET", url: url, data: null,
+            dataType: "script", cache: true,
+            complete: function(jqxhr, textstatus) {
+              if (textstatus != "success") {
+                document.getElementById("searchindexloader").src = url;
+              }
+            }});
+  },
+
+  setIndex : function(index) {
+    var q;
+    this._index = index;
+    if ((q = this._queued_query) !== null) {
+      this._queued_query = null;
+      Search.query(q);
+    }
+  },
+
+  hasIndex : function() {
+      return this._index !== null;
+  },
+
+  deferQuery : function(query) {
+      this._queued_query = query;
+  },
+
+  stopPulse : function() {
+      this._pulse_status = 0;
+  },
+
+  startPulse : function() {
+    if (this._pulse_status >= 0)
+        return;
+    function pulse() {
+      var i;
+      Search._pulse_status = (Search._pulse_status + 1) % 4;
+      var dotString = '';
+      for (i = 0; i < Search._pulse_status; i++)
+        dotString += '.';
+      Search.dots.text(dotString);
+      if (Search._pulse_status > -1)
+        window.setTimeout(pulse, 500);
+    }
+    pulse();
+  },
+
+  /**
+   * perform a search for something (or wait until index is loaded)
+   */
+  performSearch : function(query) {
+    // create the required interface elements
+    this.out = $('#search-results');
+    this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
+    this.dots = $('<span></span>').appendTo(this.title);
+    this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
+    this.output = $('<ul class="search"/>').appendTo(this.out);
+
+    $('#search-progress').text(_('Preparing search...'));
+    this.startPulse();
+
+    // index already loaded, the browser was quick!
+    if (this.hasIndex())
+      this.query(query);
+    else
+      this.deferQuery(query);
+  },
+
+  /**
+   * execute search (requires search index to be loaded)
+   */
+  query : function(query) {
+    var i;
+
+    // stem the searchterms and add them to the correct list
+    var stemmer = new Stemmer();
+    var searchterms = [];
+    var excluded = [];
+    var hlterms = [];
+    var tmp = splitQuery(query);
+    var objectterms = [];
+    for (i = 0; i < tmp.length; i++) {
+      if (tmp[i] !== "") {
+          objectterms.push(tmp[i].toLowerCase());
+      }
+
+      if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i].match(/^\d+$/) ||
+          tmp[i] === "") {
+        // skip this "word"
+        continue;
+      }
+      // stem the word
+      var word = stemmer.stemWord(tmp[i].toLowerCase());
+      // prevent stemmer from cutting word smaller than two chars
+      if(word.length < 3 && tmp[i].length >= 3) {
+        word = tmp[i];
+      }
+      var toAppend;
+      // select the correct list
+      if (word[0] == '-') {
+        toAppend = excluded;
+        word = word.substr(1);
+      }
+      else {
+        toAppend = searchterms;
+        hlterms.push(tmp[i].toLowerCase());
+      }
+      // only add if not already in the list
+      if (!$u.contains(toAppend, word))
+        toAppend.push(word);
+    }
+    var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+
+    // console.debug('SEARCH: searching for:');
+    // console.info('required: ', searchterms);
+    // console.info('excluded: ', excluded);
+
+    // prepare search
+    var terms = this._index.terms;
+    var titleterms = this._index.titleterms;
+
+    // array of [filename, title, anchor, descr, score]
+    var results = [];
+    $('#search-progress').empty();
+
+    // lookup as object
+    for (i = 0; i < objectterms.length; i++) {
+      var others = [].concat(objectterms.slice(0, i),
+                             objectterms.slice(i+1, objectterms.length));
+      results = results.concat(this.performObjectSearch(objectterms[i], others));
+    }
+
+    // lookup as search terms in fulltext
+    results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+
+    // let the scorer override scores with a custom scoring function
+    if (Scorer.score) {
+      for (i = 0; i < results.length; i++)
+        results[i][4] = Scorer.score(results[i]);
+    }
+
+    // now sort the results by score (in opposite order of appearance, since the
+    // display function below uses pop() to retrieve items) and then
+    // alphabetically
+    results.sort(function(a, b) {
+      var left = a[4];
+      var right = b[4];
+      if (left > right) {
+        return 1;
+      } else if (left < right) {
+        return -1;
+      } else {
+        // same score: sort alphabetically
+        left = a[1].toLowerCase();
+        right = b[1].toLowerCase();
+        return (left > right) ? -1 : ((left < right) ? 1 : 0);
+      }
+    });
+
+    // for debugging
+    //Search.lastresults = results.slice();  // a copy
+    //console.info('search results:', Search.lastresults);
+
+    // print the results
+    var resultCount = results.length;
+    function displayNextItem() {
+      // results left, load the summary and display it
+      if (results.length) {
+        var item = results.pop();
+        var listItem = $('<li style="display:none"></li>');
+        var requestUrl = "";
+        var linkUrl = "";
+        if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
+          // dirhtml builder
+          var dirname = item[0] + '/';
+          if (dirname.match(/\/index\/$/)) {
+            dirname = dirname.substring(0, dirname.length-6);
+          } else if (dirname == 'index/') {
+            dirname = '';
+          }
+          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
+          linkUrl = requestUrl;
+
+        } else {
+          // normal html builders
+          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+          linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+        }
+        listItem.append($('<a/>').attr('href',
+            linkUrl +
+            highlightstring + item[2]).html(item[1]));
+        if (item[3]) {
+          listItem.append($('<span> (' + item[3] + ')</span>'));
+          Search.output.append(listItem);
+          listItem.slideDown(5, function() {
+            displayNextItem();
+          });
+        } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
+          $.ajax({url: requestUrl,
+                  dataType: "text",
+                  complete: function(jqxhr, textstatus) {
+                    var data = jqxhr.responseText;
+                    if (data !== '' && data !== undefined) {
+                      listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
+                    }
+                    Search.output.append(listItem);
+                    listItem.slideDown(5, function() {
+                      displayNextItem();
+                    });
+                  }});
+        } else {
+          // no source available, just display title
+          Search.output.append(listItem);
+          listItem.slideDown(5, function() {
+            displayNextItem();
+          });
+        }
+      }
+      // search finished, update title and status message
+      else {
+        Search.stopPulse();
+        Search.title.text(_('Search Results'));
+        if (!resultCount)
+          Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
+        else
+            Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
+        Search.status.fadeIn(500);
+      }
+    }
+    displayNextItem();
+  },
+
+  /**
+   * search for object names
+   */
+  performObjectSearch : function(object, otherterms) {
+    var filenames = this._index.filenames;
+    var docnames = this._index.docnames;
+    var objects = this._index.objects;
+    var objnames = this._index.objnames;
+    var titles = this._index.titles;
+
+    var i;
+    var results = [];
+
+    for (var prefix in objects) {
+      for (var name in objects[prefix]) {
+        var fullname = (prefix ? prefix + '.' : '') + name;
+        var fullnameLower = fullname.toLowerCase()
+        if (fullnameLower.indexOf(object) > -1) {
+          var score = 0;
+          var parts = fullnameLower.split('.');
+          // check for different match types: exact matches of full name or
+          // "last name" (i.e. last dotted part)
+          if (fullnameLower == object || parts[parts.length - 1] == object) {
+            score += Scorer.objNameMatch;
+          // matches in last name
+          } else if (parts[parts.length - 1].indexOf(object) > -1) {
+            score += Scorer.objPartialMatch;
+          }
+          var match = objects[prefix][name];
+          var objname = objnames[match[1]][2];
+          var title = titles[match[0]];
+          // If more than one term searched for, we require other words to be
+          // found in the name/title/description
+          if (otherterms.length > 0) {
+            var haystack = (prefix + ' ' + name + ' ' +
+                            objname + ' ' + title).toLowerCase();
+            var allfound = true;
+            for (i = 0; i < otherterms.length; i++) {
+              if (haystack.indexOf(otherterms[i]) == -1) {
+                allfound = false;
+                break;
+              }
+            }
+            if (!allfound) {
+              continue;
+            }
+          }
+          var descr = objname + _(', in ') + title;
+
+          var anchor = match[3];
+          if (anchor === '')
+            anchor = fullname;
+          else if (anchor == '-')
+            anchor = objnames[match[1]][1] + '-' + fullname;
+          // add custom score for some objects according to scorer
+          if (Scorer.objPrio.hasOwnProperty(match[2])) {
+            score += Scorer.objPrio[match[2]];
+          } else {
+            score += Scorer.objPrioDefault;
+          }
+          results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
+        }
+      }
+    }
+
+    return results;
+  },
+
+  /**
+   * search for full-text terms in the index
+   */
+  performTermsSearch : function(searchterms, excluded, terms, titleterms) {
+    var docnames = this._index.docnames;
+    var filenames = this._index.filenames;
+    var titles = this._index.titles;
+
+    var i, j, file;
+    var fileMap = {};
+    var scoreMap = {};
+    var results = [];
+
+    // perform the search on the required terms
+    for (i = 0; i < searchterms.length; i++) {
+      var word = searchterms[i];
+      var files = [];
+      var _o = [
+        {files: terms[word], score: Scorer.term},
+        {files: titleterms[word], score: Scorer.title}
+      ];
+      // add support for partial matches
+      if (word.length > 2) {
+        for (var w in terms) {
+          if (w.match(word) && !terms[word]) {
+            _o.push({files: terms[w], score: Scorer.partialTerm})
+          }
+        }
+        for (var w in titleterms) {
+          if (w.match(word) && !titleterms[word]) {
+              _o.push({files: titleterms[w], score: Scorer.partialTitle})
+          }
+        }
+      }
+
+      // no match but word was a required one
+      if ($u.every(_o, function(o){return o.files === undefined;})) {
+        break;
+      }
+      // found search word in contents
+      $u.each(_o, function(o) {
+        var _files = o.files;
+        if (_files === undefined)
+          return
+
+        if (_files.length === undefined)
+          _files = [_files];
+        files = files.concat(_files);
+
+        // set score for the word in each file to Scorer.term
+        for (j = 0; j < _files.length; j++) {
+          file = _files[j];
+          if (!(file in scoreMap))
+            scoreMap[file] = {};
+          scoreMap[file][word] = o.score;
+        }
+      });
+
+      // create the mapping
+      for (j = 0; j < files.length; j++) {
+        file = files[j];
+        if (file in fileMap && fileMap[file].indexOf(word) === -1)
+          fileMap[file].push(word);
+        else
+          fileMap[file] = [word];
+      }
+    }
+
+    // now check if the files don't contain excluded terms
+    for (file in fileMap) {
+      var valid = true;
+
+      // check if all requirements are matched
+      var filteredTermCount = // as search terms with length < 3 are discarded: ignore
+        searchterms.filter(function(term){return term.length > 2}).length
+      if (
+        fileMap[file].length != searchterms.length &&
+        fileMap[file].length != filteredTermCount
+      ) continue;
+
+      // ensure that none of the excluded terms is in the search result
+      for (i = 0; i < excluded.length; i++) {
+        if (terms[excluded[i]] == file ||
+            titleterms[excluded[i]] == file ||
+            $u.contains(terms[excluded[i]] || [], file) ||
+            $u.contains(titleterms[excluded[i]] || [], file)) {
+          valid = false;
+          break;
+        }
+      }
+
+      // if we have still a valid result we can add it to the result list
+      if (valid) {
+        // select one (max) score for the file.
+        // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
+        var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
+        results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
+      }
+    }
+    return results;
+  },
+
+  /**
+   * helper function to return a node containing the
+   * search summary for a given text. keywords is a list
+   * of stemmed words, hlwords is the list of normal, unstemmed
+   * words. the first one is used to find the occurrence, the
+   * latter for highlighting it.
+   */
+  makeSearchSummary : function(htmlText, keywords, hlwords) {
+    var text = Search.htmlToText(htmlText);
+    var textLower = text.toLowerCase();
+    var start = 0;
+    $.each(keywords, function() {
+      var i = textLower.indexOf(this.toLowerCase());
+      if (i > -1)
+        start = i;
+    });
+    start = Math.max(start - 120, 0);
+    var excerpt = ((start > 0) ? '...' : '') +
+      $.trim(text.substr(start, 240)) +
+      ((start + 240 - text.length) ? '...' : '');
+    var rv = $('<div class="context"></div>').text(excerpt);
+    $.each(hlwords, function() {
+      rv = rv.highlightText(this, 'highlighted');
+    });
+    return rv;
+  }
+};
+
+$(document).ready(function() {
+  Search.init();
+});
diff --git a/build/_static/transparent.gif b/build/_static/transparent.gif
new file mode 100644
index 0000000000000000000000000000000000000000..0341802e5111ad58a05ef6e93e59bfa6e5d3d1a6
Binary files /dev/null and b/build/_static/transparent.gif differ
diff --git a/build/_static/underscore-1.3.1.js b/build/_static/underscore-1.3.1.js
new file mode 100644
index 0000000000000000000000000000000000000000..208d4cd890c3183d946092ebe982738ade565061
--- /dev/null
+++ b/build/_static/underscore-1.3.1.js
@@ -0,0 +1,999 @@
+//     Underscore.js 1.3.1
+//     (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
+//     Underscore is freely distributable under the MIT license.
+//     Portions of Underscore are inspired or borrowed from Prototype,
+//     Oliver Steele's Functional, and John Resig's Micro-Templating.
+//     For all details and documentation:
+//     http://documentcloud.github.com/underscore
+
+(function() {
+
+  // Baseline setup
+  // --------------
+
+  // Establish the root object, `window` in the browser, or `global` on the server.
+  var root = this;
+
+  // Save the previous value of the `_` variable.
+  var previousUnderscore = root._;
+
+  // Establish the object that gets returned to break out of a loop iteration.
+  var breaker = {};
+
+  // Save bytes in the minified (but not gzipped) version:
+  var ArrayProto = Array.prototype, ObjProto = Object.prototype, FuncProto = Function.prototype;
+
+  // Create quick reference variables for speed access to core prototypes.
+  var slice            = ArrayProto.slice,
+      unshift          = ArrayProto.unshift,
+      toString         = ObjProto.toString,
+      hasOwnProperty   = ObjProto.hasOwnProperty;
+
+  // All **ECMAScript 5** native function implementations that we hope to use
+  // are declared here.
+  var
+    nativeForEach      = ArrayProto.forEach,
+    nativeMap          = ArrayProto.map,
+    nativeReduce       = ArrayProto.reduce,
+    nativeReduceRight  = ArrayProto.reduceRight,
+    nativeFilter       = ArrayProto.filter,
+    nativeEvery        = ArrayProto.every,
+    nativeSome         = ArrayProto.some,
+    nativeIndexOf      = ArrayProto.indexOf,
+    nativeLastIndexOf  = ArrayProto.lastIndexOf,
+    nativeIsArray      = Array.isArray,
+    nativeKeys         = Object.keys,
+    nativeBind         = FuncProto.bind;
+
+  // Create a safe reference to the Underscore object for use below.
+  var _ = function(obj) { return new wrapper(obj); };
+
+  // Export the Underscore object for **Node.js**, with
+  // backwards-compatibility for the old `require()` API. If we're in
+  // the browser, add `_` as a global object via a string identifier,
+  // for Closure Compiler "advanced" mode.
+  if (typeof exports !== 'undefined') {
+    if (typeof module !== 'undefined' && module.exports) {
+      exports = module.exports = _;
+    }
+    exports._ = _;
+  } else {
+    root['_'] = _;
+  }
+
+  // Current version.
+  _.VERSION = '1.3.1';
+
+  // Collection Functions
+  // --------------------
+
+  // The cornerstone, an `each` implementation, aka `forEach`.
+  // Handles objects with the built-in `forEach`, arrays, and raw objects.
+  // Delegates to **ECMAScript 5**'s native `forEach` if available.
+  var each = _.each = _.forEach = function(obj, iterator, context) {
+    if (obj == null) return;
+    if (nativeForEach && obj.forEach === nativeForEach) {
+      obj.forEach(iterator, context);
+    } else if (obj.length === +obj.length) {
+      for (var i = 0, l = obj.length; i < l; i++) {
+        if (i in obj && iterator.call(context, obj[i], i, obj) === breaker) return;
+      }
+    } else {
+      for (var key in obj) {
+        if (_.has(obj, key)) {
+          if (iterator.call(context, obj[key], key, obj) === breaker) return;
+        }
+      }
+    }
+  };
+
+  // Return the results of applying the iterator to each element.
+  // Delegates to **ECMAScript 5**'s native `map` if available.
+  _.map = _.collect = function(obj, iterator, context) {
+    var results = [];
+    if (obj == null) return results;
+    if (nativeMap && obj.map === nativeMap) return obj.map(iterator, context);
+    each(obj, function(value, index, list) {
+      results[results.length] = iterator.call(context, value, index, list);
+    });
+    if (obj.length === +obj.length) results.length = obj.length;
+    return results;
+  };
+
+  // **Reduce** builds up a single result from a list of values, aka `inject`,
+  // or `foldl`. Delegates to **ECMAScript 5**'s native `reduce` if available.
+  _.reduce = _.foldl = _.inject = function(obj, iterator, memo, context) {
+    var initial = arguments.length > 2;
+    if (obj == null) obj = [];
+    if (nativeReduce && obj.reduce === nativeReduce) {
+      if (context) iterator = _.bind(iterator, context);
+      return initial ? obj.reduce(iterator, memo) : obj.reduce(iterator);
+    }
+    each(obj, function(value, index, list) {
+      if (!initial) {
+        memo = value;
+        initial = true;
+      } else {
+        memo = iterator.call(context, memo, value, index, list);
+      }
+    });
+    if (!initial) throw new TypeError('Reduce of empty array with no initial value');
+    return memo;
+  };
+
+  // The right-associative version of reduce, also known as `foldr`.
+  // Delegates to **ECMAScript 5**'s native `reduceRight` if available.
+  _.reduceRight = _.foldr = function(obj, iterator, memo, context) {
+    var initial = arguments.length > 2;
+    if (obj == null) obj = [];
+    if (nativeReduceRight && obj.reduceRight === nativeReduceRight) {
+      if (context) iterator = _.bind(iterator, context);
+      return initial ? obj.reduceRight(iterator, memo) : obj.reduceRight(iterator);
+    }
+    var reversed = _.toArray(obj).reverse();
+    if (context && !initial) iterator = _.bind(iterator, context);
+    return initial ? _.reduce(reversed, iterator, memo, context) : _.reduce(reversed, iterator);
+  };
+
+  // Return the first value which passes a truth test. Aliased as `detect`.
+  _.find = _.detect = function(obj, iterator, context) {
+    var result;
+    any(obj, function(value, index, list) {
+      if (iterator.call(context, value, index, list)) {
+        result = value;
+        return true;
+      }
+    });
+    return result;
+  };
+
+  // Return all the elements that pass a truth test.
+  // Delegates to **ECMAScript 5**'s native `filter` if available.
+  // Aliased as `select`.
+  _.filter = _.select = function(obj, iterator, context) {
+    var results = [];
+    if (obj == null) return results;
+    if (nativeFilter && obj.filter === nativeFilter) return obj.filter(iterator, context);
+    each(obj, function(value, index, list) {
+      if (iterator.call(context, value, index, list)) results[results.length] = value;
+    });
+    return results;
+  };
+
+  // Return all the elements for which a truth test fails.
+  _.reject = function(obj, iterator, context) {
+    var results = [];
+    if (obj == null) return results;
+    each(obj, function(value, index, list) {
+      if (!iterator.call(context, value, index, list)) results[results.length] = value;
+    });
+    return results;
+  };
+
+  // Determine whether all of the elements match a truth test.
+  // Delegates to **ECMAScript 5**'s native `every` if available.
+  // Aliased as `all`.
+  _.every = _.all = function(obj, iterator, context) {
+    var result = true;
+    if (obj == null) return result;
+    if (nativeEvery && obj.every === nativeEvery) return obj.every(iterator, context);
+    each(obj, function(value, index, list) {
+      if (!(result = result && iterator.call(context, value, index, list))) return breaker;
+    });
+    return result;
+  };
+
+  // Determine if at least one element in the object matches a truth test.
+  // Delegates to **ECMAScript 5**'s native `some` if available.
+  // Aliased as `any`.
+  var any = _.some = _.any = function(obj, iterator, context) {
+    iterator || (iterator = _.identity);
+    var result = false;
+    if (obj == null) return result;
+    if (nativeSome && obj.some === nativeSome) return obj.some(iterator, context);
+    each(obj, function(value, index, list) {
+      if (result || (result = iterator.call(context, value, index, list))) return breaker;
+    });
+    return !!result;
+  };
+
+  // Determine if a given value is included in the array or object using `===`.
+  // Aliased as `contains`.
+  _.include = _.contains = function(obj, target) {
+    var found = false;
+    if (obj == null) return found;
+    if (nativeIndexOf && obj.indexOf === nativeIndexOf) return obj.indexOf(target) != -1;
+    found = any(obj, function(value) {
+      return value === target;
+    });
+    return found;
+  };
+
+  // Invoke a method (with arguments) on every item in a collection.
+  _.invoke = function(obj, method) {
+    var args = slice.call(arguments, 2);
+    return _.map(obj, function(value) {
+      return (_.isFunction(method) ? method || value : value[method]).apply(value, args);
+    });
+  };
+
+  // Convenience version of a common use case of `map`: fetching a property.
+  _.pluck = function(obj, key) {
+    return _.map(obj, function(value){ return value[key]; });
+  };
+
+  // Return the maximum element or (element-based computation).
+  _.max = function(obj, iterator, context) {
+    if (!iterator && _.isArray(obj)) return Math.max.apply(Math, obj);
+    if (!iterator && _.isEmpty(obj)) return -Infinity;
+    var result = {computed : -Infinity};
+    each(obj, function(value, index, list) {
+      var computed = iterator ? iterator.call(context, value, index, list) : value;
+      computed >= result.computed && (result = {value : value, computed : computed});
+    });
+    return result.value;
+  };
+
+  // Return the minimum element (or element-based computation).
+  _.min = function(obj, iterator, context) {
+    if (!iterator && _.isArray(obj)) return Math.min.apply(Math, obj);
+    if (!iterator && _.isEmpty(obj)) return Infinity;
+    var result = {computed : Infinity};
+    each(obj, function(value, index, list) {
+      var computed = iterator ? iterator.call(context, value, index, list) : value;
+      computed < result.computed && (result = {value : value, computed : computed});
+    });
+    return result.value;
+  };
+
+  // Shuffle an array.
+  _.shuffle = function(obj) {
+    var shuffled = [], rand;
+    each(obj, function(value, index, list) {
+      if (index == 0) {
+        shuffled[0] = value;
+      } else {
+        rand = Math.floor(Math.random() * (index + 1));
+        shuffled[index] = shuffled[rand];
+        shuffled[rand] = value;
+      }
+    });
+    return shuffled;
+  };
+
+  // Sort the object's values by a criterion produced by an iterator.
+  _.sortBy = function(obj, iterator, context) {
+    return _.pluck(_.map(obj, function(value, index, list) {
+      return {
+        value : value,
+        criteria : iterator.call(context, value, index, list)
+      };
+    }).sort(function(left, right) {
+      var a = left.criteria, b = right.criteria;
+      return a < b ? -1 : a > b ? 1 : 0;
+    }), 'value');
+  };
+
+  // Groups the object's values by a criterion. Pass either a string attribute
+  // to group by, or a function that returns the criterion.
+  _.groupBy = function(obj, val) {
+    var result = {};
+    var iterator = _.isFunction(val) ? val : function(obj) { return obj[val]; };
+    each(obj, function(value, index) {
+      var key = iterator(value, index);
+      (result[key] || (result[key] = [])).push(value);
+    });
+    return result;
+  };
+
+  // Use a comparator function to figure out at what index an object should
+  // be inserted so as to maintain order. Uses binary search.
+  _.sortedIndex = function(array, obj, iterator) {
+    iterator || (iterator = _.identity);
+    var low = 0, high = array.length;
+    while (low < high) {
+      var mid = (low + high) >> 1;
+      iterator(array[mid]) < iterator(obj) ? low = mid + 1 : high = mid;
+    }
+    return low;
+  };
+
+  // Safely convert anything iterable into a real, live array.
+  _.toArray = function(iterable) {
+    if (!iterable)                return [];
+    if (iterable.toArray)         return iterable.toArray();
+    if (_.isArray(iterable))      return slice.call(iterable);
+    if (_.isArguments(iterable))  return slice.call(iterable);
+    return _.values(iterable);
+  };
+
+  // Return the number of elements in an object.
+  _.size = function(obj) {
+    return _.toArray(obj).length;
+  };
+
+  // Array Functions
+  // ---------------
+
+  // Get the first element of an array. Passing **n** will return the first N
+  // values in the array. Aliased as `head`. The **guard** check allows it to work
+  // with `_.map`.
+  _.first = _.head = function(array, n, guard) {
+    return (n != null) && !guard ? slice.call(array, 0, n) : array[0];
+  };
+
+  // Returns everything but the last entry of the array. Especcialy useful on
+  // the arguments object. Passing **n** will return all the values in
+  // the array, excluding the last N. The **guard** check allows it to work with
+  // `_.map`.
+  _.initial = function(array, n, guard) {
+    return slice.call(array, 0, array.length - ((n == null) || guard ? 1 : n));
+  };
+
+  // Get the last element of an array. Passing **n** will return the last N
+  // values in the array. The **guard** check allows it to work with `_.map`.
+  _.last = function(array, n, guard) {
+    if ((n != null) && !guard) {
+      return slice.call(array, Math.max(array.length - n, 0));
+    } else {
+      return array[array.length - 1];
+    }
+  };
+
+  // Returns everything but the first entry of the array. Aliased as `tail`.
+  // Especially useful on the arguments object. Passing an **index** will return
+  // the rest of the values in the array from that index onward. The **guard**
+  // check allows it to work with `_.map`.
+  _.rest = _.tail = function(array, index, guard) {
+    return slice.call(array, (index == null) || guard ? 1 : index);
+  };
+
+  // Trim out all falsy values from an array.
+  _.compact = function(array) {
+    return _.filter(array, function(value){ return !!value; });
+  };
+
+  // Return a completely flattened version of an array.
+  _.flatten = function(array, shallow) {
+    return _.reduce(array, function(memo, value) {
+      if (_.isArray(value)) return memo.concat(shallow ? value : _.flatten(value));
+      memo[memo.length] = value;
+      return memo;
+    }, []);
+  };
+
+  // Return a version of the array that does not contain the specified value(s).
+  _.without = function(array) {
+    return _.difference(array, slice.call(arguments, 1));
+  };
+
+  // Produce a duplicate-free version of the array. If the array has already
+  // been sorted, you have the option of using a faster algorithm.
+  // Aliased as `unique`.
+  _.uniq = _.unique = function(array, isSorted, iterator) {
+    var initial = iterator ? _.map(array, iterator) : array;
+    var result = [];
+    _.reduce(initial, function(memo, el, i) {
+      if (0 == i || (isSorted === true ? _.last(memo) != el : !_.include(memo, el))) {
+        memo[memo.length] = el;
+        result[result.length] = array[i];
+      }
+      return memo;
+    }, []);
+    return result;
+  };
+
+  // Produce an array that contains the union: each distinct element from all of
+  // the passed-in arrays.
+  _.union = function() {
+    return _.uniq(_.flatten(arguments, true));
+  };
+
+  // Produce an array that contains every item shared between all the
+  // passed-in arrays. (Aliased as "intersect" for back-compat.)
+  _.intersection = _.intersect = function(array) {
+    var rest = slice.call(arguments, 1);
+    return _.filter(_.uniq(array), function(item) {
+      return _.every(rest, function(other) {
+        return _.indexOf(other, item) >= 0;
+      });
+    });
+  };
+
+  // Take the difference between one array and a number of other arrays.
+  // Only the elements present in just the first array will remain.
+  _.difference = function(array) {
+    var rest = _.flatten(slice.call(arguments, 1));
+    return _.filter(array, function(value){ return !_.include(rest, value); });
+  };
+
+  // Zip together multiple lists into a single array -- elements that share
+  // an index go together.
+  _.zip = function() {
+    var args = slice.call(arguments);
+    var length = _.max(_.pluck(args, 'length'));
+    var results = new Array(length);
+    for (var i = 0; i < length; i++) results[i] = _.pluck(args, "" + i);
+    return results;
+  };
+
+  // If the browser doesn't supply us with indexOf (I'm looking at you, **MSIE**),
+  // we need this function. Return the position of the first occurrence of an
+  // item in an array, or -1 if the item is not included in the array.
+  // Delegates to **ECMAScript 5**'s native `indexOf` if available.
+  // If the array is large and already in sort order, pass `true`
+  // for **isSorted** to use binary search.
+  _.indexOf = function(array, item, isSorted) {
+    if (array == null) return -1;
+    var i, l;
+    if (isSorted) {
+      i = _.sortedIndex(array, item);
+      return array[i] === item ? i : -1;
+    }
+    if (nativeIndexOf && array.indexOf === nativeIndexOf) return array.indexOf(item);
+    for (i = 0, l = array.length; i < l; i++) if (i in array && array[i] === item) return i;
+    return -1;
+  };
+
+  // Delegates to **ECMAScript 5**'s native `lastIndexOf` if available.
+  _.lastIndexOf = function(array, item) {
+    if (array == null) return -1;
+    if (nativeLastIndexOf && array.lastIndexOf === nativeLastIndexOf) return array.lastIndexOf(item);
+    var i = array.length;
+    while (i--) if (i in array && array[i] === item) return i;
+    return -1;
+  };
+
+  // Generate an integer Array containing an arithmetic progression. A port of
+  // the native Python `range()` function. See
+  // [the Python documentation](http://docs.python.org/library/functions.html#range).
+  _.range = function(start, stop, step) {
+    if (arguments.length <= 1) {
+      stop = start || 0;
+      start = 0;
+    }
+    step = arguments[2] || 1;
+
+    var len = Math.max(Math.ceil((stop - start) / step), 0);
+    var idx = 0;
+    var range = new Array(len);
+
+    while(idx < len) {
+      range[idx++] = start;
+      start += step;
+    }
+
+    return range;
+  };
+
+  // Function (ahem) Functions
+  // ------------------
+
+  // Reusable constructor function for prototype setting.
+  var ctor = function(){};
+
+  // Create a function bound to a given object (assigning `this`, and arguments,
+  // optionally). Binding with arguments is also known as `curry`.
+  // Delegates to **ECMAScript 5**'s native `Function.bind` if available.
+  // We check for `func.bind` first, to fail fast when `func` is undefined.
+  _.bind = function bind(func, context) {
+    var bound, args;
+    if (func.bind === nativeBind && nativeBind) return nativeBind.apply(func, slice.call(arguments, 1));
+    if (!_.isFunction(func)) throw new TypeError;
+    args = slice.call(arguments, 2);
+    return bound = function() {
+      if (!(this instanceof bound)) return func.apply(context, args.concat(slice.call(arguments)));
+      ctor.prototype = func.prototype;
+      var self = new ctor;
+      var result = func.apply(self, args.concat(slice.call(arguments)));
+      if (Object(result) === result) return result;
+      return self;
+    };
+  };
+
+  // Bind all of an object's methods to that object. Useful for ensuring that
+  // all callbacks defined on an object belong to it.
+  _.bindAll = function(obj) {
+    var funcs = slice.call(arguments, 1);
+    if (funcs.length == 0) funcs = _.functions(obj);
+    each(funcs, function(f) { obj[f] = _.bind(obj[f], obj); });
+    return obj;
+  };
+
+  // Memoize an expensive function by storing its results.
+  _.memoize = function(func, hasher) {
+    var memo = {};
+    hasher || (hasher = _.identity);
+    return function() {
+      var key = hasher.apply(this, arguments);
+      return _.has(memo, key) ? memo[key] : (memo[key] = func.apply(this, arguments));
+    };
+  };
+
+  // Delays a function for the given number of milliseconds, and then calls
+  // it with the arguments supplied.
+  _.delay = function(func, wait) {
+    var args = slice.call(arguments, 2);
+    return setTimeout(function(){ return func.apply(func, args); }, wait);
+  };
+
+  // Defers a function, scheduling it to run after the current call stack has
+  // cleared.
+  _.defer = function(func) {
+    return _.delay.apply(_, [func, 1].concat(slice.call(arguments, 1)));
+  };
+
+  // Returns a function, that, when invoked, will only be triggered at most once
+  // during a given window of time.
+  _.throttle = function(func, wait) {
+    var context, args, timeout, throttling, more;
+    var whenDone = _.debounce(function(){ more = throttling = false; }, wait);
+    return function() {
+      context = this; args = arguments;
+      var later = function() {
+        timeout = null;
+        if (more) func.apply(context, args);
+        whenDone();
+      };
+      if (!timeout) timeout = setTimeout(later, wait);
+      if (throttling) {
+        more = true;
+      } else {
+        func.apply(context, args);
+      }
+      whenDone();
+      throttling = true;
+    };
+  };
+
+  // Returns a function, that, as long as it continues to be invoked, will not
+  // be triggered. The function will be called after it stops being called for
+  // N milliseconds.
+  _.debounce = function(func, wait) {
+    var timeout;
+    return function() {
+      var context = this, args = arguments;
+      var later = function() {
+        timeout = null;
+        func.apply(context, args);
+      };
+      clearTimeout(timeout);
+      timeout = setTimeout(later, wait);
+    };
+  };
+
+  // Returns a function that will be executed at most one time, no matter how
+  // often you call it. Useful for lazy initialization.
+  _.once = function(func) {
+    var ran = false, memo;
+    return function() {
+      if (ran) return memo;
+      ran = true;
+      return memo = func.apply(this, arguments);
+    };
+  };
+
+  // Returns the first function passed as an argument to the second,
+  // allowing you to adjust arguments, run code before and after, and
+  // conditionally execute the original function.
+  _.wrap = function(func, wrapper) {
+    return function() {
+      var args = [func].concat(slice.call(arguments, 0));
+      return wrapper.apply(this, args);
+    };
+  };
+
+  // Returns a function that is the composition of a list of functions, each
+  // consuming the return value of the function that follows.
+  _.compose = function() {
+    var funcs = arguments;
+    return function() {
+      var args = arguments;
+      for (var i = funcs.length - 1; i >= 0; i--) {
+        args = [funcs[i].apply(this, args)];
+      }
+      return args[0];
+    };
+  };
+
+  // Returns a function that will only be executed after being called N times.
+  _.after = function(times, func) {
+    if (times <= 0) return func();
+    return function() {
+      if (--times < 1) { return func.apply(this, arguments); }
+    };
+  };
+
+  // Object Functions
+  // ----------------
+
+  // Retrieve the names of an object's properties.
+  // Delegates to **ECMAScript 5**'s native `Object.keys`
+  _.keys = nativeKeys || function(obj) {
+    if (obj !== Object(obj)) throw new TypeError('Invalid object');
+    var keys = [];
+    for (var key in obj) if (_.has(obj, key)) keys[keys.length] = key;
+    return keys;
+  };
+
+  // Retrieve the values of an object's properties.
+  _.values = function(obj) {
+    return _.map(obj, _.identity);
+  };
+
+  // Return a sorted list of the function names available on the object.
+  // Aliased as `methods`
+  _.functions = _.methods = function(obj) {
+    var names = [];
+    for (var key in obj) {
+      if (_.isFunction(obj[key])) names.push(key);
+    }
+    return names.sort();
+  };
+
+  // Extend a given object with all the properties in passed-in object(s).
+  _.extend = function(obj) {
+    each(slice.call(arguments, 1), function(source) {
+      for (var prop in source) {
+        obj[prop] = source[prop];
+      }
+    });
+    return obj;
+  };
+
+  // Fill in a given object with default properties.
+  _.defaults = function(obj) {
+    each(slice.call(arguments, 1), function(source) {
+      for (var prop in source) {
+        if (obj[prop] == null) obj[prop] = source[prop];
+      }
+    });
+    return obj;
+  };
+
+  // Create a (shallow-cloned) duplicate of an object.
+  _.clone = function(obj) {
+    if (!_.isObject(obj)) return obj;
+    return _.isArray(obj) ? obj.slice() : _.extend({}, obj);
+  };
+
+  // Invokes interceptor with the obj, and then returns obj.
+  // The primary purpose of this method is to "tap into" a method chain, in
+  // order to perform operations on intermediate results within the chain.
+  _.tap = function(obj, interceptor) {
+    interceptor(obj);
+    return obj;
+  };
+
+  // Internal recursive comparison function.
+  function eq(a, b, stack) {
+    // Identical objects are equal. `0 === -0`, but they aren't identical.
+    // See the Harmony `egal` proposal: http://wiki.ecmascript.org/doku.php?id=harmony:egal.
+    if (a === b) return a !== 0 || 1 / a == 1 / b;
+    // A strict comparison is necessary because `null == undefined`.
+    if (a == null || b == null) return a === b;
+    // Unwrap any wrapped objects.
+    if (a._chain) a = a._wrapped;
+    if (b._chain) b = b._wrapped;
+    // Invoke a custom `isEqual` method if one is provided.
+    if (a.isEqual && _.isFunction(a.isEqual)) return a.isEqual(b);
+    if (b.isEqual && _.isFunction(b.isEqual)) return b.isEqual(a);
+    // Compare `[[Class]]` names.
+    var className = toString.call(a);
+    if (className != toString.call(b)) return false;
+    switch (className) {
+      // Strings, numbers, dates, and booleans are compared by value.
+      case '[object String]':
+        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+        // equivalent to `new String("5")`.
+        return a == String(b);
+      case '[object Number]':
+        // `NaN`s are equivalent, but non-reflexive. An `egal` comparison is performed for
+        // other numeric values.
+        return a != +a ? b != +b : (a == 0 ? 1 / a == 1 / b : a == +b);
+      case '[object Date]':
+      case '[object Boolean]':
+        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+        // millisecond representations. Note that invalid dates with millisecond representations
+        // of `NaN` are not equivalent.
+        return +a == +b;
+      // RegExps are compared by their source patterns and flags.
+      case '[object RegExp]':
+        return a.source == b.source &&
+               a.global == b.global &&
+               a.multiline == b.multiline &&
+               a.ignoreCase == b.ignoreCase;
+    }
+    if (typeof a != 'object' || typeof b != 'object') return false;
+    // Assume equality for cyclic structures. The algorithm for detecting cyclic
+    // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+    var length = stack.length;
+    while (length--) {
+      // Linear search. Performance is inversely proportional to the number of
+      // unique nested structures.
+      if (stack[length] == a) return true;
+    }
+    // Add the first object to the stack of traversed objects.
+    stack.push(a);
+    var size = 0, result = true;
+    // Recursively compare objects and arrays.
+    if (className == '[object Array]') {
+      // Compare array lengths to determine if a deep comparison is necessary.
+      size = a.length;
+      result = size == b.length;
+      if (result) {
+        // Deep compare the contents, ignoring non-numeric properties.
+        while (size--) {
+          // Ensure commutative equality for sparse arrays.
+          if (!(result = size in a == size in b && eq(a[size], b[size], stack))) break;
+        }
+      }
+    } else {
+      // Objects with different constructors are not equivalent.
+      if ('constructor' in a != 'constructor' in b || a.constructor != b.constructor) return false;
+      // Deep compare objects.
+      for (var key in a) {
+        if (_.has(a, key)) {
+          // Count the expected number of properties.
+          size++;
+          // Deep compare each member.
+          if (!(result = _.has(b, key) && eq(a[key], b[key], stack))) break;
+        }
+      }
+      // Ensure that both objects contain the same number of properties.
+      if (result) {
+        for (key in b) {
+          if (_.has(b, key) && !(size--)) break;
+        }
+        result = !size;
+      }
+    }
+    // Remove the first object from the stack of traversed objects.
+    stack.pop();
+    return result;
+  }
+
+  // Perform a deep comparison to check if two objects are equal.
+  _.isEqual = function(a, b) {
+    return eq(a, b, []);
+  };
+
+  // Is a given array, string, or object empty?
+  // An "empty" object has no enumerable own-properties.
+  _.isEmpty = function(obj) {
+    if (_.isArray(obj) || _.isString(obj)) return obj.length === 0;
+    for (var key in obj) if (_.has(obj, key)) return false;
+    return true;
+  };
+
+  // Is a given value a DOM element?
+  _.isElement = function(obj) {
+    return !!(obj && obj.nodeType == 1);
+  };
+
+  // Is a given value an array?
+  // Delegates to ECMA5's native Array.isArray
+  _.isArray = nativeIsArray || function(obj) {
+    return toString.call(obj) == '[object Array]';
+  };
+
+  // Is a given variable an object?
+  _.isObject = function(obj) {
+    return obj === Object(obj);
+  };
+
+  // Is a given variable an arguments object?
+  _.isArguments = function(obj) {
+    return toString.call(obj) == '[object Arguments]';
+  };
+  if (!_.isArguments(arguments)) {
+    _.isArguments = function(obj) {
+      return !!(obj && _.has(obj, 'callee'));
+    };
+  }
+
+  // Is a given value a function?
+  _.isFunction = function(obj) {
+    return toString.call(obj) == '[object Function]';
+  };
+
+  // Is a given value a string?
+  _.isString = function(obj) {
+    return toString.call(obj) == '[object String]';
+  };
+
+  // Is a given value a number?
+  _.isNumber = function(obj) {
+    return toString.call(obj) == '[object Number]';
+  };
+
+  // Is the given value `NaN`?
+  _.isNaN = function(obj) {
+    // `NaN` is the only value for which `===` is not reflexive.
+    return obj !== obj;
+  };
+
+  // Is a given value a boolean?
+  _.isBoolean = function(obj) {
+    return obj === true || obj === false || toString.call(obj) == '[object Boolean]';
+  };
+
+  // Is a given value a date?
+  _.isDate = function(obj) {
+    return toString.call(obj) == '[object Date]';
+  };
+
+  // Is the given value a regular expression?
+  _.isRegExp = function(obj) {
+    return toString.call(obj) == '[object RegExp]';
+  };
+
+  // Is a given value equal to null?
+  _.isNull = function(obj) {
+    return obj === null;
+  };
+
+  // Is a given variable undefined?
+  _.isUndefined = function(obj) {
+    return obj === void 0;
+  };
+
+  // Has own property?
+  _.has = function(obj, key) {
+    return hasOwnProperty.call(obj, key);
+  };
+
+  // Utility Functions
+  // -----------------
+
+  // Run Underscore.js in *noConflict* mode, returning the `_` variable to its
+  // previous owner. Returns a reference to the Underscore object.
+  _.noConflict = function() {
+    root._ = previousUnderscore;
+    return this;
+  };
+
+  // Keep the identity function around for default iterators.
+  _.identity = function(value) {
+    return value;
+  };
+
+  // Run a function **n** times.
+  _.times = function (n, iterator, context) {
+    for (var i = 0; i < n; i++) iterator.call(context, i);
+  };
+
+  // Escape a string for HTML interpolation.
+  _.escape = function(string) {
+    return (''+string).replace(/&/g, '&amp;').replace(/</g, '&lt;').replace(/>/g, '&gt;').replace(/"/g, '&quot;').replace(/'/g, '&#x27;').replace(/\//g,'&#x2F;');
+  };
+
+  // Add your own custom functions to the Underscore object, ensuring that
+  // they're correctly added to the OOP wrapper as well.
+  _.mixin = function(obj) {
+    each(_.functions(obj), function(name){
+      addToWrapper(name, _[name] = obj[name]);
+    });
+  };
+
+  // Generate a unique integer id (unique within the entire client session).
+  // Useful for temporary DOM ids.
+  var idCounter = 0;
+  _.uniqueId = function(prefix) {
+    var id = idCounter++;
+    return prefix ? prefix + id : id;
+  };
+
+  // By default, Underscore uses ERB-style template delimiters, change the
+  // following template settings to use alternative delimiters.
+  _.templateSettings = {
+    evaluate    : /<%([\s\S]+?)%>/g,
+    interpolate : /<%=([\s\S]+?)%>/g,
+    escape      : /<%-([\s\S]+?)%>/g
+  };
+
+  // When customizing `templateSettings`, if you don't want to define an
+  // interpolation, evaluation or escaping regex, we need one that is
+  // guaranteed not to match.
+  var noMatch = /.^/;
+
+  // Within an interpolation, evaluation, or escaping, remove HTML escaping
+  // that had been previously added.
+  var unescape = function(code) {
+    return code.replace(/\\\\/g, '\\').replace(/\\'/g, "'");
+  };
+
+  // JavaScript micro-templating, similar to John Resig's implementation.
+  // Underscore templating handles arbitrary delimiters, preserves whitespace,
+  // and correctly escapes quotes within interpolated code.
+  _.template = function(str, data) {
+    var c  = _.templateSettings;
+    var tmpl = 'var __p=[],print=function(){__p.push.apply(__p,arguments);};' +
+      'with(obj||{}){__p.push(\'' +
+      str.replace(/\\/g, '\\\\')
+         .replace(/'/g, "\\'")
+         .replace(c.escape || noMatch, function(match, code) {
+           return "',_.escape(" + unescape(code) + "),'";
+         })
+         .replace(c.interpolate || noMatch, function(match, code) {
+           return "'," + unescape(code) + ",'";
+         })
+         .replace(c.evaluate || noMatch, function(match, code) {
+           return "');" + unescape(code).replace(/[\r\n\t]/g, ' ') + ";__p.push('";
+         })
+         .replace(/\r/g, '\\r')
+         .replace(/\n/g, '\\n')
+         .replace(/\t/g, '\\t')
+         + "');}return __p.join('');";
+    var func = new Function('obj', '_', tmpl);
+    if (data) return func(data, _);
+    return function(data) {
+      return func.call(this, data, _);
+    };
+  };
+
+  // Add a "chain" function, which will delegate to the wrapper.
+  _.chain = function(obj) {
+    return _(obj).chain();
+  };
+
+  // The OOP Wrapper
+  // ---------------
+
+  // If Underscore is called as a function, it returns a wrapped object that
+  // can be used OO-style. This wrapper holds altered versions of all the
+  // underscore functions. Wrapped objects may be chained.
+  var wrapper = function(obj) { this._wrapped = obj; };
+
+  // Expose `wrapper.prototype` as `_.prototype`
+  _.prototype = wrapper.prototype;
+
+  // Helper function to continue chaining intermediate results.
+  var result = function(obj, chain) {
+    return chain ? _(obj).chain() : obj;
+  };
+
+  // A method to easily add functions to the OOP wrapper.
+  var addToWrapper = function(name, func) {
+    wrapper.prototype[name] = function() {
+      var args = slice.call(arguments);
+      unshift.call(args, this._wrapped);
+      return result(func.apply(_, args), this._chain);
+    };
+  };
+
+  // Add all of the Underscore functions to the wrapper object.
+  _.mixin(_);
+
+  // Add all mutator Array functions to the wrapper.
+  each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+    var method = ArrayProto[name];
+    wrapper.prototype[name] = function() {
+      var wrapped = this._wrapped;
+      method.apply(wrapped, arguments);
+      var length = wrapped.length;
+      if ((name == 'shift' || name == 'splice') && length === 0) delete wrapped[0];
+      return result(wrapped, this._chain);
+    };
+  });
+
+  // Add all accessor Array functions to the wrapper.
+  each(['concat', 'join', 'slice'], function(name) {
+    var method = ArrayProto[name];
+    wrapper.prototype[name] = function() {
+      return result(method.apply(this._wrapped, arguments), this._chain);
+    };
+  });
+
+  // Start chaining a wrapped Underscore object.
+  wrapper.prototype.chain = function() {
+    this._chain = true;
+    return this;
+  };
+
+  // Extracts the result from a wrapped and chained object.
+  wrapper.prototype.value = function() {
+    return this._wrapped;
+  };
+
+}).call(this);
diff --git a/build/_static/underscore.js b/build/_static/underscore.js
new file mode 100644
index 0000000000000000000000000000000000000000..5b55f32beaca186f84cca115514f02cddbd1bbd5
--- /dev/null
+++ b/build/_static/underscore.js
@@ -0,0 +1,31 @@
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+// (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
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+// For all details and documentation:
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diff --git a/build/base_index.html b/build/base_index.html
new file mode 100644
index 0000000000000000000000000000000000000000..6accdc8bd210fb5d332f945cd6817e3d1067bdab
--- /dev/null
+++ b/build/base_index.html
@@ -0,0 +1,92 @@
+
+<!DOCTYPE html>
+
+<html>
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>Duniter technical description &#8212; Duniter technical description 0.0.2 documentation</title>
+    <link rel="stylesheet" href="_static/pyramid.css" type="text/css" />
+    <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
+    <script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
+    <script src="_static/underscore.js"></script>
+    <script src="_static/doctools.js"></script>
+    <script src="_static/language_data.js"></script>
+    <script async="async" src="_static/./js/tex-mml-chtml.js"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" />
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Neuton&amp;subset=latin" type="text/css" media="screen" charset="utf-8" />
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Nobile:regular,italic,bold,bolditalic&amp;subset=latin" type="text/css" media="screen" charset="utf-8" />
+<!--[if lte IE 6]>
+<link rel="stylesheet" href="_static/ie6.css" type="text/css" media="screen" charset="utf-8" />
+<![endif]-->
+
+  </head><body>
+
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="nav-item nav-item-0"><a href="index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Duniter technical description</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <div class="section" id="duniter-technical-description">
+<h1>Duniter technical description<a class="headerlink" href="#duniter-technical-description" title="Permalink to this headline">¶</a></h1>
+<div class="toctree-wrapper compound">
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/base_index.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" />
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>$('#searchbox').show(0);</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             >index</a></li>
+        <li class="nav-item nav-item-0"><a href="index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Duniter technical description</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2020, Matograine.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 3.1.1.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/build/genindex.html b/build/genindex.html
new file mode 100644
index 0000000000000000000000000000000000000000..3550dc9a6782673e0d9de7c4e76cf6f73f5a3769
--- /dev/null
+++ b/build/genindex.html
@@ -0,0 +1,86 @@
+
+<!DOCTYPE html>
+
+<html>
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>Index &#8212; Duniter technical description 0.0.2 documentation</title>
+    <link rel="stylesheet" href="_static/pyramid.css" type="text/css" />
+    <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
+    <script id="documentation_options" data-url_root="./" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
+    <script src="_static/underscore.js"></script>
+    <script src="_static/doctools.js"></script>
+    <script src="_static/language_data.js"></script>
+    <script async="async" src="_static/./js/tex-mml-chtml.js"></script>
+    <link rel="index" title="Index" href="#" />
+    <link rel="search" title="Search" href="search.html" />
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Neuton&amp;subset=latin" type="text/css" media="screen" charset="utf-8" />
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Nobile:regular,italic,bold,bolditalic&amp;subset=latin" type="text/css" media="screen" charset="utf-8" />
+<!--[if lte IE 6]>
+<link rel="stylesheet" href="_static/ie6.css" type="text/css" media="screen" charset="utf-8" />
+<![endif]-->
+
+  </head><body>
+
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="#" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="nav-item nav-item-0"><a href="index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Index</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+
+<h1 id="index">Index</h1>
+
+<div class="genindex-jumpbox">
+ 
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
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+  <div class="section" id="duniter-technical-description">
+<h1>Duniter technical description<a class="headerlink" href="#duniter-technical-description" title="Permalink to this headline">¶</a></h1>
+<div class="toctree-wrapper compound">
+</div>
+<div class="section" id="abstract">
+<h2>Abstract<a class="headerlink" href="#abstract" title="Permalink to this headline">¶</a></h2>
+<p>Many currency principles involve non-equal rights to monetary creation
+between humans. We propose a monetary creation based on the Relative
+Theory of Money, which guarantee equal monetary creation for each
+willing human. This type of currency can be centralised, however, this
+could lead to censorship and arbitrary choices of the central
+institution. Thus, strongly inspired by Bitcoin example, we want the
+currency to be as decentralised as possible, in the transaction network
+as in the human identification process. We use a Web of Trust between
+living humans for identification. This web of trust allows us to impose
+personalised difficulty for transaction validation, keeping the
+calculation accessible to low-end hardware and allowing all competent
+members to secure the currency.</p>
+</div>
+<div class="section" id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+<p>Duniter is a software to create and manage “libre currencies”. Libre
+currency is a concept defined by S.Laborde in the Relative Theory of
+Money (RTM) that was published in 2010. This theory demonstrates the
+possibility of an invariant monetary unit : the Universal Dividend.
+Doing so, the RTM answers the question :</p>
+<blockquote>
+<div><p>How should a currency be created to match the principle of equality
+between all humans, now and between generations ?</p>
+</div></blockquote>
+<p>The results of this demonstration implies a monetary creation :</p>
+<ul class="simple">
+<li><p>on a regular basis</p></li>
+<li><p>for each human being</p></li>
+<li><p>which amount has to be reassessed on fixed intervals according to a
+fixed formula.</p></li>
+</ul>
+<p>Thus, Duniter project will associate a human to a digital identity. It
+will use a Web of Trust with specific rules. As the number of members
+may evolve, the Universal Dividend has to be created according to the
+formula :</p>
+<div class="math notranslate nohighlight">
+\[UD(t+1) = UD(t) + c^2 \times {M(t) \over N(t)}\]</div>
+<p>Duniter is based on a decentralized Blockchain. This technical choice
+allows irreversibility of transaction and uncensorability of trades and
+identities. While inspired by Bitcoin, Duniter uses a Web of Trust and
+the Proof of Work to secure the computation network, thus making
+obsolete the power race model used in Bitcoin.</p>
+<p>The first currency created through Duniter is Ğ1, pronounced “June”. It
+was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters
+as examples ; however, one can create another libre currency with custom
+parameters while still using Duniter software.</p>
+</div>
+<div class="section" id="state-of-the-art-bitcoin-case">
+<h2>1. State of the art : Bitcoin case<a class="headerlink" href="#state-of-the-art-bitcoin-case" title="Permalink to this headline">¶</a></h2>
+<!-- source : https://duniter.org/en/theoretical/ --><p>Duniter uses the crypto-currency concept introduced by Bitcoin <a href="#id31"><span class="problematic" id="id1">[1]_</span></a>,
+which is to use cryptographic tools such as signatures to create
+trustless digital currencies. Duniter fits this definition, but it has
+two completely different principles than Bitcoin : the Web of Trust and
+the Universal Dividend . These differences are on both monetary and
+technical aspects.</p>
+<div class="section" id="monetary-creation-of-bitcoin-a-space-time-asymmetry">
+<span id="monetary-creation-a-space-time-asymmetry"></span><h3>1.1. Monetary creation of Bitcoin : a space-time asymmetry<a class="headerlink" href="#monetary-creation-of-bitcoin-a-space-time-asymmetry" title="Permalink to this headline">¶</a></h3>
+<p>Space-time asymmetry refers to the relative access of individuals to
+newly created money <a href="#id32"><span class="problematic" id="id2">[2]_</span></a>. Concretely, most existing currencies (c. 2020)
+are both spatially and temporally asymmetrical for their users. Let’s
+take Bitcoin as an example to understand why.</p>
+<div class="section" id="spatial-asymmetry">
+<h4>1.1.1. Spatial asymmetry<a class="headerlink" href="#spatial-asymmetry" title="Permalink to this headline">¶</a></h4>
+<p>When new Bitcoins are created, only some Bitcoin users (the miners) are
+given new Bitcoins, while everyone else get nothing. We believe this is
+the first injustice. However, some might say:</p>
+<blockquote>
+<div><p>“Miners used their electricity and time to get it!”</p>
+</div></blockquote>
+<p>… we would answer that this work should not have been rewarded by
+newly created Bitcoins. New units should be distributed to the whole
+community. Miners should be rewared another way, but not by money
+issuance. Of course, Bitcoin cannot create money through Basic Income
+since Bitcoin users are not strongly identified, and one might benefit
+from money creation multiple times if they owned several wallets.
+Duniter gets rid of this problem by identifying its users and creating
+the same amount of Basic Income to everyone.</p>
+</div>
+<div class="section" id="temporal-asymmetry">
+<h4>1.1.2. Temporal-asymmetry<a class="headerlink" href="#temporal-asymmetry" title="Permalink to this headline">¶</a></h4>
+<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
+which means ever fewer bitcoins will be created over time until no new
+BTC are being generated. So, once the first adopters have mined every
+bitcoin, how will future joiners get Bitcoins? Just like most of us do
+for Euros or Dollars: to get money, they will have to work for the ones
+who already own it.</p>
+<p>We believe this is the second injustice. Every member of a monetary
+community should be equal concerning monetary creation, and get the same
+relative amount of money over time, even if they are a late adopter.
+Duniter aims to fix this by making the Universal Dividend (a.k.a. UD)
+grow by the time according to precise rules, thus making members equal
+toward money issuance on a half-lifespan.</p>
+<p>Most currencies present one of these two asymmetries, including metal
+currencies and mutual credit, as exposed in the RTM.</p>
+</div>
+<div class="section" id="a-solution">
+<h4>1.1.3. A solution<a class="headerlink" href="#a-solution" title="Permalink to this headline">¶</a></h4>
+<p>Bitcoin has taught us that it is possible to create a currency system
+allowing one to both create digital money and to exchange it without a
+central authority. What we need to change is the way money is issued so
+we finally have a symmetrical system. We need <strong>Bitcoin + Universal
+Dividend</strong>. But Universal Dividend implies that the community consists
+of only identified people. This is where the Web of Trust (WoT) comes
+into place.</p>
+<p>This concept, introduced by cryptography with the OpenPGP format <a href="#id33"><span class="problematic" id="id3">[3]_</span></a>,
+allows us to identify people in a decentralized manner. It works as
+follows: each person creates a personal identity that is linked to its
+cyptographic certificate. The identity must be confirmed by others
+members who use their own cryptographic key. It is that simple: people
+choose who is part of the community and who is not, not a central
+authority.</p>
+<p>However, Duniter will not use OpenPGP for its cryptographic features:
+Elliptic Curves <a href="#id34"><span class="problematic" id="id4">[4]_</span></a> will be used instead for the conciseness of its
+generated keys and its pratical advantages. Duniter has its own Web of
+Trust principles, that will be exposed later.</p>
+</div>
+</div>
+<div class="section" id="proof-of-work-mining-a-power-race">
+<h3>1.2. Proof-of-Work mining : a power race<a class="headerlink" href="#proof-of-work-mining-a-power-race" title="Permalink to this headline">¶</a></h3>
+<p>In Bitcoin Model, the calculation and incentive principles cause a power
+race : new Bitcoins are created for the owners of the most numerous,
+powerful (and energy-consuming) computers. This leads to a power race an
+places the control over the currency in the hands of the richest
+hardware owners. We want to make Duniter blockchain validation much less
+energy and hardware consuming while keeping a strong level of security.
+This will be further explained later. A consequence of this choice is
+the participation of low-end hardware in the Duniter network, leading to
+a better decentralization of blockchain validation.</p>
+<div class="section" id="what-about-proof-of-stake">
+<h4>1.2.1 What about Proof of Stake ?<a class="headerlink" href="#what-about-proof-of-stake" title="Permalink to this headline">¶</a></h4>
+<p>Proof of stake consensus algorythm was first introduced in 2012 <a href="#id35"><span class="problematic" id="id5">[5]_</span></a>.
+The basic principle is to allow the richest wallets to issue blocks,
+putting their coin balance as a “stake” they would lose in case of
+cheat.</p>
+<p>At the time of conceiving Duniter, the PoS algorythms had not been
+tested enough to be used as a fundamental base. We did not chose this
+consensus principle. Moreover, the principle of allowing owners of large
+amounts of money to validate transaction can only lead to placing power
+over the currency in the richests hands : this is contrary to the
+symmetical principles of a libre currency.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id6"><span class="brackets">1</span></dt>
+<dd><p>Bitcoin Whitepaper, S.Nakamoto, 2008:
+<a class="reference external" href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></p>
+</dd>
+<dt class="label" id="id7"><span class="brackets">2</span></dt>
+<dd><p>Relative Theory of Money, S.Laborde, 2010:
+<a class="reference external" href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></p>
+</dd>
+<dt class="label" id="id8"><span class="brackets">3</span></dt>
+<dd><p>OpenPGP protocol defines standard formats for encrypted messages,
+signatures, private keys, and certificates for exchanging public
+keys. The GNU Privacy Handbook, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p>
+</dd>
+<dt class="label" id="id9"><span class="brackets">4</span></dt>
+<dd><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+77–89.
+<a class="reference external" href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</p>
+</dd>
+<dt class="label" id="id10"><span class="brackets">5</span></dt>
+<dd><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp;
+S.Nadal, 2012 :
+<a class="reference external" href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="section" id="duniters-blockchain">
+<h2>2. Duniters Blockchain<a class="headerlink" href="#duniters-blockchain" title="Permalink to this headline">¶</a></h2>
+<p>Duniters Blockchain follows the basic principles of Bitcoins. This is
+essential for synchronization between peers, as to prevent double-spend
+attacks. However, Duniters Blockchain will store different informations
+than Bitcoins.</p>
+<p>The basic use of Blockchain will be registering transactions. For this
+part, we use the same principles as Bitcoin : transactions have inputs
+(spending accounts) and outputs (receiving accounts). But contrary to
+Bitcoin, no generation transaction exists : monetary creation happens
+only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
+<ul class="simple">
+<li><p>a former transaction (as in Bitcoin)</p></li>
+<li><p>a Universal Dividend (specific to Duniter).</p></li>
+</ul>
+<p>Duniters Web of Trust is also written in the Blockchain. The identity of
+each member gets registered much like transactions are, with a strong
+link to the time reference. Thus, the Blockchain is a representation of
+a space-time frame of reference, where “space” are members of the WoT
+and “time” the basic blockchain units : the blocks. On each point of
+time, one can determine which account is legitimate to create the UD,
+only with a blockchain analysis.</p>
+<div class="section" id="spam-countermeasures">
+<h3>2.1. Spam countermeasures<a class="headerlink" href="#spam-countermeasures" title="Permalink to this headline">¶</a></h3>
+<p>An issue of most cryptocurrency projects is to prevent the common ledger
+from growing too much. This would require nodes to have a lot of storage
+and computing power to be usable. In particular, we don’t want an
+attacker to be able to make the Blockchain grow too fast. Most projects
+implement transaction fees as a way to prevent this, making the attacker
+lose money. We don’t want to introduce this mean since a currency with
+automatic fees on transactions is no more neutral. Several
+countermeasuers against such spam attacks are implemented.</p>
+<div class="section" id="minimum-output-amount">
+<h4>2.1.1. Minimum output amount<a class="headerlink" href="#minimum-output-amount" title="Permalink to this headline">¶</a></h4>
+<!-- This has to be implemented in DUBPv13. --><p>Fixing a minimal output amount reduces the power of an attack. Duniter
+deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could
+create thousand accounts with only 1 UD. To prevent this, a valid
+transaction must have output amounts of minimum 1Ğ1. This reduces the
+power an attack by 100.</p>
+</div>
+<div class="section" id="limited-block-size-and-chainability">
+<h4>2.1.2. Limited block size and chainability<a class="headerlink" href="#limited-block-size-and-chainability" title="Permalink to this headline">¶</a></h4>
+<p>The block size is always limited. While the protocol allows this limit
+to evolve to address scaling issues, an attacker cannot register as many
+transaction as they wish.</p>
+<p>With the same goal to prevent too many transactions to get registered,
+while transactions can be “chained” (refer to another transaction in the
+same block), the chainability of transactions is limited to 5.</p>
+</div>
+</div>
+<div class="section" id="scaling">
+<h3>2.2. Scaling<a class="headerlink" href="#scaling" title="Permalink to this headline">¶</a></h3>
+<p>Most of the time, the scaling issue rises for distributed systems that
+should work on a very large scale. This is not the case of Duniter, for
+multiple reasons :</p>
+<ul class="simple">
+<li><p>Ğ1 is the first libre currency, and is still experimental on the
+monetary creation principle. We don’t want it to reach the whole
+world, we only want it to work, to validate or invalidate the RTM.
+Moreover, the rules chosen for the Ğ1 WoT should limit its size to
+around 16 million members.</p></li>
+<li><p>Duniter’s aim is to be used to create multiple libre currencies, that
+would fit local or regional economies. As a consequence, it would
+deal with less transactions than if it was a world-scale system. The
+RTM proposes a formula to calculate the exchange rate between two
+currencies, that could be used to create automatic exchanges for a
+member travelling away from their community.</p></li>
+</ul>
+<p>However, Duniter has assets that will help if the number of users and
+transactions grow.</p>
+<div class="section" id="dynamic-block-size">
+<h4>2.2.1 Dynamic block size<a class="headerlink" href="#dynamic-block-size" title="Permalink to this headline">¶</a></h4>
+<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve.
+On low use of the blockchain, the maximal block size is 500 bytes. On
+high use of the blockchain, the maximal block size would be 110% of the
+average size of the current window blocks(see “personalised difficulty”
+part for more information). This way, the blocks are bounded in size,
+but can slowly grow if a massive and legitimate use of the blockchain
+needs it. The block size (in bytes) is limited as so :</p>
+<div class="math notranslate nohighlight">
+\[\textrm{blockSize} &lt; \max \left({500 ; \textrm{CEIL}(1.10 \times (\textrm{average block size}))}\right)\]</div>
+</div>
+<div class="section" id="lightning-networks">
+<h4>2.2.2. Lightning Networks<a class="headerlink" href="#lightning-networks" title="Permalink to this headline">¶</a></h4>
+<p>The Lightning Networks <a href="#id36"><span class="problematic" id="id11">[1]_</span></a> allow almost instant and off-chain
+transactions. They were first implemented on Lightcoin, and are now on
+Bitcoin. One of their benefits is to make the blockchain store a lot of
+transactions at once, thus reducing the groth of the blockchain. The
+Duniter protocol allows XHX() and CSV() unlock conditions that are
+necessary to implement Lightning Networks. While not available yet, this
+payment channel might get implemented when needed.</p>
+</div>
+<div class="section" id="unit-base">
+<h4>2.2.3. Unit base<a class="headerlink" href="#unit-base" title="Permalink to this headline">¶</a></h4>
+<p>As the Universal Dividend grows exponentially, with time Duniter nodes
+would have had to deal with always largest amounts, eventually reaching
+the BIGINT limit. To avoid this, the amounts are expressed with a unit
+base in base 10. We want the UD amount to always fit in 4 digits. To
+manage it, the <code class="docutils literal notranslate"><span class="pre">unitbase</span></code> is updated each time the UD value reaches
+100.00 : it goes from <code class="docutils literal notranslate"><span class="pre">99.99*10^(unitbase)</span></code> to
+<code class="docutils literal notranslate"><span class="pre">10.00*10^(unitbase+1)</span></code>. All the unit amounts are thus divided by 10.
+While this might seem strange, this process has already hapened in state
+currencies. Moreover, the amounts expressed in UD will not change.</p>
+<p>With a monetary growth of 10% each year and a stable population, such a
+change of unit base would happen each 25 years.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id12"><span class="brackets">1</span></dt>
+<dd><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 :
+<a class="reference external" href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="section" id="duniter-web-of-trust">
+<h2>3. Duniter Web of Trust<a class="headerlink" href="#duniter-web-of-trust" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="basic-principles">
+<span id="duniter-wot-basic-principles"></span><h3>3.1. Basic Principles<a class="headerlink" href="#basic-principles" title="Permalink to this headline">¶</a></h3>
+<p>In order to identify “members” accounts - which create monetary units -
+and other accounts, Duniter uses a Web of Trust. This can be summarized
+into few principles:</p>
+<ul class="simple">
+<li><p>Each account becomes a member if it received a minimal number of
+certifications - 5 for Ğ1 currency.</p></li>
+<li><p>Only members accounts can send certifications. Certifications have a
+limited lifespan.</p></li>
+<li><p>A certification indicates that the sender accepts the receiver as a
+legitimate identity.</p></li>
+</ul>
+<p>The aim of the WoT is to identify a blockchain account to a living
+human. According to Lauterbach et.al <a href="#id37"><span class="problematic" id="id13">[1]_</span></a>, the strengh of a relationship
+should be considered when building a vouch system. For this reason, the
+Ğ1 Web of Trust rules are expressed in a licence stating what WoT
+certifications are. A certification represents a strong human
+relationship : one may certify a close relative, not an acquaintance.
+Each member has to accept this licence before being included in the WoT.
+Thus, if a member is part of an attack on the currency, they can be
+found by mutual relatives. Additional security rules occur to prevent
+cheat and attacks on a large scale.</p>
+<p>Note that non-members accounts can use the currency, but cannot create
+money. Non-members accounts can be used by individuals as secondary
+wallets, or by institutions.</p>
+<p>We were inspired by the OpenPGP Trust system <a href="#id38"><span class="problematic" id="id14">[2]_</span></a>. However, the OpenPGP
+trust principles aim at defining trust from a particular point of view
+while Duniter needs to identify humans for the whole community. To
+achieve this goal, while OpenPGP allows each user to tweak its trust
+parameters individually, Duniter sets rules in the “genesis” block for
+the whole community.</p>
+</div>
+<div class="section" id="why-do-we-need-a-web-of-trust">
+<h3>3.2. Why do we need a Web of Trust ?<a class="headerlink" href="#why-do-we-need-a-web-of-trust" title="Permalink to this headline">¶</a></h3>
+<p>There are two reasons we need it :</p>
+<ol class="arabic simple">
+<li><p>To make sure that only one Universal Dividend is produced per member
+at each specified creation interval. In the Ğ1’s case this interval
+is set as daily <code class="docutils literal notranslate"><span class="pre">86</span> <span class="pre">400</span></code> seconds, it is the <em>monetary parameter</em>
+known as <code class="docutils literal notranslate"><span class="pre">dt</span></code>.</p></li>
+<li><p>To identify the nodes hashing the blocks and assign each a
+personalised difficulty. This custom difficulty proof of work is
+there to avoid the blockchain’s validation mechanism becoming too
+centralised as is the case with many ‘non-libre’ cryptocurrencies.</p></li>
+</ol>
+<dl>
+<dt><strong>Monetary parameter</strong>:</dt><dd><p>Each currency that use Duniter has its own
+blockchain whose behaviour is dictated by a set of ‘parameters’
+defined in block zero - the so-called genesis block - that can be
+tweaked to achieve the desired results. At the time of writing the
+Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21
+parameters of which 10 are for the WoT alone. We’ll focus on these
+10.</p>
+<p>Suffice to say that in the Ğ1’s case, the DU is created every 24
+hours - 86 400 seconds. This interval is set through the time
+derivative <code class="docutils literal notranslate"><span class="pre">dt</span></code> parameter and can have a different value in other
+implementations of the protocol.</p>
+</dd>
+</dl>
+<p>We want to make sure that each member can only have one account. As we
+all know, achieving zero-risk isn’t possible <a href="#id39"><span class="problematic" id="id15">[3]_</span></a>. Our goal is therefore
+not to create a WoT within which fraud would be absolutely impossible,
+but instead to discourage it. Here is a rewording of our goal in 4
+smaller ones :</p>
+<ol class="arabic simple">
+<li><p>Make the certification process lengthy enough that all members
+exercise due diligence and are wary of risks.</p></li>
+<li><p>Make fraudulent acts as hard as we can to the extent that they become
+pointless.</p></li>
+<li><p>Ensure that any Sybil attacks have a negligible impact on the
+currency by ensuring that illegitimate double Universal Dividends
+have no significant bearing on the legitimate monetary mass</p></li>
+<li><p>Slow the growth of ‘Sybil regions’ to give enough time for the
+community to react and isolate the threat.</p></li>
+</ol>
+<dl class="simple">
+<dt><strong>Sybil attack</strong>:</dt><dd><p>A Sybil attack is an attack perpetrated on a
+reputation system through the creation of fake identities. A Web of
+Trust is a specific instance of a Reputation System.</p>
+</dd>
+</dl>
+<p>There are plenty of Sybil attack scenarios we can think of and just as
+many reasons why their perpetrators would want to carry them out. Our
+objective is that the configuration of the WoT protects both users and
+its IT backbone infrastructure against these attacks.</p>
+<p>This means that micro-attacks performed by small groups of individuals
+looking for personal enrichment are of no interest to us. The web’s role
+isn’t to deter these attacks, this being instead the role of the
+community. Just like the town you live in is responsible for providing
+your tap water and electricity but isn’t responsible for any burglaries,
+etc. Much in the same way, Duniter’s WoT guarantees us all a functional
+currency, but do not detect small fraud.</p>
+</div>
+<div class="section" id="the-importance-of-having-our-own-certification-system">
+<span id="own-certification-system"></span><h3>3.3. The importance of having our own certification system<a class="headerlink" href="#the-importance-of-having-our-own-certification-system" title="Permalink to this headline">¶</a></h3>
+<p>Centralized identification systems can achieve the goal we want. State
+Identification is an example. However, this has many drawbacks :</p>
+<ul class="simple">
+<li><p>The authority may have arbitrary criteria for identification, for
+example preventing people without an official state-provided identity
+or homeless people to be included in the WoT.</p></li>
+<li><p>Payment might be required to get identified, thus making the monetary
+creation not “free”.</p></li>
+<li><p>The authority is a point of failure for any attacker.</p></li>
+</ul>
+<p>It is of the utmost importance that we remain free from any state or
+corporation. The WoT is an answer to this criterium. To this day we
+depend only on the Internet and yet, were it to fail, there are already
+alternatives being tested around the world for a decentralised
+communication network.</p>
+</div>
+<div class="section" id="a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary">
+<span id="graph-theory-vocabulary"></span><h3>3.4. A few foundational concepts on graph theory : a bit of vocabulary<a class="headerlink" href="#a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary" title="Permalink to this headline">¶</a></h3>
+<ul class="simple">
+<li><p><strong>Graph</strong>: set of points -called ‘vertices’- joined by edges -called
+paths/walks-.</p></li>
+<li><p><strong>Simple graph</strong>: a graph with no loops and with no multiple edges.
+That is, each edge connects two distinct endpoints and no two edges
+have the same endpoints. A simple edge is an edge that is not part of
+a multiple adjacency -of edges-. In many cases, graphs are assumed to
+be simple unless specified otherwise.</p></li>
+<li><p><strong>Directed graph</strong>: a graph in which the edges have a distinguished
+direction, from one vertex to another. A directed edge can also be
+called a path or walk. Arrow A –&gt; B is therefore different from arrow
+B –&gt; A.</p></li>
+<li><p><strong>Endpoints</strong>: the edge with vertex A –&gt; B has A and B as endpoints,
+respectively as start and end of the path/walk.</p></li>
+<li><p><strong>Isolated vertex</strong>: a vertex whose degree is zero, that is, a vertex
+with no incident edges.</p></li>
+<li><p><strong>Degree of a vertex</strong>: number of its incident edges -in and out-.</p></li>
+<li><p><strong>Out-degree of vertex A</strong>: number of outbound edges / tail ends from
+A.</p></li>
+<li><p><strong>In-degree of vertex A</strong>: number of incoming edges / head ends to A.</p></li>
+</ul>
+<div class="figure align-default" id="id27">
+<a class="reference internal image-reference" href="_images/degrees_en.jpg"><img alt="degrees of a vertex diagram" src="_images/degrees_en.jpg" style="width: 40%;" /></a>
+<p class="caption"><span class="caption-text">degrees of a vertex diagram</span><a class="headerlink" href="#id27" title="Permalink to this image">¶</a></p>
+</div>
+<ul class="simple">
+<li><p><strong>Path</strong>: -aka “walk”- path to follow to get from vertex A to vertex
+B.</p></li>
+</ul>
+</div>
+<div class="section" id="definition-of-the-duniter-web-of-trust">
+<h3>3.5. Definition of the Duniter Web of Trust<a class="headerlink" href="#definition-of-the-duniter-web-of-trust" title="Permalink to this headline">¶</a></h3>
+<p>The Duniter WoTs -one per currency- are simple directed graphs without
+isolated vertices. The vertices are the members and the edges are the
+certifications given and received.</p>
+<p><em>Directed</em> means that the responsibility of issuing a certification is
+unique and personal to the certifier. The trust they place in the
+receiver cannot be imposed in the other direction although in most
+circumstances both parties equally trust each other.</p>
+<p>In addition, all vertices are either currently active members or
+past-members. Past-member vertices are in a specific ‘deactivated state’
+and can no longer issue or receive certifications although the ones
+already issued or received to/from other members are still considered
+‘pending’ to avoid a collapse of the WoT. If these old members don’t
+come back into the WoT, their pending certifications will eventually
+expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
+<p>To wrap up with old members, after a certain period of time - set in the
+currency’s parameters - their deactivated vertex is removed from the web
+and the associated identity is ‘revoked’. The person who owned the
+account can no longer use this identity but is free to join the web with
+another one.</p>
+<dl>
+<dt><strong>Identity</strong>:</dt><dd><p>An identity is a set of three pieces of information: a
+public key, a name and a blockstamp. A blockstamp points to a
+specific block in the chain. Its main use is to freeze the point in
+time at which an identity was created and to link this identity to a
+specific chain and a currency - each currency having its own
+blockchain.</p>
+<p>An identity can be in any one of 5 different status: pending, member,
+old member, revoked or excluded.</p>
+</dd>
+</dl>
+<p>Let’s take a simple example:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">-&gt;</span> <span class="n">B</span> <span class="o">-&gt;</span> <span class="n">C</span>
+     <span class="o">|</span>
+     \<span class="o">--&gt;</span> <span class="n">D</span>
+</pre></div>
+</div>
+<p>If, for whatever reason, A were to lose its member status, the web would
+crumble and all other members would be excluded as a consequence. To
+avoid this, the certification from A –&gt; B will remain valid until its
+expiry date, leaving enough time for B to receive certifications from C
+or D.</p>
+<p>Because our WoT doesn’t have any isolated vertices, each new identity
+created needs to be pulled into the web with all of the certifications
+it has received, all in the same block. This calls for a temporary
+‘buffer’ storage space for <strong>pending</strong> identities and the certifications
+they have received. This storage space is called ‘the pool’ of Duniter
+nodes, which we could also have called the ‘sandbox’ as that’s the name
+used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other
+documents and metadata not mentioned here.</p>
+</div>
+<div class="section" id="exploring-the-rules-behind-a-duniter-web-of-trust">
+<span id="exploring-the-rules-behind-duniter-wot"></span><h3>3.6. Exploring the rules behind a Duniter Web of Trust<a class="headerlink" href="#exploring-the-rules-behind-a-duniter-web-of-trust" title="Permalink to this headline">¶</a></h3>
+<p>The Duniter WoTs - one per currency - works with a set of eight
+fundamental rules enforced through eleven different parameters. Ten of
+these parameters are set within the genesis block, the eleventh one -
+<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>- having being hard-coded in the Ğ1’s code subsequently.</p>
+<div class="section" id="distance-rule-and-referent-members-stepmax-and-xpercent">
+<h4>3.6.1. Distance rule and referent members (<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> and <code class="docutils literal notranslate"><span class="pre">xPercent</span></code>)<a class="headerlink" href="#distance-rule-and-referent-members-stepmax-and-xpercent" title="Permalink to this headline">¶</a></h4>
+<p>These two parameters are closely linked and together define the
+‘distance rule’. The ‘distance rule’ can only be described after
+defining what a ‘referent member’ is:</p>
+<dl class="simple">
+<dt><strong>Referent member</strong>:</dt><dd><p>Member A is said to be ‘referent’ if and only if
+the total of their degrees are greater than or equal to
+<code class="docutils literal notranslate"><span class="pre">CEIL-N^-1/stepMax</span></code> where N is the total number of members. As the
+size of the web will grow this number will grow too, meaning it will
+take more certification issuances to become a referent member. The
+number of certifications needed to become a member shouldn’t change.</p>
+</dd>
+</dl>
+<p>Let’s now define the distance rule:</p>
+<dl class="simple">
+<dt><strong>Distance rule</strong>:</dt><dd><p>M ember A is said to observe this rule if and only
+if for a subset xPercent % of referent members R there exists a path
+of length less than or equal to <code class="docutils literal notranslate"><span class="pre">stepMax</span></code> between R and A.</p>
+</dd>
+</dl>
+<p>Referent members only exist so that the distance rule can take effect,
+they have no special privileges over non-referent members. In a perfect
+web, that is one in which each member has certified all members they
+legitimately can, all members would be referent members. However,
+because the web progressively grows in size and because members die and
+are replaced by new ones, there are always members at any given time
+<code class="docutils literal notranslate"><span class="pre">t</span></code> who haven’t yet certified all members they legitimately could.
+These members would hinder the evolution of the web if they were taken
+into account in the calculation of the distance rule and the web would
+effectively stop growing.</p>
+<p>Because verifying the application of the distance rule is
+calculation-greedy, it is only performed when a new identity gets
+confirmed into the web or an existing member gets renewed. There is an
+exception to this rule: the distance rule is not observed in the genesis
+block -when the web is first implemented.</p>
+</div>
+<div class="section" id="rule-of-the-minimum-number-of-certifications-needed-sigqty">
+<h4>3.6.2. Rule of the minimum number of certifications needed (<code class="docutils literal notranslate"><span class="pre">sigQty</span></code>)<a class="headerlink" href="#rule-of-the-minimum-number-of-certifications-needed-sigqty" title="Permalink to this headline">¶</a></h4>
+<p>This is the simplest rule, it essentially says that each member must at
+any given time -meaning in any single block- have received at least
+<code class="docutils literal notranslate"><span class="pre">sigQty</span></code> active certifications. If, for whatever reason, member A were
+to have less than <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> active certifications in a given block,
+they would cease to be a member and be required to publish a request for
+identity renewal.</p>
+</div>
+<div class="section" id="the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">
+<h4>3.6.3. The membership renewal rule (<code class="docutils literal notranslate"><span class="pre">msValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)<a class="headerlink" href="#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow" title="Permalink to this headline">¶</a></h4>
+<p>Bear in mind that a membership doesn’t last a lifetime but instead has a
+lifespan set to <code class="docutils literal notranslate"><span class="pre">msValidity</span></code> seconds.</p>
+<p>Every single member -or old member who hasn’t revoked his identity or
+been excluded- can request a membership renewal so long as the last
+request was made more than <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> seconds ago. If a member has
+never requested a renewal, the date of last renewal is equal to the
+timestamp at which his membership was first created. A new request will
+be stored in the ‘pool’ for a maximum of <code class="docutils literal notranslate"><span class="pre">msWindow</span></code> seconds before
+it’s included in the blockchain. Once again, this can only happen
+once/if the member meets both the <code class="docutils literal notranslate"><span class="pre">siqQty</span></code> rule and the distance rule
+-if these criterion are already matched it’s just a case of waiting for
+a new block to be mined-.</p>
+<p>If a member hasn’t requested a renewal for longer than <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>
+seconds, they automatically cease to be a member. From this moment on,
+the ex-member has another <code class="docutils literal notranslate"><span class="pre">msValidity</span></code> window to renew their
+membership. When this period of <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">×</span> <span class="pre">msValidity</span></code> runs out, the
+membership will expire and this identity will never be available for use
+again in the web. If the person so desires, they will have to publish
+new identity and membership documents and find enough certifiers, as any
+newcomer.</p>
+</div>
+<div class="section" id="rule-of-certification-lifespan-sigvalidity">
+<h4>3.6.4. Rule of certification lifespan (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>)<a class="headerlink" href="#rule-of-certification-lifespan-sigvalidity" title="Permalink to this headline">¶</a></h4>
+<p>All certifications included in the blockchain expire <strong>sigValidity</strong>
+seconds after they were <strong>issued</strong>.</p>
+<blockquote>
+<div><p>/!\ The issuance and the inclusion of a certification in the
+blockchain occur at different times. When member A issues a
+certification at time t1, it gets stored in the pool starting at t1
+and only finds its way into the blockchain at t2 when all of the
+web’s rules are observed. Several weeks can thus go by between t1 and
+t2!</p>
+</div></blockquote>
+</div>
+<div class="section" id="rule-of-limited-supply-of-active-certifications-sigstock">
+<h4>3.6.5. Rule of limited supply of active certifications (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)<a class="headerlink" href="#rule-of-limited-supply-of-active-certifications-sigstock" title="Permalink to this headline">¶</a></h4>
+<p>By ‘active certifications’ we refer to certifications included in the
+blockchain and that haven’t yet expired.</p>
+<p>The total of active certifications issued by any member at any single
+time must be less than or equal to <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>. When this threshold is
+reached the member will have to wait for one of his active
+certifications to expire before he/she can issue a new one.</p>
+</div>
+<div class="section" id="rule-of-the-time-period-between-two-certification-issuances-sigperiod">
+<span id="id16"></span><h4>3.6.6. Rule of the time period between two certification issuances. (<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>)<a class="headerlink" href="#rule-of-the-time-period-between-two-certification-issuances-sigperiod" title="Permalink to this headline">¶</a></h4>
+<p>As soon as a certification issued by member A gets included in the
+blockchain, they will be unable to issue a new one before another
+<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> seconds.</p>
+</div>
+<div class="section" id="expiry-of-a-certification-issuance-sigwindow">
+<h4>3.6.7. Expiry of a certification issuance (<code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>)<a class="headerlink" href="#expiry-of-a-certification-issuance-sigwindow" title="Permalink to this headline">¶</a></h4>
+<p>When a certification is issued by member A, it will be stored in the
+‘pool’ for a maximum of <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> seconds. If the certification
+hasn’t been included in the blockchain by then, it will be cancelled and
+the member’s <code class="docutils literal notranslate"><span class="pre">sigStock</span></code> will be repleted by one.</p>
+</div>
+<div class="section" id="lifespan-of-a-pending-identity-idtywindow">
+<h4>3.6.8. Lifespan of a ‘pending’ identity (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>)<a class="headerlink" href="#lifespan-of-a-pending-identity-idtywindow" title="Permalink to this headline">¶</a></h4>
+<p>When a new identity is created, it is stored in the ‘pool’ for a maximum
+of <code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code> seconds. If the person hasn’t achieved member status
+by then, the certification will simply be cancelled.</p>
+</div>
+</div>
+<div class="section" id="details-on-some-of-the-wots-peculiarities-at-the-genesis-block">
+<h3>3.7. Details on some of the WoT’s peculiarities at the genesis block<a class="headerlink" href="#details-on-some-of-the-wots-peculiarities-at-the-genesis-block" title="Permalink to this headline">¶</a></h3>
+<p>The aforementioned rules can only be enforced with an existing web. They
+cannot be observed when first creating the web, that is when defining
+the genesis block.</p>
+<p>Only rules 2 and 5 can be observed at the genesis block.</p>
+<p>The genesis block has to be manually created by the founding members. In
+practice this means that there must be a choice on which identities to
+include on the premise that all of them observe rules 2 and 5. In
+addition, the genesis block must be signed with the private key of one
+of these identities.</p>
+<p>As soon as the genesis block has been created, the other identities can
+start mining the blockchain and the member who created block #0
+effectively looses the decision power he had at creation.</p>
+</div>
+<div class="section" id="why-these-rules-and-application-cases-in-the-g1">
+<span id="id17"></span><h3>3.8. Why these rules and application cases in the Ğ1<a class="headerlink" href="#why-these-rules-and-application-cases-in-the-g1" title="Permalink to this headline">¶</a></h3>
+<div class="section" id="distance-and-maximum-size">
+<h4>3.8.1. Distance and maximum size<a class="headerlink" href="#distance-and-maximum-size" title="Permalink to this headline">¶</a></h4>
+<p>The distance rule is there to curb the maximum size of a Sybil region as
+well as that of the monetary community as a whole. The <code class="docutils literal notranslate"><span class="pre">xpercent</span></code>
+parameter prevents the creation of a ‘faction’ that could take hold of
+the blockchain.</p>
+<div class="figure align-default" id="id28">
+<a class="reference internal image-reference" href="_images/wot-sybil.jpg"><img alt="Sybil region" src="_images/wot-sybil.jpg" style="width: 90%;" /></a>
+<p class="caption"><span class="caption-text">Sybil region</span><a class="headerlink" href="#id28" title="Permalink to this image">¶</a></p>
+</div>
+<p>The Sybil regions are isolated from the rest of the graph in the sense
+that they can only receive certifications from other ill-intentioned
+Sybil members. As a consequence, the shortest edge/path between a
+legitimate member and a Sybil one has to have the attack’s author as an
+endpoint. The maximum depth the Sybil region can attain is therefore
+contingent on the distance between the attacking edge-s- and the
+xpercent% closest referent members, this distance is known as
+<code class="docutils literal notranslate"><span class="pre">stepAttackers</span></code>. The maximum size of a Sybil region created by
+<code class="docutils literal notranslate"><span class="pre">sigQty</span></code> members depends on the L parameter, defined as
+<code class="docutils literal notranslate"><span class="pre">L</span> <span class="pre">=</span> <span class="pre">sigQty/sigStock</span></code>:</p>
+<div class="math notranslate nohighlight">
+\[MaxSybilSize = (sigStock - sigQty) \times {1 - L^{(stepMax - stepAttackers)} \over 1 - L}\]</div>
+<p>The maximum size of the Web of Trust is given by the following formula:</p>
+<div class="math notranslate nohighlight">
+\[WoTmax = sigStock \times L^{(stepMax - 1)}\]</div>
+<p>However we know for a fact that members will never use all of their
+available certifications. According to Dunbar <a href="#id40"><span class="problematic" id="id18">[4]_</span></a>, on average, one is
+able to maintain relationships to around 150 people. Being conservative,
+we will consider that on average, each person will certify 50 accounts.
+We can calculate the size of the average web of trust <code class="docutils literal notranslate"><span class="pre">WoTavg</span></code> :</p>
+<div class="math notranslate nohighlight">
+\[WotAvg = 50 \times \left(\frac{\textrm{sigQty}}{50}\right)^{stepMax - 1}\]</div>
+<p>Our goal with the Ğ1 is to create a community of about one million
+members to test the consequences of a libre monetary system. Let’s see
+how we can tweak the pair of sigQty and stepMax- to reach this size:</p>
+<div class="figure align-default" id="id29">
+<a class="reference internal image-reference" href="_images/wot-moy.png"><img alt="Average WoT size graph as a function of sigQty and stepMax" src="_images/wot-moy.png" style="width: 90%;" /></a>
+<p class="caption"><span class="caption-text">Average WoT size graph as a function of sigQty and stepMax</span><a class="headerlink" href="#id29" title="Permalink to this image">¶</a></p>
+</div>
+<p>The maximum size of a Sybil region grows linearly with <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> but
+exponentially with <code class="docutils literal notranslate"><span class="pre">stepMax</span></code>. Logic has it that we need to keep
+<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> as low as possible to ensure sufficient strength to the web.
+The above graph shows that the lowest value of <code class="docutils literal notranslate"><span class="pre">stepMax</span></code> for a web of
+a million members is of 5. This is an order of magnitude and is likely
+to be much higher in reality, we cannot measure it for sure.</p>
+<p>For <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> we can choose a value of <strong>4</strong> for a web of <strong>1.5 million
+members</strong> or <strong>5</strong> for <strong>half a million members</strong>. Bear in mind these
+are gross figures and could be significantly higher, we are talking
+anywhere between 1 and 10 million in reality. Calculating WOTavg gives
+us a pretty good idea of how the web would scale bearing in mind that it
+considers all members are referent members too -which isn’t the case as
+explained previously-. Hence the maximum size of the web is likely
+larger, a ballpark figure of half a million is enough for now especially
+knowing that the smaller <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> is, the easier it is to launch a
+Sybil attack -it’s easier to find four accomplices than five-. For
+security reasons we have settled on five:</p>
+<div class="math notranslate nohighlight">
+\[stepMax = 5\]</div>
+<div class="math notranslate nohighlight">
+\[sigQty = 5\]</div>
+<div class="math notranslate nohighlight">
+\[sigStock \geq 50\]</div>
+<p>The maximum size of a Sybil region therefore is:</p>
+<div class="math notranslate nohighlight">
+\[(sigStock-sigQty) * {1 - \left({sigStock \over 5}\right)^{5-stepAttackers}} \over {1-{sigStock \over 5}}\]</div>
+<p>with sigStock = 50 we have a Sybil region of:</p>
+<div class="math notranslate nohighlight">
+\[45 \times {1 - 10^{5 - stepAttackers}} \over {- 9}\]</div>
+<p>A good practice for protecting the web is to maximise <code class="docutils literal notranslate"><span class="pre">stepAttackers</span></code>.
+That’s why we decided that referent members in the genesis block had to
+be at least four steps away from each other.</p>
+<p>Another way to keep a Sybil attack at bay, were it slow enough for
+members to notice it, would be for referent members to ‘stretch’ the web
+intentionally to limit the growth of the region by ensuring that the
+attackers’ legitimate certifications received in the first place aren’t
+renewed. But what if bot accounts were created and certified each other
+super fast and following all rules, how would we counter that? By
+introducing a minimum length of time between two certifications!</p>
+</div>
+<div class="section" id="time-is-our-friend">
+<h4>3.8.2. Time is our friend<a class="headerlink" href="#time-is-our-friend" title="Permalink to this headline">¶</a></h4>
+<p>To help us deter a Sybil attack, we’ve decided to impose a minimum
+period of time between any two certifications issued from a single
+account. This parameter called <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> affords us a greater chance
+to detect the formation of a ‘hostile’ faction.</p>
+<p>Here is a graph showing the evolution of a Sybil region with the
+variation of <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>. The simulation considers that honest members
+and attackers both issue a certification each <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> interval, in
+days:</p>
+<div class="figure align-default" id="id30">
+<a class="reference internal image-reference" href="_images/impact_sig_period.png"><img alt="size of the WoT according to sigPeriod and stepAttackers" src="_images/impact_sig_period.png" style="width: 100%;" /></a>
+<p class="caption"><span class="caption-text">size of the WoT according to sigPeriod and stepAttackers</span><a class="headerlink" href="#id30" title="Permalink to this image">¶</a></p>
+</div>
+<p>As we see, there is a strong link between the growth speed of the region
+and <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>. As evidenced here, we need a <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> high
+enough in order to ensure that the legitimate web can grow at least as
+fast as a Sybil region. In addition, the higher <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> is, the
+more members will exercise their certification power gingerly, the
+action coming at a higher ‘cost’.</p>
+<p>There are numerous advantages to giving <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> a high value and
+no technical barriers to it, hence our choice of five days.</p>
+<p>We could have also gone for one week for the sake of simplicity. However
+there is an underlying idea behind our choice which was quite simply the
+pace of today’s life. Certifying someone can be a lengthy process as one
+needs to make sure they are correctly applying the Ğ1 licence and people
+nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
+to allow one to certify at the end of every working week -five days-
+instead of a whole calendar one.</p>
+</div>
+<div class="section" id="trust-me-now-trust-me-forever-sigvalidity-msvalidity">
+<h4>3.8.3. Trust me now, trust me forever ? (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>)<a class="headerlink" href="#trust-me-now-trust-me-forever-sigvalidity-msvalidity" title="Permalink to this headline">¶</a></h4>
+<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s
+Web of Trust:</p>
+<ul class="simple">
+<li><p>First of all, some members will pass and those accounts should no
+longer produce the Universal Dividend.</p></li>
+<li><p>Secondly it is of the utmost importance that ‘rogue’ accounts can be
+excluded from the web at some point.</p></li>
+</ul>
+<p>To achieve this, certifications have a limited lifespan. Members need to
+seek renewal from their peers after <code class="docutils literal notranslate"><span class="pre">sigValidity</span></code> time. On the other
+hand, this time can’t be too short that members would spend more time
+seeking renewal than they would exchanging in the currency. Furthermore,
+a certification with too short a lifespan would foster careless
+certifying behaviours. The act of certifying must have a high-enough
+‘perceived’ cost to make it feel like an important act. Lastly, we also
+wanted this lifespan to be easy to remember. Historically speaking, we
+first settled on the values of <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>, meant one
+could issue all of their certifications in 495 days, one year was
+therefore not long enough. We deemed three years to be too much and
+that’s how we agreed on two years in the end.</p>
+<p>Thinking that a deceased member could continue producing the UD for two
+long years without anyone benefitting from it was also something we
+needed to address. We chose a value of one year for <strong>msValidity</strong>. The
+act of renewing every year is done through one of the clients
+interacting with the blockchain, through a simple click on a button.
+This parameter is less important than others and is mostly there to
+‘prune’ the web of past or inactive members who don’t renew their
+membership.</p>
+</div>
+<div class="section" id="keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">
+<h4>3.8.4. Keeping the pools free of information glut (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)<a class="headerlink" href="#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow" title="Permalink to this headline">¶</a></h4>
+<p>The pools need to be cleaned up on a regular basis to avoid them
+clogging up with information and to ensure that machines with less
+calculating power can still run a Duniter node.</p>
+<p>To achieve this, identities with pending membership approval and the
+corresponding certifications have to remain the shortest time possible
+in the pool while still having a chance of making it into the
+blockchain.</p>
+<p>For the Ğ1, our opinion was that two months would be enough for all
+potential certifiers to agree on a specific identity to certify. We also
+wanted a time period that would be easy enough to remember by all. We
+settled on two months, and gave this value to all three parameters
+<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>.</p>
+</div>
+<div class="section" id="avoiding-single-members-from-knowing-too-many-people-sigstock">
+<h4>3.8.5. Avoiding single members from ‘knowing too many people’ (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)<a class="headerlink" href="#avoiding-single-members-from-knowing-too-many-people-sigstock" title="Permalink to this headline">¶</a></h4>
+<div class="line-block">
+<div class="line">We considered that on average, each person will certify 50 people.
+However, we know for a fact that some members will use more than 50
+certifications. The maximum social network of one individual is around
+150 people <a href="#id41"><span class="problematic" id="id19">[5]_</span></a>. Being conservative, we settled on a maximum
+certification number <code class="docutils literal notranslate"><span class="pre">sigstock</span></code> of 100.</div>
+<div class="line">Since <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>’s impact on the size of a Sybil region is fairly
+limited, we did not investigate further this parameter.</div>
+</div>
+</div>
+<div class="section" id="avoiding-locking-minorities-xpercent">
+<h4>3.8.6. Avoiding locking minorities (<code class="docutils literal notranslate"><span class="pre">xpercent</span></code>)<a class="headerlink" href="#avoiding-locking-minorities-xpercent" title="Permalink to this headline">¶</a></h4>
+<p>It’s easy enough to become a referent member, one of the Sybil
+strategies could therefore be to create a region of referent members.
+Such a region would grow slower than otherwise but could confer a
+locking power to its members by using the distance rule. That’s why the
+distance rule cannot be calculated on 100% of the referent members.
+Hence the introduction of the <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> parameter which defines the
+percentage of referent members needing to be less than five edges
+-steps- from each other.</p>
+<p>This percentage needs to be low enough to prevent the formation of a
+locking minority -referent Sybil members being too far from legitimate
+referent members-. On the other hand, it needs to be high enough so as
+to restrict the maximum size of the Sybil region through the distance
+rule. The <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> parameter was one of the hardest to define,
+therefore we might decide to change its value during the Ğ1 experiment.</p>
+<p>We were inspired by the Pareto principle <a class="footnote-reference brackets" href="#id26" id="id20">6</a>: if at least 20% of
+members give good density to the web, 80% of the referent members will
+be five or less steps from any other member -referent or not-. The
+maximum value for <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> is therefore 80%, anything above that and
+the distance rule could be too restrictive for legitimate use cases.
+With security our top concern, we chose the maximum value of 80%.</p>
+</div>
+<div class="section" id="spam-protection-with-msperiod">
+<h4>3.8.7. Spam protection with (<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>)<a class="headerlink" href="#spam-protection-with-msperiod" title="Permalink to this headline">¶</a></h4>
+<p>This parameter stands out a bit on its own, as it was added after the
+genesis block. It is there to protect the Duniter P2P infrastructure
+against ‘spam’ attacks. We had to think of a strategy against attacks
+such as high-frequency membership renewal requests -i.e: in every block,
+every five minutes- or worse still, hundreds of these requests per
+minute to flood the Duniter nodes. Without such limits, nodes are
+supposed to address all renewal requests, even in cases where they were
+last published five minutes ago! The <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> parameter was given
+the same value as <code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>,
+i.e. two months.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id21"><span class="brackets">1</span></dt>
+<dd><p>Surfing a Web of Trust, Reputation and Reciprocity on
+CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic:
+<a class="reference external" href="http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf">snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf</a></p>
+</dd>
+<dt class="label" id="id22"><span class="brackets">2</span></dt>
+<dd><p>Public key validation on GnuPG manual, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p>
+</dd>
+<dt class="label" id="id23"><span class="brackets">3</span></dt>
+<dd><p>The Sibyl Attack, J.R.Douceur:
+<a class="reference external" href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></p>
+</dd>
+<dt class="label" id="id24"><span class="brackets">4</span></dt>
+<dd><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p>
+</dd>
+<dt class="label" id="id25"><span class="brackets">5</span></dt>
+<dd><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p>
+</dd>
+<dt class="label" id="id26"><span class="brackets"><a class="fn-backref" href="#id20">6</a></span></dt>
+<dd><p>Pareto principle :
+<a class="reference external" href="https://en.wikipedia.org/wiki/Pareto_principle">en.wikipedia.org/wiki/Pareto_principle</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+<div class="section" id="proof-of-work-with-personal-difficulty">
+<span id="proof-of-work-with-personalized-difficulty"></span><h2>4. Proof of Work with personal difficulty<a class="headerlink" href="#proof-of-work-with-personal-difficulty" title="Permalink to this headline">¶</a></h2>
+<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers.
+It uses a proof of Work (PoW) to write the Blockchain on a regular
+basis, much like BitCoin. However, Duniter has a unique asset : the WoT,
+where each member represents a unique living human.</p>
+<p>This difference might seem minimal, but it has an enormous consequence :
+while Bitcoin uses a race based on computing power only, Duniter creates
+a validation frame that is no race. It is more like a lottery where each
+“winning” member is excluded for a certain amount of time. Moreover,
+those who have more computing power get a handicap, as a way to let
+other peers win. All this is possible through the WoT, that allows
+personalised difficulty while PoW is used for synchronization. All the
+rules of this PoW/WoT mechanism can be verified by reading the
+blockchain. As a consequence, a peer only needs to have an up-to-date
+copy of the blockchain to apply the rules. A view of the whole network
+is not needed.</p>
+<p>Another strong difference is that forging peers are not rewarded by the
+protocol. There is no economical incentive on forging lots of blocs,
+neither on having a lot of computing power.</p>
+<p>One could say that Duniter uses a PoW that needs very low energy
+consumption compared to BitCoin : an “ecological” PoW ?</p>
+<div class="section" id="why-do-we-need-proof-of-work">
+<span id="why-proof-of-work"></span><h3>4.1. Why do we need Proof of Work ?<a class="headerlink" href="#why-do-we-need-proof-of-work" title="Permalink to this headline">¶</a></h3>
+<p>Duniter nodes share a database as part of a p2p environment. The proof
+of work (PoW) allows machines to synchronize with each other. In
+Duniter’s case, the blockchain is our database, and acts as a ledger
+keeping a trace of all transactions, status of the WoT and more. How can
+we let several machines add data (ie: a transaction) at the same time?
+In addition, how do we settle on how much time has gone by since the
+blockchain was last updated? Agreement on time is of the utmost
+importance as we want to create Universal Dividends on a regular basis,
+and keep track of membership status, both in human time.</p>
+<p>Proof-of-work provides a clever solution to both problems:</p>
+<ol class="arabic simple">
+<li><p>Any machine can write into the blockchain (create a new block) but is
+only authorised to do so if it has previously solved a mathematical
+equation that require a certain amount of work. The challenge has to
+be hard enough to prevent two machines to solve it at the same time,
+ensuring the unicity of a block’s creator.</p></li>
+<li><p>Solving this challenge takes a certain amount of time, which depends
+on the calculating power of the whole network. This provides a common
+ground for defining the needed time reference. A block time is set
+(ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to
+get an average duration corresponding to this block time.</p></li>
+</ol>
+</div>
+<div class="section" id="only-members-can-mine">
+<h3>4.2. Only members can “mine”<a class="headerlink" href="#only-members-can-mine" title="Permalink to this headline">¶</a></h3>
+<p>One of Duniter’s major differences with other PoW-based cryptocurrencies
+is that only members are allowed to author blocks. Each block is signed
+with the member’s private key, allowing the algorithm to determine a
+personalised difficulty.</p>
+<p>This personalised difficulty eliminates the rat-race for the most
+sophisticated and powerful mining equipment. Another benefit is the fact
+that no “supercomputer” can take control of the blockchain. Lastly,
+Duniter implements a rotation in forging members thanks to this
+personalized difficulty.</p>
+<p>This lightweight PoW is much less energy-consuming than other PoW
+cryptocurrencies. Members can mine with anything from a raspberry pi to
+a privacy-first internet cube.</p>
+</div>
+<div class="section" id="how-does-it-work">
+<span id="how-does-duniter-pow-work"></span><h3>4.3. How does it work ?<a class="headerlink" href="#how-does-it-work" title="Permalink to this headline">¶</a></h3>
+<div class="section" id="the-hash-aka-digest">
+<span id="the-hash"></span><h4>4.3.1. The hash (aka digest)<a class="headerlink" href="#the-hash-aka-digest" title="Permalink to this headline">¶</a></h4>
+<p>Example of a valid hash:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">00000276902793</span><span class="n">AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</span>
+</pre></div>
+</div>
+<p>As you can see this hash starts with five zeros which was very hard to
+achieve and took a lot of work for someone’s computer. Hence the term
+“proof of work”.</p>
+</div>
+<div class="section" id="the-common-difficulty">
+<span id="common-difficulty"></span><h4>4.3.2. The common difficulty<a class="headerlink" href="#the-common-difficulty" title="Permalink to this headline">¶</a></h4>
+<p>A common difficulty is needed to settle on a yardstick for our time
+reference. Its role is to make sure the blockchain moves forward at a
+steady pace - one block every <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code> seconds, <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code>
+being one of the 20 parameters behind the Duniter protocol-.</p>
+<p>This difficulty’s initial value can be set to any arbitrary value
+(<code class="docutils literal notranslate"><span class="pre">70</span></code> in Duniter <code class="docutils literal notranslate"><span class="pre">v1.5.x</span></code>) and then acts as a spring, regulating
+blocktime creation by increasing itself if the creation interval drops
+under <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code> and vice-versa.</p>
+<div class="section" id="how-is-difficulty-applied">
+<h5>4.3.2.1. How is difficulty applied ?<a class="headerlink" href="#how-is-difficulty-applied" title="Permalink to this headline">¶</a></h5>
+<p>The numeric value of difficulty is taken from an array of possible
+hashes out of all possible hashes. In DUBPv13 the hash of a block is its
+sha256 hexadecimal hash.</p>
+<p>To understand the difficulty, we make a euclidiean division of the
+difficulty by 16.</p>
+<p>Here’s an example with a difficulty value of 70 :</p>
+<p>The valid hashes are the ones starting with four zeros and with the
+fifth character less than or equal to 9 (6 in hexadecimal notation). The
+valid hashes are then written as starting with : <code class="docutils literal notranslate"><span class="pre">0000[0-9]</span></code>. This is
+a bit different from Bitcoin, where the difficulty is only ruled by the
+number of zeroes.</p>
+</div>
+<div class="section" id="the-nonce">
+<h5>4.3.2.2. The Nonce<a class="headerlink" href="#the-nonce" title="Permalink to this headline">¶</a></h5>
+<p>When a member is forging a new block, his computer freezes the block’s
+content and changes the Nonce until the hash reaches the required number
+of zeroes.</p>
+<p>The nonce allows us to mine a new block by finding a hash. The hash
+value allows us to determine the difficulty level of the proof-of-work
+performed. Examples of possible Nonce values:</p>
+<ul class="simple">
+<li><p>10100000112275</p></li>
+<li><p>10300000288743</p></li>
+<li><p>10400000008538</p></li>
+<li><p>10700000079653</p></li>
+<li><p>10300000070919</p></li>
+</ul>
+<p>In reality the <code class="docutils literal notranslate"><span class="pre">Nonce</span></code> value follows a pre-determined format akin to
+<code class="docutils literal notranslate"><span class="pre">XYY00000000000</span></code>. The Nonce’s value isn’t the number of attempts but
+rather a value within a set of possible ones. This is how the Nonce is
+built:</p>
+<ul class="simple">
+<li><p>X is a number assigned to a specific peer. Let’s assume that someone
+has several nodes each with the same private key, this would lead to
+possible collisions if this person were to mine the same block with
+different nodes. Each [STRIKEOUT:block] <strong>node ?</strong> will therefore
+have its own unique X to prevent this from happening.</p></li>
+<li><p>Y is the number of cores of the processor. The Nonce starting with
+<code class="docutils literal notranslate"><span class="pre">107[…]</span></code> belongs to a seven cores processor, while <code class="docutils literal notranslate"><span class="pre">199[...]</span></code>
+could be the proof generated by a 99 cores processor.</p></li>
+</ul>
+<p>The rest of the Nonce, the part that follows after the XYY, is the
+numerical space for this individual node and is unique to each of the
+CPU’s core. This space is comprised of eleven digits (<code class="docutils literal notranslate"><span class="pre">00000000000</span></code>).
+For the sake of accuracy, we use the term CPU in the wider sense, it can
+be understood as a bi-CPU for example. We take into consideration the
+number of cores for the resulting PoW.</p>
+</div>
+</div>
+</div>
+<div class="section" id="personalised-difficulty">
+<h3>4.4. Personalised difficulty<a class="headerlink" href="#personalised-difficulty" title="Permalink to this headline">¶</a></h3>
+<p>Earlier in this article, we explained that the personalised difficulty
+is the new and key concept that sets Duniter apart from other PoW-based
+cryptocurrencies.</p>
+<p>Here is how this personalised difficulty is calculated and assigned:</p>
+<p>It is determined by a combination of two different constraints with
+complimentary roles: the <strong>exclusion factor</strong> and the <strong>handicap</strong>.</p>
+<p>Let <code class="docutils literal notranslate"><span class="pre">powMin</span></code> be the common difficulty, <code class="docutils literal notranslate"><span class="pre">exFact</span></code> a member’s exclusion
+factor and <code class="docutils literal notranslate"><span class="pre">handicap</span></code> their handicap. This member’s personalised
+difficulty <code class="docutils literal notranslate"><span class="pre">diff</span></code> is:</p>
+<div class="math notranslate nohighlight">
+\[{\textrm{diff} = \textrm{powMin} \times \textrm{exFact} + \textrm{handicap}}\]</div>
+<div class="section" id="understanding-exfact-the-exclusion-factor">
+<span id="the-exclusion-factor"></span><h4>4.4.1. Understanding <code class="docutils literal notranslate"><span class="pre">exFact</span></code>, the exclusion factor<a class="headerlink" href="#understanding-exfact-the-exclusion-factor" title="Permalink to this headline">¶</a></h4>
+<p>Members who have never produced blocks or haven’t for quite some time
+are assigned an exclusion factor of <code class="docutils literal notranslate"><span class="pre">1</span></code>. Their personalised difficulty
+is therefore simply the sum of <code class="docutils literal notranslate"><span class="pre">powMin</span> <span class="pre">+</span> <span class="pre">handicap</span></code>.</p>
+<p>Before reading on, let’s precise the role of this exclusion factor. When
+a member adds a block to the chain, his <code class="docutils literal notranslate"><span class="pre">exFact</span></code> jumps up from one to
+a very high value, to prevent them from forging other blocks immediately
+after and taking control of the blockchain.</p>
+<p>The exclusion factor will then rapidly return to one. This delay is
+expressed as a number of blocks. It is calculated as a proportion of the
+number of members forging. In the Ğ1’s case, this proportion is 1/3,
+meaning that if there are fifteen members currently forging, the
+member’s exclusion factor will drop down to one after five blocks.</p>
+<div class="section" id="what-is-intended-by-the-number-of-members-forging">
+<h5>4.4.1.1. What is intended by “the number of members forging” ?<a class="headerlink" href="#what-is-intended-by-the-number-of-members-forging" title="Permalink to this headline">¶</a></h5>
+<p>We mean the number of members trying to create the next block. In
+reality, there is no way to precisely know how many members are
+calculating at any given time, because it is impossible to view the
+entire network. But we need this information, whithout which assigning a
+personalised difficulty is impossible. To achieve this, Duniter looks
+back at the blockchain and assumes that there is as much members forging
+as those who have found at least one block in the last blocks in the
+current window, minus the very last one.</p>
+</div>
+<div class="section" id="current-window">
+<h5>4.4.1.2. Current window<a class="headerlink" href="#current-window" title="Permalink to this headline">¶</a></h5>
+<p>We use the concept of <strong>current window</strong>. The current window is the
+number of blocks we look back at to determine how many members are
+forging. Let’s see how it works:</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> is the size of the current window in blocks.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> the number of members who have calculated at least
+one block during the current window.</p></li>
+</ul>
+<p>Both <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> and <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> are block fields. When first
+starting a blockchain, the very first block has an <code class="docutils literal notranslate"><span class="pre">issuersFrame=1</span></code>
+and an <code class="docutils literal notranslate"><span class="pre">issuersCount=0</span></code>. The genesis block is excluded as there are no
+members in the current window!</p>
+<p>From the second block onwards (block #1) we track the variation of
+<code class="docutils literal notranslate"><span class="pre">issuersCount</span></code>. The member having mined block #0 enters the current
+window and in block #1 we will therefore mention <code class="docutils literal notranslate"><span class="pre">issuersCount=1</span></code>.</p>
+<p><code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> then varies as follows:</p>
+<ul class="simple">
+<li><p>if <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> increases by N (with a maximum step of N = 1),
+then <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> will increase by one unit over a period of 5N
+blocks.</p></li>
+<li><p>Conversely, if <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> decreases by Y (with a maximum step
+of Y = 2 = current window inching forward + loss of one calculating
+member), then <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> will decrease by one unit during 5Y
+blocks.</p></li>
+<li><p>When such events overlap, <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> evolves as so :</p></li>
+</ul>
+<table class="docutils align-default">
+<colgroup>
+<col style="width: 11%" />
+<col style="width: 67%" />
+<col style="width: 23%" />
+</colgroup>
+<thead>
+<tr class="row-odd"><th class="head"><p>bloc</p></th>
+<th class="head"><p>event</p></th>
+<th class="head"><p>issuersFrame</p></th>
+</tr>
+</thead>
+<tbody>
+<tr class="row-even"><td><p>T</p></td>
+<td><p>Babar writes a block and enters issuersCount</p></td>
+<td><p>160</p></td>
+</tr>
+<tr class="row-odd"><td><p>T+1</p></td>
+<td><p>Celeste leaves issuersCount</p></td>
+<td><p>160 +1 = 161</p></td>
+</tr>
+<tr class="row-even"><td><p>T+2</p></td>
+<td><p>N/a</p></td>
+<td><p>161 +1 -1 = 161</p></td>
+</tr>
+<tr class="row-odd"><td><p>T+3/4/5</p></td>
+<td><p>N/a</p></td>
+<td><p>161 +1 -1 = 161</p></td>
+</tr>
+<tr class="row-even"><td><p>T+6</p></td>
+<td><p>N/a</p></td>
+<td><p>161 -1 = 160</p></td>
+</tr>
+</tbody>
+</table>
+<p>The calculation can be found under rules
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe">BR_G05</a>
+and
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar">BR_G06</a>
+of the DUP protocol.</p>
+</div>
+<div class="section" id="exfact-and-the-personalised-difficulty">
+<h5>4.4.1.3. exFact and the personalised difficulty<a class="headerlink" href="#exfact-and-the-personalised-difficulty" title="Permalink to this headline">¶</a></h5>
+<p>We explained that <code class="docutils literal notranslate"><span class="pre">exFact</span></code> spikes immediately after the member has
+found a block. It decreases then rapidly to <code class="docutils literal notranslate"><span class="pre">1</span></code> after a number of
+blocks equal to <code class="docutils literal notranslate"><span class="pre">1/3</span> <span class="pre">*</span> <span class="pre">issuersCount</span></code>. Let’s see precisely how we
+calculate <code class="docutils literal notranslate"><span class="pre">exFact</span></code>:</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">nbPreviousIssuers</span></code> is the value of issuersCount at the last block
+<code class="docutils literal notranslate"><span class="pre">N</span></code> found by the member.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span></code> is the number of blocks found by the rest of the
+network since block <code class="docutils literal notranslate"><span class="pre">N</span></code>.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">percentRot</span></code> is the number of <em>not excluded</em> peers we want. It is a
+monetary parameter, its value is 0.67 for Ğ1 currency.</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[exFact = MAX[ 1 ; FLOOR ({{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}}) ]\]</div>
+<p>The FLOOR is a simple truncate function. For <code class="docutils literal notranslate"><span class="pre">exFact</span></code> to exclude the
+member, we need :</p>
+<div class="math notranslate nohighlight">
+\[{{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}} &gt;= 2\]</div>
+<p>We can see that the member is not excluded if <code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span></code> is
+greater than 1/3 of the calculating members. Take as an example
+<code class="docutils literal notranslate"><span class="pre">nbPreviousIssuers</span> <span class="pre">=</span> <span class="pre">6</span></code> and <code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span> <span class="pre">=</span> <span class="pre">3</span></code>:</p>
+<div class="math notranslate nohighlight">
+\[{0.67 \times {6 \over {1 + 3}} = 1.005} \Rightarrow exFact = 1\]</div>
+<p>However, if the member computed a block one block ago (nbBlocksSince =
+1), exFact = 2 and the forging peer is excluded:</p>
+<div class="math notranslate nohighlight">
+\[{0.67 \times {6 \over {1 + 1}} = 2.01} \Rightarrow exFact = 2\]</div>
+<p>Moreover if the last block was authored by the said member, then:</p>
+<div class="math notranslate nohighlight">
+\[nbBlocksSince = 0\]</div>
+<div class="math notranslate nohighlight">
+\[exFact = 0.67 \times nbPreviousIssuers\]</div>
+<p>ExFact value increases according to the number of members calculating.
+Thus, if there is enough members calculating, even mining farms would be
+excluded. We have therefore succeeded in our intent to deter attempts to
+seize the blockchain and its currency.</p>
+<p>However, at any time <code class="docutils literal notranslate"><span class="pre">t</span></code>, the two-thirds of calculating members all
+have an exclusion factor of <code class="docutils literal notranslate"><span class="pre">1</span></code>, even though they might not all have
+the same computational power at hand. If the personalised difficulty
+only took into account the exclusion factor, then only the members with
+the highest computational power from the remaining third would be able
+to author new blocks and the other 2/3s would almost always be excluded.
+Lesser machines wouldn’t stand a chance…</p>
+</div>
+</div>
+<div class="section" id="the-handicap">
+<h4>4.4.2. The handicap<a class="headerlink" href="#the-handicap" title="Permalink to this headline">¶</a></h4>
+<p>The handicap is the second parameter of the personalised difficulty. Its
+main role is to improve the rotation of forging peers. A higher handicap
+is assigned to members with higher calculating power, so lesser machines
+can also compute blocks. As a consequence, there is no incentive on
+forging with powerful computers. Security can be achieved with less
+computing power than with pure PoW.</p>
+<p>The aim is to handicap the half that has authored most blocks (the most
+powerful half) to favour the other one. So, the handicap formula will
+use the median number of blocks authored by peers within the current
+window.</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">nbPersonalBlocksInFrame</span></code> is the number of blocks authored by a
+single member within the current window.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">medianOfBlocksInFrame</span></code> is the median number of blocks written by
+the calculating members during the same timeframe.</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[handicap = FLOOR( {\ln({ \max({ 1 ; {{nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame} )} )} \over \ln{1.189} })\]</div>
+<p>Let’s unwrap the formula:</p>
+<div class="math notranslate nohighlight">
+\[{ {nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame}\]</div>
+<p>is simply the ratio between the number of blocks authored by the peer
+and the median number of blocks. For example, if a peer has authored
+<code class="docutils literal notranslate"><span class="pre">9</span></code> blocks in the current window and the median is <code class="docutils literal notranslate"><span class="pre">5</span></code>, then the
+ratio will be <code class="docutils literal notranslate"><span class="pre">(9+1)/5</span> <span class="pre">=</span> <span class="pre">2</span></code>.</p>
+<ul class="simple">
+<li><p>The MAX function allows us to ensure that</p></li>
+</ul>
+<p>the handicap has a value at least equal to <code class="docutils literal notranslate"><span class="pre">1</span></code>.</p>
+<ul class="simple">
+<li><p>The Napierian Logarithm of this ratio prevents the handicap from</p></li>
+</ul>
+<p>becoming excluding. We want the handicap to level the calculating field
+so that all peers stand a chance, not to exclude peers.</p>
+<ul class="simple">
+<li><p>If we wanted the handicap to be applied as soon as the median is</p></li>
+</ul>
+<p>reached, we would divide it by <code class="docutils literal notranslate"><span class="pre">LN(1)</span></code>. The problem is that we have
+already set a minimum value of <code class="docutils literal notranslate"><span class="pre">1</span></code> with the MAX function. If we were
+to divide the ratio by <code class="docutils literal notranslate"><span class="pre">LN(1)</span></code> all calculating peers would have a
+handicap <code class="docutils literal notranslate"><span class="pre">\&gt;=</span> <span class="pre">1</span></code>. In addition, is it really fair to handicap a member
+who is right on the median?</p>
+<p>That’s why we went for <code class="docutils literal notranslate"><span class="pre">1.189</span></code> rather than <code class="docutils literal notranslate"><span class="pre">1</span></code>. A member has to be
+at least <code class="docutils literal notranslate"><span class="pre">18.9%</span></code> above the median to be assigned a handicap. 18.9% is
+actually 16^(1/16), the difficulty factor between two levels of the
+proof work (hexadecimal hash).</p>
+<p>To conclude, you have to remember that :</p>
+<ul class="simple">
+<li><p>The handicap is indexed on the logarithm of the ratio to the median,</p></li>
+<li><p>Handicap is only applied on members whose ratio to the median is
+greater than the ratio between two levels of the proof-of-work’s
+difficulty.</p></li>
+</ul>
+</div>
+</div>
+</div>
+<div class="section" id="conclusion">
+<h2>Conclusion<a class="headerlink" href="#conclusion" title="Permalink to this headline">¶</a></h2>
+<!-- source : https://duniter.org/en/theoretical/ --><p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document
+retracing the history of the currency. However, Duniter registers not
+only trades, but also the history of relationships in the community as a
+mean to identify a human to a digital account. This way, Duniter has
+information about the fondamental reference of RTM : living humans. A
+libre Currency can be issued thanks to the Universal Dividend.</p>
+<p>More than that, Duniter proposes a new model for securing a Blockchain
+in an efficient and decentralized way. Basing the security on a Web of
+Trust with an individualised security makes the calculation rules more
+fair. A side-effect of this choice is a network consisting mostly of
+low-end computers, maintaining a good security and helping
+decentralization of calculation.</p>
+<p>The ultimate goal of Duniter project is to allow people to participate
+in a libre economy, thanks to a libre currency. What is a libre economy
+? The Relative Theory of Money defines it through four economic
+liberties :</p>
+<ul class="simple">
+<li><p>The freedom to choose your currency system: because money should not
+be imposed.</p></li>
+<li><p>The freedom to access resources: because we all should have access to
+economic &amp; monetary resources.</p></li>
+<li><p>The freedom to estimate and produce value: because value is a purely
+relative to each individual.</p></li>
+<li><p>The freedom to trade with the money: because we should not be limited
+by the avaible money supply.</p></li>
+</ul>
+<p>Those 4 economic freedoms should be understood together, not
+exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So
+here, freedom does not mean the right to take all of a resource (like
+water source in a desert) so no more is available to the others. Now you
+get it, this is the goal: free economy through free currency.</p>
+</div>
+<div class="section" id="sources">
+<h2>Sources :<a class="headerlink" href="#sources" title="Permalink to this headline">¶</a></h2>
+<ul class="simple">
+<li><p>Relative Theory of Money, S.Laborde, 2010:
+<a class="reference external" href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></p></li>
+<li><p>Bitcoin Whitepaper, S.Nakamoto, 2008:
+<a class="reference external" href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></p></li>
+<li><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 :
+<a class="reference external" href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></p></li>
+<li><p>The GNU Privacy Handbook, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p></li>
+<li><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+77–89.
+<a class="reference external" href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</p></li>
+<li><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp;
+S.Nadal, 2012 :
+<a class="reference external" href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></p></li>
+<li><p>Duniter Blockchain Protocol, v13, draft by Elois :
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md">git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</a></p></li>
+<li><p>The Sibyl Attack, J.R.Douceur:
+<a class="reference external" href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></p></li>
+<li><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p></li>
+</ul>
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="#">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">Duniter technical description</a><ul>
+<li><a class="reference internal" href="#abstract">Abstract</a></li>
+<li><a class="reference internal" href="#introduction">Introduction</a></li>
+<li><a class="reference internal" href="#state-of-the-art-bitcoin-case">1. State of the art : Bitcoin case</a><ul>
+<li><a class="reference internal" href="#monetary-creation-of-bitcoin-a-space-time-asymmetry">1.1. Monetary creation of Bitcoin : a space-time asymmetry</a><ul>
+<li><a class="reference internal" href="#spatial-asymmetry">1.1.1. Spatial asymmetry</a></li>
+<li><a class="reference internal" href="#temporal-asymmetry">1.1.2. Temporal-asymmetry</a></li>
+<li><a class="reference internal" href="#a-solution">1.1.3. A solution</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#proof-of-work-mining-a-power-race">1.2. Proof-of-Work mining : a power race</a><ul>
+<li><a class="reference internal" href="#what-about-proof-of-stake">1.2.1 What about Proof of Stake ?</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#duniters-blockchain">2. Duniters Blockchain</a><ul>
+<li><a class="reference internal" href="#spam-countermeasures">2.1. Spam countermeasures</a><ul>
+<li><a class="reference internal" href="#minimum-output-amount">2.1.1. Minimum output amount</a></li>
+<li><a class="reference internal" href="#limited-block-size-and-chainability">2.1.2. Limited block size and chainability</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#scaling">2.2. Scaling</a><ul>
+<li><a class="reference internal" href="#dynamic-block-size">2.2.1 Dynamic block size</a></li>
+<li><a class="reference internal" href="#lightning-networks">2.2.2. Lightning Networks</a></li>
+<li><a class="reference internal" href="#unit-base">2.2.3. Unit base</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#duniter-web-of-trust">3. Duniter Web of Trust</a><ul>
+<li><a class="reference internal" href="#basic-principles">3.1. Basic Principles</a></li>
+<li><a class="reference internal" href="#why-do-we-need-a-web-of-trust">3.2. Why do we need a Web of Trust ?</a></li>
+<li><a class="reference internal" href="#the-importance-of-having-our-own-certification-system">3.3. The importance of having our own certification system</a></li>
+<li><a class="reference internal" href="#a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary">3.4. A few foundational concepts on graph theory : a bit of vocabulary</a></li>
+<li><a class="reference internal" href="#definition-of-the-duniter-web-of-trust">3.5. Definition of the Duniter Web of Trust</a></li>
+<li><a class="reference internal" href="#exploring-the-rules-behind-a-duniter-web-of-trust">3.6. Exploring the rules behind a Duniter Web of Trust</a><ul>
+<li><a class="reference internal" href="#distance-rule-and-referent-members-stepmax-and-xpercent">3.6.1. Distance rule and referent members (<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> and <code class="docutils literal notranslate"><span class="pre">xPercent</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-the-minimum-number-of-certifications-needed-sigqty">3.6.2. Rule of the minimum number of certifications needed (<code class="docutils literal notranslate"><span class="pre">sigQty</span></code>)</a></li>
+<li><a class="reference internal" href="#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">3.6.3. The membership renewal rule (<code class="docutils literal notranslate"><span class="pre">msValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-certification-lifespan-sigvalidity">3.6.4. Rule of certification lifespan (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-limited-supply-of-active-certifications-sigstock">3.6.5. Rule of limited supply of active certifications (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-the-time-period-between-two-certification-issuances-sigperiod">3.6.6. Rule of the time period between two certification issuances. (<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>)</a></li>
+<li><a class="reference internal" href="#expiry-of-a-certification-issuance-sigwindow">3.6.7. Expiry of a certification issuance (<code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#lifespan-of-a-pending-identity-idtywindow">3.6.8. Lifespan of a ‘pending’ identity (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>)</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#details-on-some-of-the-wots-peculiarities-at-the-genesis-block">3.7. Details on some of the WoT’s peculiarities at the genesis block</a></li>
+<li><a class="reference internal" href="#why-these-rules-and-application-cases-in-the-g1">3.8. Why these rules and application cases in the Ğ1</a><ul>
+<li><a class="reference internal" href="#distance-and-maximum-size">3.8.1. Distance and maximum size</a></li>
+<li><a class="reference internal" href="#time-is-our-friend">3.8.2. Time is our friend</a></li>
+<li><a class="reference internal" href="#trust-me-now-trust-me-forever-sigvalidity-msvalidity">3.8.3. Trust me now, trust me forever ? (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>)</a></li>
+<li><a class="reference internal" href="#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">3.8.4. Keeping the pools free of information glut (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#avoiding-single-members-from-knowing-too-many-people-sigstock">3.8.5. Avoiding single members from ‘knowing too many people’ (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)</a></li>
+<li><a class="reference internal" href="#avoiding-locking-minorities-xpercent">3.8.6. Avoiding locking minorities (<code class="docutils literal notranslate"><span class="pre">xpercent</span></code>)</a></li>
+<li><a class="reference internal" href="#spam-protection-with-msperiod">3.8.7. Spam protection with (<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>)</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#proof-of-work-with-personal-difficulty">4. Proof of Work with personal difficulty</a><ul>
+<li><a class="reference internal" href="#why-do-we-need-proof-of-work">4.1. Why do we need Proof of Work ?</a></li>
+<li><a class="reference internal" href="#only-members-can-mine">4.2. Only members can “mine”</a></li>
+<li><a class="reference internal" href="#how-does-it-work">4.3. How does it work ?</a><ul>
+<li><a class="reference internal" href="#the-hash-aka-digest">4.3.1. The hash (aka digest)</a></li>
+<li><a class="reference internal" href="#the-common-difficulty">4.3.2. The common difficulty</a><ul>
+<li><a class="reference internal" href="#how-is-difficulty-applied">4.3.2.1. How is difficulty applied ?</a></li>
+<li><a class="reference internal" href="#the-nonce">4.3.2.2. The Nonce</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#personalised-difficulty">4.4. Personalised difficulty</a><ul>
+<li><a class="reference internal" href="#understanding-exfact-the-exclusion-factor">4.4.1. Understanding <code class="docutils literal notranslate"><span class="pre">exFact</span></code>, the exclusion factor</a><ul>
+<li><a class="reference internal" href="#what-is-intended-by-the-number-of-members-forging">4.4.1.1. What is intended by “the number of members forging” ?</a></li>
+<li><a class="reference internal" href="#current-window">4.4.1.2. Current window</a></li>
+<li><a class="reference internal" href="#exfact-and-the-personalised-difficulty">4.4.1.3. exFact and the personalised difficulty</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#the-handicap">4.4.2. The handicap</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#conclusion">Conclusion</a></li>
+<li><a class="reference internal" href="#sources">Sources :</a></li>
+</ul>
+</li>
+</ul>
+
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/index.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
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+        <li class="nav-item nav-item-this"><a href="">Duniter technical description</a></li> 
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+
+<!DOCTYPE html>
+
+<html>
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>Abstract &#8212; Duniter technical description 0.0.2 documentation</title>
+    <link rel="stylesheet" href="../../_static/pyramid.css" type="text/css" />
+    <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
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+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Neuton&amp;subset=latin" type="text/css" media="screen" charset="utf-8" />
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+<!--[if lte IE 6]>
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+<![endif]-->
+
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+
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+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Abstract</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <div class="section" id="abstract">
+<h1>Abstract<a class="headerlink" href="#abstract" title="Permalink to this headline">¶</a></h1>
+<p>Many currency principles involve non-equal rights to monetary creation
+between humans. We propose a monetary creation based on the Relative
+Theory of Money, which guarantee equal monetary creation for each
+willing human. This type of currency can be centralised, however, this
+could lead to censorship and arbitrary choices of the central
+institution. Thus, strongly inspired by Bitcoin example, we want the
+currency to be as decentralised as possible, in the transaction network
+as in the human identification process. We use a Web of Trust between
+living humans for identification. This web of trust allows us to impose
+personalised difficulty for transaction validation, keeping the
+calculation accessible to low-end hardware and allowing all competent
+members to secure the currency.</p>
+</div>
+<div class="section" id="introduction">
+<h1>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h1>
+<p>Duniter is a software to create and manage “libre currencies”. Libre
+currency is a concept defined by S.Laborde in the Relative Theory of
+Money (RTM) that was published in 2010. This theory demonstrates the
+possibility of an invariant monetary unit : the Universal Dividend.
+Doing so, the RTM answers the question :</p>
+<blockquote>
+<div><p>How should a currency be created to match the principle of equality
+between all humans, now and between generations ?</p>
+</div></blockquote>
+<p>The results of this demonstration implies a monetary creation :</p>
+<ul class="simple">
+<li><p>on a regular basis</p></li>
+<li><p>for each human being</p></li>
+<li><p>which amount has to be reassessed on fixed intervals according to a
+fixed formula.</p></li>
+</ul>
+<p>Thus, Duniter project will associate a human to a digital identity. It
+will use a Web of Trust with specific rules. As the number of members
+may evolve, the Universal Dividend has to be created according to the
+formula :</p>
+<div class="math notranslate nohighlight">
+\[UD(t+1) = UD(t) + c^2 \times {M(t) \over N(t)}\]</div>
+<p>Duniter is based on a decentralized Blockchain. This technical choice
+allows irreversibility of transaction and uncensorability of trades and
+identities. While inspired by Bitcoin, Duniter uses a Web of Trust and
+the Proof of Work to secure the computation network, thus making
+obsolete the power race model used in Bitcoin.</p>
+<p>The first currency created through Duniter is Ğ1, pronounced “June”. It
+was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters
+as examples ; however, one can create another libre currency with custom
+parameters while still using Duniter software.</p>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="../../index.html">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">Abstract</a></li>
+<li><a class="reference internal" href="#introduction">Introduction</a></li>
+</ul>
+
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="../../_sources/parts/en/1_intro.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" />
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+</div>
+<script>$('#searchbox').show(0);</script>
+        </div>
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+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Abstract</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2020, Matograine.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 3.1.1.
+    </div>
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+</html>
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diff --git a/build/parts/en/2_looking_at_Bitcoin.html b/build/parts/en/2_looking_at_Bitcoin.html
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+
+<!DOCTYPE html>
+
+<html>
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>1. State of the art : Bitcoin case &#8212; Duniter technical description 0.0.2 documentation</title>
+    <link rel="stylesheet" href="../../_static/pyramid.css" type="text/css" />
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+      <h3>Navigation</h3>
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+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">1. State of the art : Bitcoin case</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <div class="section" id="state-of-the-art-bitcoin-case">
+<h1>1. State of the art : Bitcoin case<a class="headerlink" href="#state-of-the-art-bitcoin-case" title="Permalink to this headline">¶</a></h1>
+<!-- source : https://duniter.org/en/theoretical/ --><p>Duniter uses the crypto-currency concept introduced by Bitcoin <a class="footnote-reference brackets" href="#id6" id="id1">1</a>,
+which is to use cryptographic tools such as signatures to create
+trustless digital currencies. Duniter fits this definition, but it has
+two completely different principles than Bitcoin : the Web of Trust and
+the Universal Dividend . These differences are on both monetary and
+technical aspects.</p>
+<div class="section" id="monetary-creation-of-bitcoin-a-space-time-asymmetry">
+<span id="monetary-creation-a-space-time-asymmetry"></span><h2>1.1. Monetary creation of Bitcoin : a space-time asymmetry<a class="headerlink" href="#monetary-creation-of-bitcoin-a-space-time-asymmetry" title="Permalink to this headline">¶</a></h2>
+<p>Space-time asymmetry refers to the relative access of individuals to
+newly created money <a class="footnote-reference brackets" href="#id7" id="id2">2</a>. Concretely, most existing currencies (c. 2020)
+are both spatially and temporally asymmetrical for their users. Let’s
+take Bitcoin as an example to understand why.</p>
+<div class="section" id="spatial-asymmetry">
+<h3>1.1.1. Spatial asymmetry<a class="headerlink" href="#spatial-asymmetry" title="Permalink to this headline">¶</a></h3>
+<p>When new Bitcoins are created, only some Bitcoin users (the miners) are
+given new Bitcoins, while everyone else get nothing. We believe this is
+the first injustice. However, some might say:</p>
+<blockquote>
+<div><p>“Miners used their electricity and time to get it!”</p>
+</div></blockquote>
+<p>… we would answer that this work should not have been rewarded by
+newly created Bitcoins. New units should be distributed to the whole
+community. Miners should be rewared another way, but not by money
+issuance. Of course, Bitcoin cannot create money through Basic Income
+since Bitcoin users are not strongly identified, and one might benefit
+from money creation multiple times if they owned several wallets.
+Duniter gets rid of this problem by identifying its users and creating
+the same amount of Basic Income to everyone.</p>
+</div>
+<div class="section" id="temporal-asymmetry">
+<h3>1.1.2. Temporal-asymmetry<a class="headerlink" href="#temporal-asymmetry" title="Permalink to this headline">¶</a></h3>
+<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
+which means ever fewer bitcoins will be created over time until no new
+BTC are being generated. So, once the first adopters have mined every
+bitcoin, how will future joiners get Bitcoins? Just like most of us do
+for Euros or Dollars: to get money, they will have to work for the ones
+who already own it.</p>
+<p>We believe this is the second injustice. Every member of a monetary
+community should be equal concerning monetary creation, and get the same
+relative amount of money over time, even if they are a late adopter.
+Duniter aims to fix this by making the Universal Dividend (a.k.a. UD)
+grow by the time according to precise rules, thus making members equal
+toward money issuance on a half-lifespan.</p>
+<p>Most currencies present one of these two asymmetries, including metal
+currencies and mutual credit, as exposed in the RTM.</p>
+</div>
+<div class="section" id="a-solution">
+<h3>1.1.3. A solution<a class="headerlink" href="#a-solution" title="Permalink to this headline">¶</a></h3>
+<p>Bitcoin has taught us that it is possible to create a currency system
+allowing one to both create digital money and to exchange it without a
+central authority. What we need to change is the way money is issued so
+we finally have a symmetrical system. We need <strong>Bitcoin + Universal
+Dividend</strong>. But Universal Dividend implies that the community consists
+of only identified people. This is where the Web of Trust (WoT) comes
+into place.</p>
+<p>This concept, introduced by cryptography with the OpenPGP format <a class="footnote-reference brackets" href="#id8" id="id3">3</a>,
+allows us to identify people in a decentralized manner. It works as
+follows: each person creates a personal identity that is linked to its
+cyptographic certificate. The identity must be confirmed by others
+members who use their own cryptographic key. It is that simple: people
+choose who is part of the community and who is not, not a central
+authority.</p>
+<p>However, Duniter will not use OpenPGP for its cryptographic features:
+Elliptic Curves <a class="footnote-reference brackets" href="#id9" id="id4">4</a> will be used instead for the conciseness of its
+generated keys and its pratical advantages. Duniter has its own Web of
+Trust principles, that will be exposed later.</p>
+</div>
+</div>
+<div class="section" id="proof-of-work-mining-a-power-race">
+<h2>1.2. Proof-of-Work mining : a power race<a class="headerlink" href="#proof-of-work-mining-a-power-race" title="Permalink to this headline">¶</a></h2>
+<p>In Bitcoin Model, the calculation and incentive principles cause a power
+race : new Bitcoins are created for the owners of the most numerous,
+powerful (and energy-consuming) computers. This leads to a power race an
+places the control over the currency in the hands of the richest
+hardware owners. We want to make Duniter blockchain validation much less
+energy and hardware consuming while keeping a strong level of security.
+This will be further explained later. A consequence of this choice is
+the participation of low-end hardware in the Duniter network, leading to
+a better decentralization of blockchain validation.</p>
+<div class="section" id="what-about-proof-of-stake">
+<h3>1.2.1 What about Proof of Stake ?<a class="headerlink" href="#what-about-proof-of-stake" title="Permalink to this headline">¶</a></h3>
+<p>Proof of stake consensus algorythm was first introduced in 2012 <a class="footnote-reference brackets" href="#id10" id="id5">5</a>.
+The basic principle is to allow the richest wallets to issue blocks,
+putting their coin balance as a “stake” they would lose in case of
+cheat.</p>
+<p>At the time of conceiving Duniter, the PoS algorythms had not been
+tested enough to be used as a fundamental base. We did not chose this
+consensus principle. Moreover, the principle of allowing owners of large
+amounts of money to validate transaction can only lead to placing power
+over the currency in the richests hands : this is contrary to the
+symmetical principles of a libre currency.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id6"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
+<dd><p>Bitcoin Whitepaper, S.Nakamoto, 2008:
+<a class="reference external" href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></p>
+</dd>
+<dt class="label" id="id7"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
+<dd><p>Relative Theory of Money, S.Laborde, 2010:
+<a class="reference external" href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></p>
+</dd>
+<dt class="label" id="id8"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
+<dd><p>OpenPGP protocol defines standard formats for encrypted messages,
+signatures, private keys, and certificates for exchanging public
+keys. The GNU Privacy Handbook, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p>
+</dd>
+<dt class="label" id="id9"><span class="brackets"><a class="fn-backref" href="#id4">4</a></span></dt>
+<dd><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+77–89.
+<a class="reference external" href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</p>
+</dd>
+<dt class="label" id="id10"><span class="brackets"><a class="fn-backref" href="#id5">5</a></span></dt>
+<dd><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp;
+S.Nadal, 2012 :
+<a class="reference external" href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="../../index.html">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">1. State of the art : Bitcoin case</a><ul>
+<li><a class="reference internal" href="#monetary-creation-of-bitcoin-a-space-time-asymmetry">1.1. Monetary creation of Bitcoin : a space-time asymmetry</a><ul>
+<li><a class="reference internal" href="#spatial-asymmetry">1.1.1. Spatial asymmetry</a></li>
+<li><a class="reference internal" href="#temporal-asymmetry">1.1.2. Temporal-asymmetry</a></li>
+<li><a class="reference internal" href="#a-solution">1.1.3. A solution</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#proof-of-work-mining-a-power-race">1.2. Proof-of-Work mining : a power race</a><ul>
+<li><a class="reference internal" href="#what-about-proof-of-stake">1.2.1 What about Proof of Stake ?</a></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="../../_sources/parts/en/2_looking_at_Bitcoin.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
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+          <a href="../../genindex.html" title="General Index"
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+        <li class="nav-item nav-item-this"><a href="">1. State of the art : Bitcoin case</a></li> 
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+</html>
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+<!DOCTYPE html>
+
+<html>
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>2. Duniters Blockchain &#8212; Duniter technical description 0.0.2 documentation</title>
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+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">2. Duniters Blockchain</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
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+          <div class="body" role="main">
+            
+  <div class="section" id="duniters-blockchain">
+<h1>2. Duniters Blockchain<a class="headerlink" href="#duniters-blockchain" title="Permalink to this headline">¶</a></h1>
+<p>Duniters Blockchain follows the basic principles of Bitcoins. This is
+essential for synchronization between peers, as to prevent double-spend
+attacks. However, Duniters Blockchain will store different informations
+than Bitcoins.</p>
+<p>The basic use of Blockchain will be registering transactions. For this
+part, we use the same principles as Bitcoin : transactions have inputs
+(spending accounts) and outputs (receiving accounts). But contrary to
+Bitcoin, no generation transaction exists : monetary creation happens
+only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
+<ul class="simple">
+<li><p>a former transaction (as in Bitcoin)</p></li>
+<li><p>a Universal Dividend (specific to Duniter).</p></li>
+</ul>
+<p>Duniters Web of Trust is also written in the Blockchain. The identity of
+each member gets registered much like transactions are, with a strong
+link to the time reference. Thus, the Blockchain is a representation of
+a space-time frame of reference, where “space” are members of the WoT
+and “time” the basic blockchain units : the blocks. On each point of
+time, one can determine which account is legitimate to create the UD,
+only with a blockchain analysis.</p>
+<div class="section" id="spam-countermeasures">
+<h2>2.1. Spam countermeasures<a class="headerlink" href="#spam-countermeasures" title="Permalink to this headline">¶</a></h2>
+<p>An issue of most cryptocurrency projects is to prevent the common ledger
+from growing too much. This would require nodes to have a lot of storage
+and computing power to be usable. In particular, we don’t want an
+attacker to be able to make the Blockchain grow too fast. Most projects
+implement transaction fees as a way to prevent this, making the attacker
+lose money. We don’t want to introduce this mean since a currency with
+automatic fees on transactions is no more neutral. Several
+countermeasuers against such spam attacks are implemented.</p>
+<div class="section" id="minimum-output-amount">
+<h3>2.1.1. Minimum output amount<a class="headerlink" href="#minimum-output-amount" title="Permalink to this headline">¶</a></h3>
+<!-- This has to be implemented in DUBPv13. --><p>Fixing a minimal output amount reduces the power of an attack. Duniter
+deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could
+create thousand accounts with only 1 UD. To prevent this, a valid
+transaction must have output amounts of minimum 1Ğ1. This reduces the
+power an attack by 100.</p>
+</div>
+<div class="section" id="limited-block-size-and-chainability">
+<h3>2.1.2. Limited block size and chainability<a class="headerlink" href="#limited-block-size-and-chainability" title="Permalink to this headline">¶</a></h3>
+<p>The block size is always limited. While the protocol allows this limit
+to evolve to address scaling issues, an attacker cannot register as many
+transaction as they wish.</p>
+<p>With the same goal to prevent too many transactions to get registered,
+while transactions can be “chained” (refer to another transaction in the
+same block), the chainability of transactions is limited to 5.</p>
+</div>
+</div>
+<div class="section" id="scaling">
+<h2>2.2. Scaling<a class="headerlink" href="#scaling" title="Permalink to this headline">¶</a></h2>
+<p>Most of the time, the scaling issue rises for distributed systems that
+should work on a very large scale. This is not the case of Duniter, for
+multiple reasons :</p>
+<ul class="simple">
+<li><p>Ğ1 is the first libre currency, and is still experimental on the
+monetary creation principle. We don’t want it to reach the whole
+world, we only want it to work, to validate or invalidate the RTM.
+Moreover, the rules chosen for the Ğ1 WoT should limit its size to
+around 16 million members.</p></li>
+<li><p>Duniter’s aim is to be used to create multiple libre currencies, that
+would fit local or regional economies. As a consequence, it would
+deal with less transactions than if it was a world-scale system. The
+RTM proposes a formula to calculate the exchange rate between two
+currencies, that could be used to create automatic exchanges for a
+member travelling away from their community.</p></li>
+</ul>
+<p>However, Duniter has assets that will help if the number of users and
+transactions grow.</p>
+<div class="section" id="dynamic-block-size">
+<h3>2.2.1 Dynamic block size<a class="headerlink" href="#dynamic-block-size" title="Permalink to this headline">¶</a></h3>
+<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve.
+On low use of the blockchain, the maximal block size is 500 bytes. On
+high use of the blockchain, the maximal block size would be 110% of the
+average size of the current window blocks(see “personalised difficulty”
+part for more information). This way, the blocks are bounded in size,
+but can slowly grow if a massive and legitimate use of the blockchain
+needs it. The block size (in bytes) is limited as so :</p>
+<div class="math notranslate nohighlight">
+\[\textrm{blockSize} &lt; \max \left({500 ; \textrm{CEIL}(1.10 \times (\textrm{average block size}))}\right)\]</div>
+</div>
+<div class="section" id="lightning-networks">
+<h3>2.2.2. Lightning Networks<a class="headerlink" href="#lightning-networks" title="Permalink to this headline">¶</a></h3>
+<p>The Lightning Networks <a class="footnote-reference brackets" href="#id2" id="id1">1</a> allow almost instant and off-chain
+transactions. They were first implemented on Lightcoin, and are now on
+Bitcoin. One of their benefits is to make the blockchain store a lot of
+transactions at once, thus reducing the groth of the blockchain. The
+Duniter protocol allows XHX() and CSV() unlock conditions that are
+necessary to implement Lightning Networks. While not available yet, this
+payment channel might get implemented when needed.</p>
+</div>
+<div class="section" id="unit-base">
+<h3>2.2.3. Unit base<a class="headerlink" href="#unit-base" title="Permalink to this headline">¶</a></h3>
+<p>As the Universal Dividend grows exponentially, with time Duniter nodes
+would have had to deal with always largest amounts, eventually reaching
+the BIGINT limit. To avoid this, the amounts are expressed with a unit
+base in base 10. We want the UD amount to always fit in 4 digits. To
+manage it, the <code class="docutils literal notranslate"><span class="pre">unitbase</span></code> is updated each time the UD value reaches
+100.00 : it goes from <code class="docutils literal notranslate"><span class="pre">99.99*10^(unitbase)</span></code> to
+<code class="docutils literal notranslate"><span class="pre">10.00*10^(unitbase+1)</span></code>. All the unit amounts are thus divided by 10.
+While this might seem strange, this process has already hapened in state
+currencies. Moreover, the amounts expressed in UD will not change.</p>
+<p>With a monetary growth of 10% each year and a stable population, such a
+change of unit base would happen each 25 years.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
+<dd><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 :
+<a class="reference external" href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
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+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="../../index.html">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">2. Duniters Blockchain</a><ul>
+<li><a class="reference internal" href="#spam-countermeasures">2.1. Spam countermeasures</a><ul>
+<li><a class="reference internal" href="#minimum-output-amount">2.1.1. Minimum output amount</a></li>
+<li><a class="reference internal" href="#limited-block-size-and-chainability">2.1.2. Limited block size and chainability</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#scaling">2.2. Scaling</a><ul>
+<li><a class="reference internal" href="#dynamic-block-size">2.2.1 Dynamic block size</a></li>
+<li><a class="reference internal" href="#lightning-networks">2.2.2. Lightning Networks</a></li>
+<li><a class="reference internal" href="#unit-base">2.2.3. Unit base</a></li>
+</ul>
+</li>
+</ul>
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+        <li class="nav-item nav-item-this"><a href="">3. Duniter Web of Trust</a></li> 
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+            
+  <div class="section" id="duniter-web-of-trust">
+<h1>3. Duniter Web of Trust<a class="headerlink" href="#duniter-web-of-trust" title="Permalink to this headline">¶</a></h1>
+<div class="section" id="basic-principles">
+<span id="duniter-wot-basic-principles"></span><h2>3.1. Basic Principles<a class="headerlink" href="#basic-principles" title="Permalink to this headline">¶</a></h2>
+<p>In order to identify “members” accounts - which create monetary units -
+and other accounts, Duniter uses a Web of Trust. This can be summarized
+into few principles:</p>
+<ul class="simple">
+<li><p>Each account becomes a member if it received a minimal number of
+certifications - 5 for Ğ1 currency.</p></li>
+<li><p>Only members accounts can send certifications. Certifications have a
+limited lifespan.</p></li>
+<li><p>A certification indicates that the sender accepts the receiver as a
+legitimate identity.</p></li>
+</ul>
+<p>The aim of the WoT is to identify a blockchain account to a living
+human. According to Lauterbach et.al <a class="footnote-reference brackets" href="#id9" id="id1">1</a>, the strengh of a relationship
+should be considered when building a vouch system. For this reason, the
+Ğ1 Web of Trust rules are expressed in a licence stating what WoT
+certifications are. A certification represents a strong human
+relationship : one may certify a close relative, not an acquaintance.
+Each member has to accept this licence before being included in the WoT.
+Thus, if a member is part of an attack on the currency, they can be
+found by mutual relatives. Additional security rules occur to prevent
+cheat and attacks on a large scale.</p>
+<p>Note that non-members accounts can use the currency, but cannot create
+money. Non-members accounts can be used by individuals as secondary
+wallets, or by institutions.</p>
+<p>We were inspired by the OpenPGP Trust system <a class="footnote-reference brackets" href="#id10" id="id2">2</a>. However, the OpenPGP
+trust principles aim at defining trust from a particular point of view
+while Duniter needs to identify humans for the whole community. To
+achieve this goal, while OpenPGP allows each user to tweak its trust
+parameters individually, Duniter sets rules in the “genesis” block for
+the whole community.</p>
+</div>
+<div class="section" id="why-do-we-need-a-web-of-trust">
+<h2>3.2. Why do we need a Web of Trust ?<a class="headerlink" href="#why-do-we-need-a-web-of-trust" title="Permalink to this headline">¶</a></h2>
+<p>There are two reasons we need it :</p>
+<ol class="arabic simple">
+<li><p>To make sure that only one Universal Dividend is produced per member
+at each specified creation interval. In the Ğ1’s case this interval
+is set as daily <code class="docutils literal notranslate"><span class="pre">86</span> <span class="pre">400</span></code> seconds, it is the <em>monetary parameter</em>
+known as <code class="docutils literal notranslate"><span class="pre">dt</span></code>.</p></li>
+<li><p>To identify the nodes hashing the blocks and assign each a
+personalised difficulty. This custom difficulty proof of work is
+there to avoid the blockchain’s validation mechanism becoming too
+centralised as is the case with many ‘non-libre’ cryptocurrencies.</p></li>
+</ol>
+<dl>
+<dt><strong>Monetary parameter</strong>:</dt><dd><p>Each currency that use Duniter has its own
+blockchain whose behaviour is dictated by a set of ‘parameters’
+defined in block zero - the so-called genesis block - that can be
+tweaked to achieve the desired results. At the time of writing the
+Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21
+parameters of which 10 are for the WoT alone. We’ll focus on these
+10.</p>
+<p>Suffice to say that in the Ğ1’s case, the DU is created every 24
+hours - 86 400 seconds. This interval is set through the time
+derivative <code class="docutils literal notranslate"><span class="pre">dt</span></code> parameter and can have a different value in other
+implementations of the protocol.</p>
+</dd>
+</dl>
+<p>We want to make sure that each member can only have one account. As we
+all know, achieving zero-risk isn’t possible <a class="footnote-reference brackets" href="#id11" id="id3">3</a>. Our goal is therefore
+not to create a WoT within which fraud would be absolutely impossible,
+but instead to discourage it. Here is a rewording of our goal in 4
+smaller ones :</p>
+<ol class="arabic simple">
+<li><p>Make the certification process lengthy enough that all members
+exercise due diligence and are wary of risks.</p></li>
+<li><p>Make fraudulent acts as hard as we can to the extent that they become
+pointless.</p></li>
+<li><p>Ensure that any Sybil attacks have a negligible impact on the
+currency by ensuring that illegitimate double Universal Dividends
+have no significant bearing on the legitimate monetary mass</p></li>
+<li><p>Slow the growth of ‘Sybil regions’ to give enough time for the
+community to react and isolate the threat.</p></li>
+</ol>
+<dl class="simple">
+<dt><strong>Sybil attack</strong>:</dt><dd><p>A Sybil attack is an attack perpetrated on a
+reputation system through the creation of fake identities. A Web of
+Trust is a specific instance of a Reputation System.</p>
+</dd>
+</dl>
+<p>There are plenty of Sybil attack scenarios we can think of and just as
+many reasons why their perpetrators would want to carry them out. Our
+objective is that the configuration of the WoT protects both users and
+its IT backbone infrastructure against these attacks.</p>
+<p>This means that micro-attacks performed by small groups of individuals
+looking for personal enrichment are of no interest to us. The web’s role
+isn’t to deter these attacks, this being instead the role of the
+community. Just like the town you live in is responsible for providing
+your tap water and electricity but isn’t responsible for any burglaries,
+etc. Much in the same way, Duniter’s WoT guarantees us all a functional
+currency, but do not detect small fraud.</p>
+</div>
+<div class="section" id="the-importance-of-having-our-own-certification-system">
+<span id="own-certification-system"></span><h2>3.3. The importance of having our own certification system<a class="headerlink" href="#the-importance-of-having-our-own-certification-system" title="Permalink to this headline">¶</a></h2>
+<p>Centralized identification systems can achieve the goal we want. State
+Identification is an example. However, this has many drawbacks :</p>
+<ul class="simple">
+<li><p>The authority may have arbitrary criteria for identification, for
+example preventing people without an official state-provided identity
+or homeless people to be included in the WoT.</p></li>
+<li><p>Payment might be required to get identified, thus making the monetary
+creation not “free”.</p></li>
+<li><p>The authority is a point of failure for any attacker.</p></li>
+</ul>
+<p>It is of the utmost importance that we remain free from any state or
+corporation. The WoT is an answer to this criterium. To this day we
+depend only on the Internet and yet, were it to fail, there are already
+alternatives being tested around the world for a decentralised
+communication network.</p>
+</div>
+<div class="section" id="a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary">
+<span id="graph-theory-vocabulary"></span><h2>3.4. A few foundational concepts on graph theory : a bit of vocabulary<a class="headerlink" href="#a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary" title="Permalink to this headline">¶</a></h2>
+<ul class="simple">
+<li><p><strong>Graph</strong>: set of points -called ‘vertices’- joined by edges -called
+paths/walks-.</p></li>
+<li><p><strong>Simple graph</strong>: a graph with no loops and with no multiple edges.
+That is, each edge connects two distinct endpoints and no two edges
+have the same endpoints. A simple edge is an edge that is not part of
+a multiple adjacency -of edges-. In many cases, graphs are assumed to
+be simple unless specified otherwise.</p></li>
+<li><p><strong>Directed graph</strong>: a graph in which the edges have a distinguished
+direction, from one vertex to another. A directed edge can also be
+called a path or walk. Arrow A –&gt; B is therefore different from arrow
+B –&gt; A.</p></li>
+<li><p><strong>Endpoints</strong>: the edge with vertex A –&gt; B has A and B as endpoints,
+respectively as start and end of the path/walk.</p></li>
+<li><p><strong>Isolated vertex</strong>: a vertex whose degree is zero, that is, a vertex
+with no incident edges.</p></li>
+<li><p><strong>Degree of a vertex</strong>: number of its incident edges -in and out-.</p></li>
+<li><p><strong>Out-degree of vertex A</strong>: number of outbound edges / tail ends from
+A.</p></li>
+<li><p><strong>In-degree of vertex A</strong>: number of incoming edges / head ends to A.</p></li>
+</ul>
+<div class="figure align-default" id="id15">
+<a class="reference internal image-reference" href="parts/en/img/degrees_en.jpg"><img alt="degrees of a vertex diagram" src="parts/en/img/degrees_en.jpg" style="width: 40%;" /></a>
+<p class="caption"><span class="caption-text">degrees of a vertex diagram</span><a class="headerlink" href="#id15" title="Permalink to this image">¶</a></p>
+</div>
+<ul class="simple">
+<li><p><strong>Path</strong>: -aka “walk”- path to follow to get from vertex A to vertex
+B.</p></li>
+</ul>
+</div>
+<div class="section" id="definition-of-the-duniter-web-of-trust">
+<h2>3.5. Definition of the Duniter Web of Trust<a class="headerlink" href="#definition-of-the-duniter-web-of-trust" title="Permalink to this headline">¶</a></h2>
+<p>The Duniter WoTs -one per currency- are simple directed graphs without
+isolated vertices. The vertices are the members and the edges are the
+certifications given and received.</p>
+<p><em>Directed</em> means that the responsibility of issuing a certification is
+unique and personal to the certifier. The trust they place in the
+receiver cannot be imposed in the other direction although in most
+circumstances both parties equally trust each other.</p>
+<p>In addition, all vertices are either currently active members or
+past-members. Past-member vertices are in a specific ‘deactivated state’
+and can no longer issue or receive certifications although the ones
+already issued or received to/from other members are still considered
+‘pending’ to avoid a collapse of the WoT. If these old members don’t
+come back into the WoT, their pending certifications will eventually
+expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
+<p>To wrap up with old members, after a certain period of time - set in the
+currency’s parameters - their deactivated vertex is removed from the web
+and the associated identity is ‘revoked’. The person who owned the
+account can no longer use this identity but is free to join the web with
+another one.</p>
+<dl>
+<dt><strong>Identity</strong>:</dt><dd><p>An identity is a set of three pieces of information: a
+public key, a name and a blockstamp. A blockstamp points to a
+specific block in the chain. Its main use is to freeze the point in
+time at which an identity was created and to link this identity to a
+specific chain and a currency - each currency having its own
+blockchain.</p>
+<p>An identity can be in any one of 5 different status: pending, member,
+old member, revoked or excluded.</p>
+</dd>
+</dl>
+<p>Let’s take a simple example:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">-&gt;</span> <span class="n">B</span> <span class="o">-&gt;</span> <span class="n">C</span>
+     <span class="o">|</span>
+     \<span class="o">--&gt;</span> <span class="n">D</span>
+</pre></div>
+</div>
+<p>If, for whatever reason, A were to lose its member status, the web would
+crumble and all other members would be excluded as a consequence. To
+avoid this, the certification from A –&gt; B will remain valid until its
+expiry date, leaving enough time for B to receive certifications from C
+or D.</p>
+<p>Because our WoT doesn’t have any isolated vertices, each new identity
+created needs to be pulled into the web with all of the certifications
+it has received, all in the same block. This calls for a temporary
+‘buffer’ storage space for <strong>pending</strong> identities and the certifications
+they have received. This storage space is called ‘the pool’ of Duniter
+nodes, which we could also have called the ‘sandbox’ as that’s the name
+used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other
+documents and metadata not mentioned here.</p>
+</div>
+<div class="section" id="exploring-the-rules-behind-a-duniter-web-of-trust">
+<span id="exploring-the-rules-behind-duniter-wot"></span><h2>3.6. Exploring the rules behind a Duniter Web of Trust<a class="headerlink" href="#exploring-the-rules-behind-a-duniter-web-of-trust" title="Permalink to this headline">¶</a></h2>
+<p>The Duniter WoTs - one per currency - works with a set of eight
+fundamental rules enforced through eleven different parameters. Ten of
+these parameters are set within the genesis block, the eleventh one -
+<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>- having being hard-coded in the Ğ1’s code subsequently.</p>
+<div class="section" id="distance-rule-and-referent-members-stepmax-and-xpercent">
+<h3>3.6.1. Distance rule and referent members (<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> and <code class="docutils literal notranslate"><span class="pre">xPercent</span></code>)<a class="headerlink" href="#distance-rule-and-referent-members-stepmax-and-xpercent" title="Permalink to this headline">¶</a></h3>
+<p>These two parameters are closely linked and together define the
+‘distance rule’. The ‘distance rule’ can only be described after
+defining what a ‘referent member’ is:</p>
+<dl class="simple">
+<dt><strong>Referent member</strong>:</dt><dd><p>Member A is said to be ‘referent’ if and only if
+the total of their degrees are greater than or equal to
+<code class="docutils literal notranslate"><span class="pre">CEIL-N^-1/stepMax</span></code> where N is the total number of members. As the
+size of the web will grow this number will grow too, meaning it will
+take more certification issuances to become a referent member. The
+number of certifications needed to become a member shouldn’t change.</p>
+</dd>
+</dl>
+<p>Let’s now define the distance rule:</p>
+<dl class="simple">
+<dt><strong>Distance rule</strong>:</dt><dd><p>M ember A is said to observe this rule if and only
+if for a subset xPercent % of referent members R there exists a path
+of length less than or equal to <code class="docutils literal notranslate"><span class="pre">stepMax</span></code> between R and A.</p>
+</dd>
+</dl>
+<p>Referent members only exist so that the distance rule can take effect,
+they have no special privileges over non-referent members. In a perfect
+web, that is one in which each member has certified all members they
+legitimately can, all members would be referent members. However,
+because the web progressively grows in size and because members die and
+are replaced by new ones, there are always members at any given time
+<code class="docutils literal notranslate"><span class="pre">t</span></code> who haven’t yet certified all members they legitimately could.
+These members would hinder the evolution of the web if they were taken
+into account in the calculation of the distance rule and the web would
+effectively stop growing.</p>
+<p>Because verifying the application of the distance rule is
+calculation-greedy, it is only performed when a new identity gets
+confirmed into the web or an existing member gets renewed. There is an
+exception to this rule: the distance rule is not observed in the genesis
+block -when the web is first implemented.</p>
+</div>
+<div class="section" id="rule-of-the-minimum-number-of-certifications-needed-sigqty">
+<h3>3.6.2. Rule of the minimum number of certifications needed (<code class="docutils literal notranslate"><span class="pre">sigQty</span></code>)<a class="headerlink" href="#rule-of-the-minimum-number-of-certifications-needed-sigqty" title="Permalink to this headline">¶</a></h3>
+<p>This is the simplest rule, it essentially says that each member must at
+any given time -meaning in any single block- have received at least
+<code class="docutils literal notranslate"><span class="pre">sigQty</span></code> active certifications. If, for whatever reason, member A were
+to have less than <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> active certifications in a given block,
+they would cease to be a member and be required to publish a request for
+identity renewal.</p>
+</div>
+<div class="section" id="the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">
+<h3>3.6.3. The membership renewal rule (<code class="docutils literal notranslate"><span class="pre">msValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)<a class="headerlink" href="#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow" title="Permalink to this headline">¶</a></h3>
+<p>Bear in mind that a membership doesn’t last a lifetime but instead has a
+lifespan set to <code class="docutils literal notranslate"><span class="pre">msValidity</span></code> seconds.</p>
+<p>Every single member -or old member who hasn’t revoked his identity or
+been excluded- can request a membership renewal so long as the last
+request was made more than <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> seconds ago. If a member has
+never requested a renewal, the date of last renewal is equal to the
+timestamp at which his membership was first created. A new request will
+be stored in the ‘pool’ for a maximum of <code class="docutils literal notranslate"><span class="pre">msWindow</span></code> seconds before
+it’s included in the blockchain. Once again, this can only happen
+once/if the member meets both the <code class="docutils literal notranslate"><span class="pre">siqQty</span></code> rule and the distance rule
+-if these criterion are already matched it’s just a case of waiting for
+a new block to be mined-.</p>
+<p>If a member hasn’t requested a renewal for longer than <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>
+seconds, they automatically cease to be a member. From this moment on,
+the ex-member has another <code class="docutils literal notranslate"><span class="pre">msValidity</span></code> window to renew their
+membership. When this period of <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">×</span> <span class="pre">msValidity</span></code> runs out, the
+membership will expire and this identity will never be available for use
+again in the web. If the person so desires, they will have to publish
+new identity and membership documents and find enough certifiers, as any
+newcomer.</p>
+</div>
+<div class="section" id="rule-of-certification-lifespan-sigvalidity">
+<h3>3.6.4. Rule of certification lifespan (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>)<a class="headerlink" href="#rule-of-certification-lifespan-sigvalidity" title="Permalink to this headline">¶</a></h3>
+<p>All certifications included in the blockchain expire <strong>sigValidity</strong>
+seconds after they were <strong>issued</strong>.</p>
+<blockquote>
+<div><p>/!\ The issuance and the inclusion of a certification in the
+blockchain occur at different times. When member A issues a
+certification at time t1, it gets stored in the pool starting at t1
+and only finds its way into the blockchain at t2 when all of the
+web’s rules are observed. Several weeks can thus go by between t1 and
+t2!</p>
+</div></blockquote>
+</div>
+<div class="section" id="rule-of-limited-supply-of-active-certifications-sigstock">
+<h3>3.6.5. Rule of limited supply of active certifications (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)<a class="headerlink" href="#rule-of-limited-supply-of-active-certifications-sigstock" title="Permalink to this headline">¶</a></h3>
+<p>By ‘active certifications’ we refer to certifications included in the
+blockchain and that haven’t yet expired.</p>
+<p>The total of active certifications issued by any member at any single
+time must be less than or equal to <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>. When this threshold is
+reached the member will have to wait for one of his active
+certifications to expire before he/she can issue a new one.</p>
+</div>
+<div class="section" id="rule-of-the-time-period-between-two-certification-issuances-sigperiod">
+<span id="id4"></span><h3>3.6.6. Rule of the time period between two certification issuances. (<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>)<a class="headerlink" href="#rule-of-the-time-period-between-two-certification-issuances-sigperiod" title="Permalink to this headline">¶</a></h3>
+<p>As soon as a certification issued by member A gets included in the
+blockchain, they will be unable to issue a new one before another
+<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> seconds.</p>
+</div>
+<div class="section" id="expiry-of-a-certification-issuance-sigwindow">
+<h3>3.6.7. Expiry of a certification issuance (<code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>)<a class="headerlink" href="#expiry-of-a-certification-issuance-sigwindow" title="Permalink to this headline">¶</a></h3>
+<p>When a certification is issued by member A, it will be stored in the
+‘pool’ for a maximum of <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> seconds. If the certification
+hasn’t been included in the blockchain by then, it will be cancelled and
+the member’s <code class="docutils literal notranslate"><span class="pre">sigStock</span></code> will be repleted by one.</p>
+</div>
+<div class="section" id="lifespan-of-a-pending-identity-idtywindow">
+<h3>3.6.8. Lifespan of a ‘pending’ identity (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>)<a class="headerlink" href="#lifespan-of-a-pending-identity-idtywindow" title="Permalink to this headline">¶</a></h3>
+<p>When a new identity is created, it is stored in the ‘pool’ for a maximum
+of <code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code> seconds. If the person hasn’t achieved member status
+by then, the certification will simply be cancelled.</p>
+</div>
+</div>
+<div class="section" id="details-on-some-of-the-wots-peculiarities-at-the-genesis-block">
+<h2>3.7. Details on some of the WoT’s peculiarities at the genesis block<a class="headerlink" href="#details-on-some-of-the-wots-peculiarities-at-the-genesis-block" title="Permalink to this headline">¶</a></h2>
+<p>The aforementioned rules can only be enforced with an existing web. They
+cannot be observed when first creating the web, that is when defining
+the genesis block.</p>
+<p>Only rules 2 and 5 can be observed at the genesis block.</p>
+<p>The genesis block has to be manually created by the founding members. In
+practice this means that there must be a choice on which identities to
+include on the premise that all of them observe rules 2 and 5. In
+addition, the genesis block must be signed with the private key of one
+of these identities.</p>
+<p>As soon as the genesis block has been created, the other identities can
+start mining the blockchain and the member who created block #0
+effectively looses the decision power he had at creation.</p>
+</div>
+<div class="section" id="why-these-rules-and-application-cases-in-the-g1">
+<span id="id5"></span><h2>3.8. Why these rules and application cases in the Ğ1<a class="headerlink" href="#why-these-rules-and-application-cases-in-the-g1" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="distance-and-maximum-size">
+<h3>3.8.1. Distance and maximum size<a class="headerlink" href="#distance-and-maximum-size" title="Permalink to this headline">¶</a></h3>
+<p>The distance rule is there to curb the maximum size of a Sybil region as
+well as that of the monetary community as a whole. The <code class="docutils literal notranslate"><span class="pre">xpercent</span></code>
+parameter prevents the creation of a ‘faction’ that could take hold of
+the blockchain.</p>
+<div class="figure align-default" id="id16">
+<a class="reference internal image-reference" href="parts/en/img/wot-sybil.jpg"><img alt="Sybil region" src="parts/en/img/wot-sybil.jpg" style="width: 90%;" /></a>
+<p class="caption"><span class="caption-text">Sybil region</span><a class="headerlink" href="#id16" title="Permalink to this image">¶</a></p>
+</div>
+<p>The Sybil regions are isolated from the rest of the graph in the sense
+that they can only receive certifications from other ill-intentioned
+Sybil members. As a consequence, the shortest edge/path between a
+legitimate member and a Sybil one has to have the attack’s author as an
+endpoint. The maximum depth the Sybil region can attain is therefore
+contingent on the distance between the attacking edge-s- and the
+xpercent% closest referent members, this distance is known as
+<code class="docutils literal notranslate"><span class="pre">stepAttackers</span></code>. The maximum size of a Sybil region created by
+<code class="docutils literal notranslate"><span class="pre">sigQty</span></code> members depends on the L parameter, defined as
+<code class="docutils literal notranslate"><span class="pre">L</span> <span class="pre">=</span> <span class="pre">sigQty/sigStock</span></code>:</p>
+<div class="math notranslate nohighlight">
+\[MaxSybilSize = (sigStock - sigQty) \times {1 - L^{(stepMax - stepAttackers)} \over 1 - L}\]</div>
+<p>The maximum size of the Web of Trust is given by the following formula:</p>
+<div class="math notranslate nohighlight">
+\[WoTmax = sigStock \times L^{(stepMax - 1)}\]</div>
+<p>However we know for a fact that members will never use all of their
+available certifications. According to Dunbar <a class="footnote-reference brackets" href="#id12" id="id6">4</a>, on average, one is
+able to maintain relationships to around 150 people. Being conservative,
+we will consider that on average, each person will certify 50 accounts.
+We can calculate the size of the average web of trust <code class="docutils literal notranslate"><span class="pre">WoTavg</span></code> :</p>
+<div class="math notranslate nohighlight">
+\[WotAvg = 50 \times \left(\frac{\textrm{sigQty}}{50}\right)^{stepMax - 1}\]</div>
+<p>Our goal with the Ğ1 is to create a community of about one million
+members to test the consequences of a libre monetary system. Let’s see
+how we can tweak the pair of sigQty and stepMax- to reach this size:</p>
+<div class="figure align-default" id="id17">
+<a class="reference internal image-reference" href="parts/en/img/wot-moy.png"><img alt="Average WoT size graph as a function of sigQty and stepMax" src="parts/en/img/wot-moy.png" style="width: 90%;" /></a>
+<p class="caption"><span class="caption-text">Average WoT size graph as a function of sigQty and stepMax</span><a class="headerlink" href="#id17" title="Permalink to this image">¶</a></p>
+</div>
+<p>The maximum size of a Sybil region grows linearly with <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> but
+exponentially with <code class="docutils literal notranslate"><span class="pre">stepMax</span></code>. Logic has it that we need to keep
+<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> as low as possible to ensure sufficient strength to the web.
+The above graph shows that the lowest value of <code class="docutils literal notranslate"><span class="pre">stepMax</span></code> for a web of
+a million members is of 5. This is an order of magnitude and is likely
+to be much higher in reality, we cannot measure it for sure.</p>
+<p>For <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> we can choose a value of <strong>4</strong> for a web of <strong>1.5 million
+members</strong> or <strong>5</strong> for <strong>half a million members</strong>. Bear in mind these
+are gross figures and could be significantly higher, we are talking
+anywhere between 1 and 10 million in reality. Calculating WOTavg gives
+us a pretty good idea of how the web would scale bearing in mind that it
+considers all members are referent members too -which isn’t the case as
+explained previously-. Hence the maximum size of the web is likely
+larger, a ballpark figure of half a million is enough for now especially
+knowing that the smaller <code class="docutils literal notranslate"><span class="pre">sigQty</span></code> is, the easier it is to launch a
+Sybil attack -it’s easier to find four accomplices than five-. For
+security reasons we have settled on five:</p>
+<div class="math notranslate nohighlight">
+\[stepMax = 5\]</div>
+<div class="math notranslate nohighlight">
+\[sigQty = 5\]</div>
+<div class="math notranslate nohighlight">
+\[sigStock \geq 50\]</div>
+<p>The maximum size of a Sybil region therefore is:</p>
+<div class="math notranslate nohighlight">
+\[(sigStock-sigQty) * {1 - \left({sigStock \over 5}\right)^{5-stepAttackers}} \over {1-{sigStock \over 5}}\]</div>
+<p>with sigStock = 50 we have a Sybil region of:</p>
+<div class="math notranslate nohighlight">
+\[45 \times {1 - 10^{5 - stepAttackers}} \over {- 9}\]</div>
+<p>A good practice for protecting the web is to maximise <code class="docutils literal notranslate"><span class="pre">stepAttackers</span></code>.
+That’s why we decided that referent members in the genesis block had to
+be at least four steps away from each other.</p>
+<p>Another way to keep a Sybil attack at bay, were it slow enough for
+members to notice it, would be for referent members to ‘stretch’ the web
+intentionally to limit the growth of the region by ensuring that the
+attackers’ legitimate certifications received in the first place aren’t
+renewed. But what if bot accounts were created and certified each other
+super fast and following all rules, how would we counter that? By
+introducing a minimum length of time between two certifications!</p>
+</div>
+<div class="section" id="time-is-our-friend">
+<h3>3.8.2. Time is our friend<a class="headerlink" href="#time-is-our-friend" title="Permalink to this headline">¶</a></h3>
+<p>To help us deter a Sybil attack, we’ve decided to impose a minimum
+period of time between any two certifications issued from a single
+account. This parameter called <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> affords us a greater chance
+to detect the formation of a ‘hostile’ faction.</p>
+<p>Here is a graph showing the evolution of a Sybil region with the
+variation of <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>. The simulation considers that honest members
+and attackers both issue a certification each <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> interval, in
+days:</p>
+<div class="figure align-default" id="id18">
+<a class="reference internal image-reference" href="parts/en/img/impact_sig_period.png"><img alt="size of the WoT according to sigPeriod and stepAttackers" src="parts/en/img/impact_sig_period.png" style="width: 100%;" /></a>
+<p class="caption"><span class="caption-text">size of the WoT according to sigPeriod and stepAttackers</span><a class="headerlink" href="#id18" title="Permalink to this image">¶</a></p>
+</div>
+<p>As we see, there is a strong link between the growth speed of the region
+and <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>. As evidenced here, we need a <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> high
+enough in order to ensure that the legitimate web can grow at least as
+fast as a Sybil region. In addition, the higher <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> is, the
+more members will exercise their certification power gingerly, the
+action coming at a higher ‘cost’.</p>
+<p>There are numerous advantages to giving <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> a high value and
+no technical barriers to it, hence our choice of five days.</p>
+<p>We could have also gone for one week for the sake of simplicity. However
+there is an underlying idea behind our choice which was quite simply the
+pace of today’s life. Certifying someone can be a lengthy process as one
+needs to make sure they are correctly applying the Ğ1 licence and people
+nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
+to allow one to certify at the end of every working week -five days-
+instead of a whole calendar one.</p>
+</div>
+<div class="section" id="trust-me-now-trust-me-forever-sigvalidity-msvalidity">
+<h3>3.8.3. Trust me now, trust me forever ? (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>)<a class="headerlink" href="#trust-me-now-trust-me-forever-sigvalidity-msvalidity" title="Permalink to this headline">¶</a></h3>
+<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s
+Web of Trust:</p>
+<ul class="simple">
+<li><p>First of all, some members will pass and those accounts should no
+longer produce the Universal Dividend.</p></li>
+<li><p>Secondly it is of the utmost importance that ‘rogue’ accounts can be
+excluded from the web at some point.</p></li>
+</ul>
+<p>To achieve this, certifications have a limited lifespan. Members need to
+seek renewal from their peers after <code class="docutils literal notranslate"><span class="pre">sigValidity</span></code> time. On the other
+hand, this time can’t be too short that members would spend more time
+seeking renewal than they would exchanging in the currency. Furthermore,
+a certification with too short a lifespan would foster careless
+certifying behaviours. The act of certifying must have a high-enough
+‘perceived’ cost to make it feel like an important act. Lastly, we also
+wanted this lifespan to be easy to remember. Historically speaking, we
+first settled on the values of <code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>, meant one
+could issue all of their certifications in 495 days, one year was
+therefore not long enough. We deemed three years to be too much and
+that’s how we agreed on two years in the end.</p>
+<p>Thinking that a deceased member could continue producing the UD for two
+long years without anyone benefitting from it was also something we
+needed to address. We chose a value of one year for <strong>msValidity</strong>. The
+act of renewing every year is done through one of the clients
+interacting with the blockchain, through a simple click on a button.
+This parameter is less important than others and is mostly there to
+‘prune’ the web of past or inactive members who don’t renew their
+membership.</p>
+</div>
+<div class="section" id="keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">
+<h3>3.8.4. Keeping the pools free of information glut (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)<a class="headerlink" href="#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow" title="Permalink to this headline">¶</a></h3>
+<p>The pools need to be cleaned up on a regular basis to avoid them
+clogging up with information and to ensure that machines with less
+calculating power can still run a Duniter node.</p>
+<p>To achieve this, identities with pending membership approval and the
+corresponding certifications have to remain the shortest time possible
+in the pool while still having a chance of making it into the
+blockchain.</p>
+<p>For the Ğ1, our opinion was that two months would be enough for all
+potential certifiers to agree on a specific identity to certify. We also
+wanted a time period that would be easy enough to remember by all. We
+settled on two months, and gave this value to all three parameters
+<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>.</p>
+</div>
+<div class="section" id="avoiding-single-members-from-knowing-too-many-people-sigstock">
+<h3>3.8.5. Avoiding single members from ‘knowing too many people’ (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)<a class="headerlink" href="#avoiding-single-members-from-knowing-too-many-people-sigstock" title="Permalink to this headline">¶</a></h3>
+<div class="line-block">
+<div class="line">We considered that on average, each person will certify 50 people.
+However, we know for a fact that some members will use more than 50
+certifications. The maximum social network of one individual is around
+150 people <a class="footnote-reference brackets" href="#id13" id="id7">5</a>. Being conservative, we settled on a maximum
+certification number <code class="docutils literal notranslate"><span class="pre">sigstock</span></code> of 100.</div>
+<div class="line">Since <code class="docutils literal notranslate"><span class="pre">sigStock</span></code>’s impact on the size of a Sybil region is fairly
+limited, we did not investigate further this parameter.</div>
+</div>
+</div>
+<div class="section" id="avoiding-locking-minorities-xpercent">
+<h3>3.8.6. Avoiding locking minorities (<code class="docutils literal notranslate"><span class="pre">xpercent</span></code>)<a class="headerlink" href="#avoiding-locking-minorities-xpercent" title="Permalink to this headline">¶</a></h3>
+<p>It’s easy enough to become a referent member, one of the Sybil
+strategies could therefore be to create a region of referent members.
+Such a region would grow slower than otherwise but could confer a
+locking power to its members by using the distance rule. That’s why the
+distance rule cannot be calculated on 100% of the referent members.
+Hence the introduction of the <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> parameter which defines the
+percentage of referent members needing to be less than five edges
+-steps- from each other.</p>
+<p>This percentage needs to be low enough to prevent the formation of a
+locking minority -referent Sybil members being too far from legitimate
+referent members-. On the other hand, it needs to be high enough so as
+to restrict the maximum size of the Sybil region through the distance
+rule. The <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> parameter was one of the hardest to define,
+therefore we might decide to change its value during the Ğ1 experiment.</p>
+<p>We were inspired by the Pareto principle <a class="footnote-reference brackets" href="#id14" id="id8">6</a>: if at least 20% of
+members give good density to the web, 80% of the referent members will
+be five or less steps from any other member -referent or not-. The
+maximum value for <code class="docutils literal notranslate"><span class="pre">xpercent</span></code> is therefore 80%, anything above that and
+the distance rule could be too restrictive for legitimate use cases.
+With security our top concern, we chose the maximum value of 80%.</p>
+</div>
+<div class="section" id="spam-protection-with-msperiod">
+<h3>3.8.7. Spam protection with (<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>)<a class="headerlink" href="#spam-protection-with-msperiod" title="Permalink to this headline">¶</a></h3>
+<p>This parameter stands out a bit on its own, as it was added after the
+genesis block. It is there to protect the Duniter P2P infrastructure
+against ‘spam’ attacks. We had to think of a strategy against attacks
+such as high-frequency membership renewal requests -i.e: in every block,
+every five minutes- or worse still, hundreds of these requests per
+minute to flood the Duniter nodes. Without such limits, nodes are
+supposed to address all renewal requests, even in cases where they were
+last published five minutes ago! The <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> parameter was given
+the same value as <code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>,
+i.e. two months.</p>
+<dl class="footnote brackets">
+<dt class="label" id="id9"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
+<dd><p>Surfing a Web of Trust, Reputation and Reciprocity on
+CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic:
+<a class="reference external" href="http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf">snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf</a></p>
+</dd>
+<dt class="label" id="id10"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
+<dd><p>Public key validation on GnuPG manual, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p>
+</dd>
+<dt class="label" id="id11"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
+<dd><p>The Sibyl Attack, J.R.Douceur:
+<a class="reference external" href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></p>
+</dd>
+<dt class="label" id="id12"><span class="brackets"><a class="fn-backref" href="#id6">4</a></span></dt>
+<dd><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p>
+</dd>
+<dt class="label" id="id13"><span class="brackets"><a class="fn-backref" href="#id7">5</a></span></dt>
+<dd><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p>
+</dd>
+<dt class="label" id="id14"><span class="brackets"><a class="fn-backref" href="#id8">6</a></span></dt>
+<dd><p>Pareto principle :
+<a class="reference external" href="https://en.wikipedia.org/wiki/Pareto_principle">en.wikipedia.org/wiki/Pareto_principle</a></p>
+</dd>
+</dl>
+</div>
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="../../index.html">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">3. Duniter Web of Trust</a><ul>
+<li><a class="reference internal" href="#basic-principles">3.1. Basic Principles</a></li>
+<li><a class="reference internal" href="#why-do-we-need-a-web-of-trust">3.2. Why do we need a Web of Trust ?</a></li>
+<li><a class="reference internal" href="#the-importance-of-having-our-own-certification-system">3.3. The importance of having our own certification system</a></li>
+<li><a class="reference internal" href="#a-few-foundational-concepts-on-graph-theory-a-bit-of-vocabulary">3.4. A few foundational concepts on graph theory : a bit of vocabulary</a></li>
+<li><a class="reference internal" href="#definition-of-the-duniter-web-of-trust">3.5. Definition of the Duniter Web of Trust</a></li>
+<li><a class="reference internal" href="#exploring-the-rules-behind-a-duniter-web-of-trust">3.6. Exploring the rules behind a Duniter Web of Trust</a><ul>
+<li><a class="reference internal" href="#distance-rule-and-referent-members-stepmax-and-xpercent">3.6.1. Distance rule and referent members (<code class="docutils literal notranslate"><span class="pre">stepMax</span></code> and <code class="docutils literal notranslate"><span class="pre">xPercent</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-the-minimum-number-of-certifications-needed-sigqty">3.6.2. Rule of the minimum number of certifications needed (<code class="docutils literal notranslate"><span class="pre">sigQty</span></code>)</a></li>
+<li><a class="reference internal" href="#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">3.6.3. The membership renewal rule (<code class="docutils literal notranslate"><span class="pre">msValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msPeriod</span></code> and <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-certification-lifespan-sigvalidity">3.6.4. Rule of certification lifespan (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-limited-supply-of-active-certifications-sigstock">3.6.5. Rule of limited supply of active certifications (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)</a></li>
+<li><a class="reference internal" href="#rule-of-the-time-period-between-two-certification-issuances-sigperiod">3.6.6. Rule of the time period between two certification issuances. (<code class="docutils literal notranslate"><span class="pre">sigPeriod</span></code>)</a></li>
+<li><a class="reference internal" href="#expiry-of-a-certification-issuance-sigwindow">3.6.7. Expiry of a certification issuance (<code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#lifespan-of-a-pending-identity-idtywindow">3.6.8. Lifespan of a ‘pending’ identity (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>)</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#details-on-some-of-the-wots-peculiarities-at-the-genesis-block">3.7. Details on some of the WoT’s peculiarities at the genesis block</a></li>
+<li><a class="reference internal" href="#why-these-rules-and-application-cases-in-the-g1">3.8. Why these rules and application cases in the Ğ1</a><ul>
+<li><a class="reference internal" href="#distance-and-maximum-size">3.8.1. Distance and maximum size</a></li>
+<li><a class="reference internal" href="#time-is-our-friend">3.8.2. Time is our friend</a></li>
+<li><a class="reference internal" href="#trust-me-now-trust-me-forever-sigvalidity-msvalidity">3.8.3. Trust me now, trust me forever ? (<code class="docutils literal notranslate"><span class="pre">sigValidity</span></code>, <code class="docutils literal notranslate"><span class="pre">msValidity</span></code>)</a></li>
+<li><a class="reference internal" href="#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">3.8.4. Keeping the pools free of information glut (<code class="docutils literal notranslate"><span class="pre">idtyWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">sigWindow</span></code>, <code class="docutils literal notranslate"><span class="pre">msWindow</span></code>)</a></li>
+<li><a class="reference internal" href="#avoiding-single-members-from-knowing-too-many-people-sigstock">3.8.5. Avoiding single members from ‘knowing too many people’ (<code class="docutils literal notranslate"><span class="pre">sigStock</span></code>)</a></li>
+<li><a class="reference internal" href="#avoiding-locking-minorities-xpercent">3.8.6. Avoiding locking minorities (<code class="docutils literal notranslate"><span class="pre">xpercent</span></code>)</a></li>
+<li><a class="reference internal" href="#spam-protection-with-msperiod">3.8.7. Spam protection with (<code class="docutils literal notranslate"><span class="pre">msPeriod</span></code>)</a></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
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+  <div class="section" id="proof-of-work-with-personal-difficulty">
+<span id="proof-of-work-with-personalized-difficulty"></span><h1>4. Proof of Work with personal difficulty<a class="headerlink" href="#proof-of-work-with-personal-difficulty" title="Permalink to this headline">¶</a></h1>
+<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers.
+It uses a proof of Work (PoW) to write the Blockchain on a regular
+basis, much like BitCoin. However, Duniter has a unique asset : the WoT,
+where each member represents a unique living human.</p>
+<p>This difference might seem minimal, but it has an enormous consequence :
+while Bitcoin uses a race based on computing power only, Duniter creates
+a validation frame that is no race. It is more like a lottery where each
+“winning” member is excluded for a certain amount of time. Moreover,
+those who have more computing power get a handicap, as a way to let
+other peers win. All this is possible through the WoT, that allows
+personalised difficulty while PoW is used for synchronization. All the
+rules of this PoW/WoT mechanism can be verified by reading the
+blockchain. As a consequence, a peer only needs to have an up-to-date
+copy of the blockchain to apply the rules. A view of the whole network
+is not needed.</p>
+<p>Another strong difference is that forging peers are not rewarded by the
+protocol. There is no economical incentive on forging lots of blocs,
+neither on having a lot of computing power.</p>
+<p>One could say that Duniter uses a PoW that needs very low energy
+consumption compared to BitCoin : an “ecological” PoW ?</p>
+<div class="section" id="why-do-we-need-proof-of-work">
+<span id="why-proof-of-work"></span><h2>4.1. Why do we need Proof of Work ?<a class="headerlink" href="#why-do-we-need-proof-of-work" title="Permalink to this headline">¶</a></h2>
+<p>Duniter nodes share a database as part of a p2p environment. The proof
+of work (PoW) allows machines to synchronize with each other. In
+Duniter’s case, the blockchain is our database, and acts as a ledger
+keeping a trace of all transactions, status of the WoT and more. How can
+we let several machines add data (ie: a transaction) at the same time?
+In addition, how do we settle on how much time has gone by since the
+blockchain was last updated? Agreement on time is of the utmost
+importance as we want to create Universal Dividends on a regular basis,
+and keep track of membership status, both in human time.</p>
+<p>Proof-of-work provides a clever solution to both problems:</p>
+<ol class="arabic simple">
+<li><p>Any machine can write into the blockchain (create a new block) but is
+only authorised to do so if it has previously solved a mathematical
+equation that require a certain amount of work. The challenge has to
+be hard enough to prevent two machines to solve it at the same time,
+ensuring the unicity of a block’s creator.</p></li>
+<li><p>Solving this challenge takes a certain amount of time, which depends
+on the calculating power of the whole network. This provides a common
+ground for defining the needed time reference. A block time is set
+(ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to
+get an average duration corresponding to this block time.</p></li>
+</ol>
+</div>
+<div class="section" id="only-members-can-mine">
+<h2>4.2. Only members can “mine”<a class="headerlink" href="#only-members-can-mine" title="Permalink to this headline">¶</a></h2>
+<p>One of Duniter’s major differences with other PoW-based cryptocurrencies
+is that only members are allowed to author blocks. Each block is signed
+with the member’s private key, allowing the algorithm to determine a
+personalised difficulty.</p>
+<p>This personalised difficulty eliminates the rat-race for the most
+sophisticated and powerful mining equipment. Another benefit is the fact
+that no “supercomputer” can take control of the blockchain. Lastly,
+Duniter implements a rotation in forging members thanks to this
+personalized difficulty.</p>
+<p>This lightweight PoW is much less energy-consuming than other PoW
+cryptocurrencies. Members can mine with anything from a raspberry pi to
+a privacy-first internet cube.</p>
+</div>
+<div class="section" id="how-does-it-work">
+<span id="how-does-duniter-pow-work"></span><h2>4.3. How does it work ?<a class="headerlink" href="#how-does-it-work" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="the-hash-aka-digest">
+<span id="the-hash"></span><h3>4.3.1. The hash (aka digest)<a class="headerlink" href="#the-hash-aka-digest" title="Permalink to this headline">¶</a></h3>
+<p>Example of a valid hash:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">00000276902793</span><span class="n">AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</span>
+</pre></div>
+</div>
+<p>As you can see this hash starts with five zeros which was very hard to
+achieve and took a lot of work for someone’s computer. Hence the term
+“proof of work”.</p>
+</div>
+<div class="section" id="the-common-difficulty">
+<span id="common-difficulty"></span><h3>4.3.2. The common difficulty<a class="headerlink" href="#the-common-difficulty" title="Permalink to this headline">¶</a></h3>
+<p>A common difficulty is needed to settle on a yardstick for our time
+reference. Its role is to make sure the blockchain moves forward at a
+steady pace - one block every <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code> seconds, <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code>
+being one of the 20 parameters behind the Duniter protocol-.</p>
+<p>This difficulty’s initial value can be set to any arbitrary value
+(<code class="docutils literal notranslate"><span class="pre">70</span></code> in Duniter <code class="docutils literal notranslate"><span class="pre">v1.5.x</span></code>) and then acts as a spring, regulating
+blocktime creation by increasing itself if the creation interval drops
+under <code class="docutils literal notranslate"><span class="pre">avgGenTime</span></code> and vice-versa.</p>
+<div class="section" id="how-is-difficulty-applied">
+<h4>4.3.2.1. How is difficulty applied ?<a class="headerlink" href="#how-is-difficulty-applied" title="Permalink to this headline">¶</a></h4>
+<p>The numeric value of difficulty is taken from an array of possible
+hashes out of all possible hashes. In DUBPv13 the hash of a block is its
+sha256 hexadecimal hash.</p>
+<p>To understand the difficulty, we make a euclidiean division of the
+difficulty by 16.</p>
+<p>Here’s an example with a difficulty value of 70 :</p>
+<p>The valid hashes are the ones starting with four zeros and with the
+fifth character less than or equal to 9 (6 in hexadecimal notation). The
+valid hashes are then written as starting with : <code class="docutils literal notranslate"><span class="pre">0000[0-9]</span></code>. This is
+a bit different from Bitcoin, where the difficulty is only ruled by the
+number of zeroes.</p>
+</div>
+<div class="section" id="the-nonce">
+<h4>4.3.2.2. The Nonce<a class="headerlink" href="#the-nonce" title="Permalink to this headline">¶</a></h4>
+<p>When a member is forging a new block, his computer freezes the block’s
+content and changes the Nonce until the hash reaches the required number
+of zeroes.</p>
+<p>The nonce allows us to mine a new block by finding a hash. The hash
+value allows us to determine the difficulty level of the proof-of-work
+performed. Examples of possible Nonce values:</p>
+<ul class="simple">
+<li><p>10100000112275</p></li>
+<li><p>10300000288743</p></li>
+<li><p>10400000008538</p></li>
+<li><p>10700000079653</p></li>
+<li><p>10300000070919</p></li>
+</ul>
+<p>In reality the <code class="docutils literal notranslate"><span class="pre">Nonce</span></code> value follows a pre-determined format akin to
+<code class="docutils literal notranslate"><span class="pre">XYY00000000000</span></code>. The Nonce’s value isn’t the number of attempts but
+rather a value within a set of possible ones. This is how the Nonce is
+built:</p>
+<ul class="simple">
+<li><p>X is a number assigned to a specific peer. Let’s assume that someone
+has several nodes each with the same private key, this would lead to
+possible collisions if this person were to mine the same block with
+different nodes. Each [STRIKEOUT:block] <strong>node ?</strong> will therefore
+have its own unique X to prevent this from happening.</p></li>
+<li><p>Y is the number of cores of the processor. The Nonce starting with
+<code class="docutils literal notranslate"><span class="pre">107[…]</span></code> belongs to a seven cores processor, while <code class="docutils literal notranslate"><span class="pre">199[...]</span></code>
+could be the proof generated by a 99 cores processor.</p></li>
+</ul>
+<p>The rest of the Nonce, the part that follows after the XYY, is the
+numerical space for this individual node and is unique to each of the
+CPU’s core. This space is comprised of eleven digits (<code class="docutils literal notranslate"><span class="pre">00000000000</span></code>).
+For the sake of accuracy, we use the term CPU in the wider sense, it can
+be understood as a bi-CPU for example. We take into consideration the
+number of cores for the resulting PoW.</p>
+</div>
+</div>
+</div>
+<div class="section" id="personalised-difficulty">
+<h2>4.4. Personalised difficulty<a class="headerlink" href="#personalised-difficulty" title="Permalink to this headline">¶</a></h2>
+<p>Earlier in this article, we explained that the personalised difficulty
+is the new and key concept that sets Duniter apart from other PoW-based
+cryptocurrencies.</p>
+<p>Here is how this personalised difficulty is calculated and assigned:</p>
+<p>It is determined by a combination of two different constraints with
+complimentary roles: the <strong>exclusion factor</strong> and the <strong>handicap</strong>.</p>
+<p>Let <code class="docutils literal notranslate"><span class="pre">powMin</span></code> be the common difficulty, <code class="docutils literal notranslate"><span class="pre">exFact</span></code> a member’s exclusion
+factor and <code class="docutils literal notranslate"><span class="pre">handicap</span></code> their handicap. This member’s personalised
+difficulty <code class="docutils literal notranslate"><span class="pre">diff</span></code> is:</p>
+<div class="math notranslate nohighlight">
+\[{\textrm{diff} = \textrm{powMin} \times \textrm{exFact} + \textrm{handicap}}\]</div>
+<div class="section" id="understanding-exfact-the-exclusion-factor">
+<span id="the-exclusion-factor"></span><h3>4.4.1. Understanding <code class="docutils literal notranslate"><span class="pre">exFact</span></code>, the exclusion factor<a class="headerlink" href="#understanding-exfact-the-exclusion-factor" title="Permalink to this headline">¶</a></h3>
+<p>Members who have never produced blocks or haven’t for quite some time
+are assigned an exclusion factor of <code class="docutils literal notranslate"><span class="pre">1</span></code>. Their personalised difficulty
+is therefore simply the sum of <code class="docutils literal notranslate"><span class="pre">powMin</span> <span class="pre">+</span> <span class="pre">handicap</span></code>.</p>
+<p>Before reading on, let’s precise the role of this exclusion factor. When
+a member adds a block to the chain, his <code class="docutils literal notranslate"><span class="pre">exFact</span></code> jumps up from one to
+a very high value, to prevent them from forging other blocks immediately
+after and taking control of the blockchain.</p>
+<p>The exclusion factor will then rapidly return to one. This delay is
+expressed as a number of blocks. It is calculated as a proportion of the
+number of members forging. In the Ğ1’s case, this proportion is 1/3,
+meaning that if there are fifteen members currently forging, the
+member’s exclusion factor will drop down to one after five blocks.</p>
+<div class="section" id="what-is-intended-by-the-number-of-members-forging">
+<h4>4.4.1.1. What is intended by “the number of members forging” ?<a class="headerlink" href="#what-is-intended-by-the-number-of-members-forging" title="Permalink to this headline">¶</a></h4>
+<p>We mean the number of members trying to create the next block. In
+reality, there is no way to precisely know how many members are
+calculating at any given time, because it is impossible to view the
+entire network. But we need this information, whithout which assigning a
+personalised difficulty is impossible. To achieve this, Duniter looks
+back at the blockchain and assumes that there is as much members forging
+as those who have found at least one block in the last blocks in the
+current window, minus the very last one.</p>
+</div>
+<div class="section" id="current-window">
+<h4>4.4.1.2. Current window<a class="headerlink" href="#current-window" title="Permalink to this headline">¶</a></h4>
+<p>We use the concept of <strong>current window</strong>. The current window is the
+number of blocks we look back at to determine how many members are
+forging. Let’s see how it works:</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> is the size of the current window in blocks.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> the number of members who have calculated at least
+one block during the current window.</p></li>
+</ul>
+<p>Both <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> and <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> are block fields. When first
+starting a blockchain, the very first block has an <code class="docutils literal notranslate"><span class="pre">issuersFrame=1</span></code>
+and an <code class="docutils literal notranslate"><span class="pre">issuersCount=0</span></code>. The genesis block is excluded as there are no
+members in the current window!</p>
+<p>From the second block onwards (block #1) we track the variation of
+<code class="docutils literal notranslate"><span class="pre">issuersCount</span></code>. The member having mined block #0 enters the current
+window and in block #1 we will therefore mention <code class="docutils literal notranslate"><span class="pre">issuersCount=1</span></code>.</p>
+<p><code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> then varies as follows:</p>
+<ul class="simple">
+<li><p>if <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> increases by N (with a maximum step of N = 1),
+then <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> will increase by one unit over a period of 5N
+blocks.</p></li>
+<li><p>Conversely, if <code class="docutils literal notranslate"><span class="pre">issuersCount</span></code> decreases by Y (with a maximum step
+of Y = 2 = current window inching forward + loss of one calculating
+member), then <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> will decrease by one unit during 5Y
+blocks.</p></li>
+<li><p>When such events overlap, <code class="docutils literal notranslate"><span class="pre">issuersFrame</span></code> evolves as so :</p></li>
+</ul>
+<table class="docutils align-default">
+<colgroup>
+<col style="width: 11%" />
+<col style="width: 67%" />
+<col style="width: 23%" />
+</colgroup>
+<thead>
+<tr class="row-odd"><th class="head"><p>bloc</p></th>
+<th class="head"><p>event</p></th>
+<th class="head"><p>issuersFrame</p></th>
+</tr>
+</thead>
+<tbody>
+<tr class="row-even"><td><p>T</p></td>
+<td><p>Babar writes a block and enters issuersCount</p></td>
+<td><p>160</p></td>
+</tr>
+<tr class="row-odd"><td><p>T+1</p></td>
+<td><p>Celeste leaves issuersCount</p></td>
+<td><p>160 +1 = 161</p></td>
+</tr>
+<tr class="row-even"><td><p>T+2</p></td>
+<td><p>N/a</p></td>
+<td><p>161 +1 -1 = 161</p></td>
+</tr>
+<tr class="row-odd"><td><p>T+3/4/5</p></td>
+<td><p>N/a</p></td>
+<td><p>161 +1 -1 = 161</p></td>
+</tr>
+<tr class="row-even"><td><p>T+6</p></td>
+<td><p>N/a</p></td>
+<td><p>161 -1 = 160</p></td>
+</tr>
+</tbody>
+</table>
+<p>The calculation can be found under rules
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe">BR_G05</a>
+and
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar">BR_G06</a>
+of the DUP protocol.</p>
+</div>
+<div class="section" id="exfact-and-the-personalised-difficulty">
+<h4>4.4.1.3. exFact and the personalised difficulty<a class="headerlink" href="#exfact-and-the-personalised-difficulty" title="Permalink to this headline">¶</a></h4>
+<p>We explained that <code class="docutils literal notranslate"><span class="pre">exFact</span></code> spikes immediately after the member has
+found a block. It decreases then rapidly to <code class="docutils literal notranslate"><span class="pre">1</span></code> after a number of
+blocks equal to <code class="docutils literal notranslate"><span class="pre">1/3</span> <span class="pre">*</span> <span class="pre">issuersCount</span></code>. Let’s see precisely how we
+calculate <code class="docutils literal notranslate"><span class="pre">exFact</span></code>:</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">nbPreviousIssuers</span></code> is the value of issuersCount at the last block
+<code class="docutils literal notranslate"><span class="pre">N</span></code> found by the member.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span></code> is the number of blocks found by the rest of the
+network since block <code class="docutils literal notranslate"><span class="pre">N</span></code>.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">percentRot</span></code> is the number of <em>not excluded</em> peers we want. It is a
+monetary parameter, its value is 0.67 for Ğ1 currency.</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[exFact = MAX[ 1 ; FLOOR ({{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}}) ]\]</div>
+<p>The FLOOR is a simple truncate function. For <code class="docutils literal notranslate"><span class="pre">exFact</span></code> to exclude the
+member, we need :</p>
+<div class="math notranslate nohighlight">
+\[{{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}} &gt;= 2\]</div>
+<p>We can see that the member is not excluded if <code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span></code> is
+greater than 1/3 of the calculating members. Take as an example
+<code class="docutils literal notranslate"><span class="pre">nbPreviousIssuers</span> <span class="pre">=</span> <span class="pre">6</span></code> and <code class="docutils literal notranslate"><span class="pre">nbBlocksSince</span> <span class="pre">=</span> <span class="pre">3</span></code>:</p>
+<div class="math notranslate nohighlight">
+\[{0.67 \times {6 \over {1 + 3}} = 1.005} \Rightarrow exFact = 1\]</div>
+<p>However, if the member computed a block one block ago (nbBlocksSince =
+1), exFact = 2 and the forging peer is excluded:</p>
+<div class="math notranslate nohighlight">
+\[{0.67 \times {6 \over {1 + 1}} = 2.01} \Rightarrow exFact = 2\]</div>
+<p>Moreover if the last block was authored by the said member, then:</p>
+<div class="math notranslate nohighlight">
+\[nbBlocksSince = 0\]</div>
+<div class="math notranslate nohighlight">
+\[exFact = 0.67 \times nbPreviousIssuers\]</div>
+<p>ExFact value increases according to the number of members calculating.
+Thus, if there is enough members calculating, even mining farms would be
+excluded. We have therefore succeeded in our intent to deter attempts to
+seize the blockchain and its currency.</p>
+<p>However, at any time <code class="docutils literal notranslate"><span class="pre">t</span></code>, the two-thirds of calculating members all
+have an exclusion factor of <code class="docutils literal notranslate"><span class="pre">1</span></code>, even though they might not all have
+the same computational power at hand. If the personalised difficulty
+only took into account the exclusion factor, then only the members with
+the highest computational power from the remaining third would be able
+to author new blocks and the other 2/3s would almost always be excluded.
+Lesser machines wouldn’t stand a chance…</p>
+</div>
+</div>
+<div class="section" id="the-handicap">
+<h3>4.4.2. The handicap<a class="headerlink" href="#the-handicap" title="Permalink to this headline">¶</a></h3>
+<p>The handicap is the second parameter of the personalised difficulty. Its
+main role is to improve the rotation of forging peers. A higher handicap
+is assigned to members with higher calculating power, so lesser machines
+can also compute blocks. As a consequence, there is no incentive on
+forging with powerful computers. Security can be achieved with less
+computing power than with pure PoW.</p>
+<p>The aim is to handicap the half that has authored most blocks (the most
+powerful half) to favour the other one. So, the handicap formula will
+use the median number of blocks authored by peers within the current
+window.</p>
+<ul class="simple">
+<li><p><code class="docutils literal notranslate"><span class="pre">nbPersonalBlocksInFrame</span></code> is the number of blocks authored by a
+single member within the current window.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">medianOfBlocksInFrame</span></code> is the median number of blocks written by
+the calculating members during the same timeframe.</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[handicap = FLOOR( {\ln({ \max({ 1 ; {{nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame} )} )} \over \ln{1.189} })\]</div>
+<p>Let’s unwrap the formula:</p>
+<div class="math notranslate nohighlight">
+\[{ {nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame}\]</div>
+<p>is simply the ratio between the number of blocks authored by the peer
+and the median number of blocks. For example, if a peer has authored
+<code class="docutils literal notranslate"><span class="pre">9</span></code> blocks in the current window and the median is <code class="docutils literal notranslate"><span class="pre">5</span></code>, then the
+ratio will be <code class="docutils literal notranslate"><span class="pre">(9+1)/5</span> <span class="pre">=</span> <span class="pre">2</span></code>.</p>
+<ul class="simple">
+<li><p>The MAX function allows us to ensure that</p></li>
+</ul>
+<p>the handicap has a value at least equal to <code class="docutils literal notranslate"><span class="pre">1</span></code>.</p>
+<ul class="simple">
+<li><p>The Napierian Logarithm of this ratio prevents the handicap from</p></li>
+</ul>
+<p>becoming excluding. We want the handicap to level the calculating field
+so that all peers stand a chance, not to exclude peers.</p>
+<ul class="simple">
+<li><p>If we wanted the handicap to be applied as soon as the median is</p></li>
+</ul>
+<p>reached, we would divide it by <code class="docutils literal notranslate"><span class="pre">LN(1)</span></code>. The problem is that we have
+already set a minimum value of <code class="docutils literal notranslate"><span class="pre">1</span></code> with the MAX function. If we were
+to divide the ratio by <code class="docutils literal notranslate"><span class="pre">LN(1)</span></code> all calculating peers would have a
+handicap <code class="docutils literal notranslate"><span class="pre">\&gt;=</span> <span class="pre">1</span></code>. In addition, is it really fair to handicap a member
+who is right on the median?</p>
+<p>That’s why we went for <code class="docutils literal notranslate"><span class="pre">1.189</span></code> rather than <code class="docutils literal notranslate"><span class="pre">1</span></code>. A member has to be
+at least <code class="docutils literal notranslate"><span class="pre">18.9%</span></code> above the median to be assigned a handicap. 18.9% is
+actually 16^(1/16), the difficulty factor between two levels of the
+proof work (hexadecimal hash).</p>
+<p>To conclude, you have to remember that :</p>
+<ul class="simple">
+<li><p>The handicap is indexed on the logarithm of the ratio to the median,</p></li>
+<li><p>Handicap is only applied on members whose ratio to the median is
+greater than the ratio between two levels of the proof-of-work’s
+difficulty.</p></li>
+</ul>
+</div>
+</div>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="../../index.html">Table of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">4. Proof of Work with personal difficulty</a><ul>
+<li><a class="reference internal" href="#why-do-we-need-proof-of-work">4.1. Why do we need Proof of Work ?</a></li>
+<li><a class="reference internal" href="#only-members-can-mine">4.2. Only members can “mine”</a></li>
+<li><a class="reference internal" href="#how-does-it-work">4.3. How does it work ?</a><ul>
+<li><a class="reference internal" href="#the-hash-aka-digest">4.3.1. The hash (aka digest)</a></li>
+<li><a class="reference internal" href="#the-common-difficulty">4.3.2. The common difficulty</a><ul>
+<li><a class="reference internal" href="#how-is-difficulty-applied">4.3.2.1. How is difficulty applied ?</a></li>
+<li><a class="reference internal" href="#the-nonce">4.3.2.2. The Nonce</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#personalised-difficulty">4.4. Personalised difficulty</a><ul>
+<li><a class="reference internal" href="#understanding-exfact-the-exclusion-factor">4.4.1. Understanding <code class="docutils literal notranslate"><span class="pre">exFact</span></code>, the exclusion factor</a><ul>
+<li><a class="reference internal" href="#what-is-intended-by-the-number-of-members-forging">4.4.1.1. What is intended by “the number of members forging” ?</a></li>
+<li><a class="reference internal" href="#current-window">4.4.1.2. Current window</a></li>
+<li><a class="reference internal" href="#exfact-and-the-personalised-difficulty">4.4.1.3. exFact and the personalised difficulty</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#the-handicap">4.4.2. The handicap</a></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
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+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Conclusion</a></li> 
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+          <div class="body" role="main">
+            
+  <div class="section" id="conclusion">
+<h1>Conclusion<a class="headerlink" href="#conclusion" title="Permalink to this headline">¶</a></h1>
+<!-- source : https://duniter.org/en/theoretical/ --><p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document
+retracing the history of the currency. However, Duniter registers not
+only trades, but also the history of relationships in the community as a
+mean to identify a human to a digital account. This way, Duniter has
+information about the fondamental reference of RTM : living humans. A
+libre Currency can be issued thanks to the Universal Dividend.</p>
+<p>More than that, Duniter proposes a new model for securing a Blockchain
+in an efficient and decentralized way. Basing the security on a Web of
+Trust with an individualised security makes the calculation rules more
+fair. A side-effect of this choice is a network consisting mostly of
+low-end computers, maintaining a good security and helping
+decentralization of calculation.</p>
+<p>The ultimate goal of Duniter project is to allow people to participate
+in a libre economy, thanks to a libre currency. What is a libre economy
+? The Relative Theory of Money defines it through four economic
+liberties :</p>
+<ul class="simple">
+<li><p>The freedom to choose your currency system: because money should not
+be imposed.</p></li>
+<li><p>The freedom to access resources: because we all should have access to
+economic &amp; monetary resources.</p></li>
+<li><p>The freedom to estimate and produce value: because value is a purely
+relative to each individual.</p></li>
+<li><p>The freedom to trade with the money: because we should not be limited
+by the avaible money supply.</p></li>
+</ul>
+<p>Those 4 economic freedoms should be understood together, not
+exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So
+here, freedom does not mean the right to take all of a resource (like
+water source in a desert) so no more is available to the others. Now you
+get it, this is the goal: free economy through free currency.</p>
+</div>
+
+
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+          </div>
+        </div>
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+        <li class="nav-item nav-item-this"><a href="">Conclusion</a></li> 
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+    <title>Sources : &#8212; Duniter technical description 0.0.2 documentation</title>
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+        <li class="nav-item nav-item-0"><a href="../../index.html">Duniter technical description 0.0.2 documentation</a> &#187;</li>
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+  <div class="section" id="sources">
+<h1>Sources :<a class="headerlink" href="#sources" title="Permalink to this headline">¶</a></h1>
+<ul class="simple">
+<li><p>Relative Theory of Money, S.Laborde, 2010:
+<a class="reference external" href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></p></li>
+<li><p>Bitcoin Whitepaper, S.Nakamoto, 2008:
+<a class="reference external" href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></p></li>
+<li><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 :
+<a class="reference external" href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></p></li>
+<li><p>The GNU Privacy Handbook, M.Ashley, 1999 :
+<a class="reference external" href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></p></li>
+<li><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+77–89.
+<a class="reference external" href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</p></li>
+<li><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp;
+S.Nadal, 2012 :
+<a class="reference external" href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></p></li>
+<li><p>Duniter Blockchain Protocol, v13, draft by Elois :
+<a class="reference external" href="https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md">git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</a></p></li>
+<li><p>The Sibyl Attack, J.R.Douceur:
+<a class="reference external" href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></p></li>
+<li><p>Neocortex size as a constraint on group size in primates,
+R.I.M.Dunbar, Journal of Human Evolution, 1992</p></li>
+</ul>
+</div>
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diff --git a/build/whitepaper_en.epub b/build/whitepaper_en.epub
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-<?xml version="1.0" encoding="UTF-8"?>
-<FictionBook xmlns="http://www.gribuser.ru/xml/fictionbook/2.0" xmlns:xlink="http://www.w3.org/1999/xlink">
-    <description>
-        <title-info>
-            <genre>antique</genre>
-                <author><first-name></first-name><last-name>Inconnu(e)</last-name></author>
-            <book-title>whitepaper en</book-title>
-            
-            <lang>fr</lang>
-            
-            
-            
-        </title-info>
-        <document-info>
-            <author><first-name></first-name><last-name>Inconnu(e)</last-name></author>
-            <program-used>calibre 3.46.0</program-used>
-            <date>5.5.2020</date>
-            <id>5e6bf4d6-ac49-48cd-9e7e-afc96068fd4a</id>
-            <version>1.0</version>
-        </document-info>
-        <publish-info>
-            
-            
-            
-        </publish-info>
-    </description>
-<body>
-<section>
-<empty-line /><p>Duniter: A libre currency blockchain generator.</p>
-
-<p>Abstract</p>
-
-<p>Many currency principles involve non-equal rights to monetary creation between humans. We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human. This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution. Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process. We use a Web of Trust between living humans for identification. This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.</p>
-
-<p>Introduction</p>
-
-<p>Duniter is a software to create and manage “libre currencies”. Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :</p>
-
-<p>How should a currency be created to match the principle of equality between all humans, now and between generations ?</p>
-
-<p>The results of this demonstration implies a monetary creation :</p>
-
-<p>on a regular basis</p>
-
-<p>for each human being</p>
-
-<p>which amount has to be reassessed on fixed intervals according to a fixed formula.</p>
-
-<p>Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :</p><empty-line /><p>$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$</p><empty-line /><p>Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.</p>
-
-<p>The first currency created through Duniter is Ğ1, pronounced “June”. It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.</p>
-
-<p>1. State of the art : Bitcoin case</p>
-
-<p>Duniter uses the crypto-currency concept introduced by Bitcoin<sup>1</sup>, which is to use cryptographic tools such as signatures to create trustless digital currencies. Duniter fits this definition, but it has two completely different principles than Bitcoin : the Web of Trust and the Universal Dividend . These differences are on both monetary and technical aspects.</p>
-
-<p>1.1. Monetary creation of Bitcoin : a space-time asymmetry</p>
-
-<p>Space-time asymmetry refers to the relative access of individuals to newly created money<sup>2</sup>. Concretely, most existing currencies (c. 2020) are both spatially and temporally asymmetrical for their users. Let's take Bitcoin as an example to understand why.</p>
-
-<p>1.1.1. Spatial asymmetry</p>
-
-<p>When new Bitcoins are created, only some Bitcoin users (the miners) are given new Bitcoins, while everyone else get nothing. We believe this is the first injustice. However, some might say:</p>
-
-<p>"Miners used their electricity and time to get it!"</p>
-
-<p>... we would answer that this work should not have been rewarded by newly created Bitcoins. New units should be distributed to the whole community. Miners should be rewared another way, but not by money issuance. Of course, Bitcoin cannot create money through Basic Income since Bitcoin users are not strongly identified, and one might benefit from money creation multiple times if they owned several wallets. Duniter gets rid of this problem by identifying its users and creating the same amount of Basic Income to everyone.</p>
-
-<p>1.1.2. Temporal-asymmetry</p>
-
-<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency), which means ever fewer bitcoins will be created over time until no new BTC are being generated. So, once the first adopters have mined every bitcoin, how will future joiners get Bitcoins? Just like most of us do for Euros or Dollars: to get money, they will have to work for the ones who already own it.</p>
-
-<p>We believe this is the second injustice. Every member of a monetary community should be equal concerning monetary creation, and get the same relative amount of money over time, even if they are a late adopter. Duniter aims to fix this by making the Universal Dividend (a.k.a. UD) grow by the time according to precise rules, thus making members equal toward money issuance on a half-lifespan.</p>
-
-<p>Most currencies present one of these two asymmetries, including metal currencies and mutual credit, as exposed in the RTM.</p>
-
-<p>1.1.3. A solution</p>
-
-<p>Bitcoin has taught us that it is possible to create a currency system allowing one to both create digital money and to exchange it without a central authority. What we need to change is the way money is issued so we finally have a symmetrical system. We need Bitcoin + Universal Dividend. But Universal Dividend implies that the community consists of only identified people. This is where the Web of Trust (WoT) comes into place.</p>
-
-<p>This concept, introduced by cryptography with the OpenPGP format<sup>3</sup>, allows us to identify people in a decentralized manner. It works as follows: each person creates a personal identity that is linked to its cyptographic certificate. The identity must be confirmed by others members who use their own cryptographic key. It is that simple: people choose who is part of the community and who is not, not a central authority.</p>
-
-<p>However, Duniter will not use OpenPGP for its cryptographic features: Elliptic Curves<sup>4</sup> will be used instead for the conciseness of its generated keys and its pratical advantages. Duniter has its own Web of Trust principles, that will be exposed later.</p>
-
-<p>1.2. Proof-of-Work mining : a power race</p>
-
-<p>In Bitcoin Model, the calculation and incentive principles cause a power race : new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers. This leads to a power race an places the control over the currency in the hands of the richest hardware owners. We want to make Duniter blockchain validation much less energy and hardware consuming while keeping a strong level of security. This will be further explained later. A consequence of this choice is the participation of low-end hardware in the Duniter network, leading to a better decentralization of blockchain validation.</p>
-
-<p>1.2.1 What about Proof of Stake ?</p>
-
-<p>Proof of stake consensus algorythm was first introduced in 2012<sup>5</sup>. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a “stake” they would lose in case of cheat.</p>
-
-<p>At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle. Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.</p>
-
-<p>2. Duniters Blockchain</p>
-
-<p>Duniters Blockchain follows the basic principles of Bitcoins. This is essential for synchronization between peers, as to prevent double-spend attacks. However, Duniters Blockchain will store different informations than Bitcoins.</p>
-
-<p>The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
-
-<p>a former transaction (as in Bitcoin)</p>
-
-<p>a Universal Dividend (specific to Duniter).</p>
-
-<p>Duniters Web of Trust is also written in the Blockchain. The identity of each member gets registered much like transactions are, with a strong link to the time reference. Thus, the Blockchain is a representation of a space-time frame of reference, where “space” are members of the WoT and “time” the basic blockchain units : the blocks. On each point of time, one can determine which account is legitimate to create the UD, only with a blockchain analysis.</p>
-
-<p>2.1. Spam countermeasures</p>
-
-<p>An issue of most cryptocurrency projects is to prevent the common ledger from growing too much. This would require nodes to have a lot of storage and computing power to be usable. In particular, we don’t want an attacker to be able to make the Blockchain grow too fast. Most projects implement transaction fees as a way to prevent this, making the attacker lose money. We don’t want to introduce this mean since a currency with automatic fees on transactions is no more neutral. Several countermeasuers against such spam attacks are implemented.</p>
-
-<p>2.1.1. Minimum output amount</p>
-
-<p>Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.</p>
-
-<p>2.1.2. Limited block size and chainability</p>
-
-<p>The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.</p>
-
-<p>With the same goal to prevent too many transactions to get registered, while transactions can be “chained” (refer to another transaction in the same block), the chainability of transactions is limited to 5.</p>
-
-<p>2.2. Scaling</p>
-
-<p>Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :</p>
-
-<p>Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don’t want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.</p>
-
-<p>Duniter’s aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.</p>
-
-<p>However, Duniter has assets that will help if the number of users and transactions grow.</p>
-
-<p>2.2.1 Dynamic block size</p>
-
-<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve. On low use of the blockchain, the maximal block size is 500 bytes. On high use of the blockchain, the maximal block size would be 110% of the average size of the current window blocks(see “personalised difficulty” part for more information). This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :</p>
-
-<p>block_size &lt; max(500 ; CEIL(1.10 * (average block size))</p>
-
-<p>2.2.2. Lightning Networks</p>
-
-<p>The Lightning Networks<sup>6</sup> allow almost instant and off-chain transactions. They were first implemented on Lightcoin, and are now on Bitcoin. One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain. The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks. While not available yet, this payment channel might get implemented when needed.</p>
-
-<p>2.2.3. Unit base</p>
-
-<p>As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the unitbase is updated each time the UD value reaches 100.00 : it goes from 99.99*10^(unitbase) to 10.00*10^(unitbase+1). All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.</p>
-
-<p>With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.</p>
-
-<p>3. Duniter Web of Trust</p>
-
-<p>3.1. Basic Principles</p>
-
-<p>In order to identify “members” accounts - which create monetary units - and other accounts, Duniter uses a Web of Trust. This can be summarized into few principles:</p>
-
-<p>Each account becomes a member if it received a minimal number of certifications - 5 for Ğ1 currency.</p>
-
-<p>Only members accounts can send certifications. Certifications have a limited lifespan.</p>
-
-<p>A certification indicates that the sender accepts the receiver as a legitimate identity.</p>
-
-<p>The aim of the WoT is to identify a blockchain account to a living human. According to Lauterbach et.al<sup>7</sup>, the strengh of a relationship should be considered when building a vouch system. For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are. A certification represents a strong human relationship : one may certify a close relative, not an acquaintance. Each member has to accept this licence before being included in the WoT. Thus, if a member is part of an attack on the currency, they can be found by mutual relatives. Additional security rules occur to prevent cheat and attacks on a large scale.</p>
-
-<p>Note that non-members accounts can use the currency, but cannot create money. Non-members accounts can be used by individuals as secondary wallets, or by institutions.</p>
-
-<p>We were inspired by the OpenPGP Trust system<sup>8</sup>. However, the OpenPGP trust principles aim at defining trust from a particular point of view while Duniter needs to identify humans for the whole community. To achieve this goal, while OpenPGP allows each user to tweak its trust parameters individually, Duniter sets rules in the “genesis” block for the whole community.</p>
-
-<p>3.2. Why do we need a Web of Trust ?</p>
-
-<p>There are two reasons we need it :</p>
-
-<p>To make sure that only one Universal Dividend is produced per member at each specified creation interval. In the Ğ1’s case this interval is set as daily 86 400 seconds, it is the <emphasis>monetary parameter</emphasis> known as dt.</p>
-
-<p>To identify the nodes hashing the blocks and assign each a personalised difficulty. This custom difficulty proof of work is there to avoid the blockchain’s validation mechanism becoming too centralised as is the case with many 'non-libre’ cryptocurrencies.</p><empty-line /><p>Monetary parameter : Each currency that use Duniter has its own blockchain whose behaviour is dictated by a set of ‘parameters’ defined in block zero - the so-called genesis block - that can be tweaked to achieve the desired results. At the time of writing the Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21 parameters of which 10 are for the WoT alone. We’ll focus on these 10.</p>
-
-<p>Suffice to say that in the Ğ1’s case, the DU is created every 24 hours - 86 400 seconds. This interval is set through the time derivative dt parameter and can have a different value in other implementations of the protocol.</p>
-
-<p>We want to make sure that each member can only have one account. As we all know, achieving zero-risk isn’t possible<sup>9</sup>. Our goal is therefore not to create a WoT within which fraud would be absolutely impossible, but instead to discourage it. Here is a rewording of our goal in 4 smaller ones :</p>
-
-<p>Make the certification process lengthy enough that all members exercise due diligence and are wary of risks.</p>
-
-<p>Make fraudulent acts as hard as we can to the extent that they become pointless.</p>
-
-<p>Ensure that any Sybil attacks have a negligible impact on the currency by ensuring that illegitimate double Universal Dividends have no significant bearing on the legitimate monetary mass</p>
-
-<p>Slow the growth of ‘Sybil regions’ to give enough time for the community to react and isolate the threat.</p><empty-line /><p>Sybil attack : A Sybil attack is an attack perpetrated on a reputation system through the creation of fake identities. A Web of Trust is a specific instance of a Reputation System.</p>
-
-<p>There are plenty of Sybil attack scenarios we can think of and just as many reasons why their perpetrators would want to carry them out. Our objective is that the configuration of the WoT protects both users and its IT backbone infrastructure against these attacks.</p>
-
-<p>This means that micro-attacks performed by small groups of individuals looking for personal enrichment are of no interest to us. The web’s role isn’t to deter these attacks, this being instead the role of the community. Just like the town you live in is responsible for providing your tap water and electricity but isn’t responsible for any burglaries, etc. Much in the same way, Duniter’s WoT guarantees us all a functional currency, but do not detect small fraud.</p>
-
-<p>3.3. The importance of having our own certification system</p>
-
-<p>Centralized identification systems can achieve the goal we want. State Identification is an example. However, this has many drawbacks :</p>
-
-<p>The authority may have arbitrary criteria for identification, for example preventing people without an official state-provided identity or homeless people to be included in the WoT.</p>
-
-<p>Payment might be required to get identified, thus making the monetary creation not “free”.</p>
-
-<p>The authority is a point of failure for any attacker.</p>
-
-<p>It is of the utmost importance that we remain free from any state or corporation. The WoT is an answer to this criterium. To this day we depend only on the Internet and yet, were it to fail, there are already alternatives being tested around the world for a decentralised communication network.</p>
-
-<p>3.4. A few foundational concepts on graph theory : a bit of vocabulary</p><empty-line /><p>Graph: set of points -called ‘vertices’- joined by edges -called paths/walks-.</p>
-
-<p>Simple graph: a graph with no loops and with no multiple edges. That is, each edge connects two distinct endpoints and no two edges have the same endpoints. A simple edge is an edge that is not part of a multiple adjacency -of edges-. In many cases, graphs are assumed to be simple unless specified otherwise.</p>
-
-<p>Directed graph: a graph in which the edges have a distinguished direction, from one vertex to another. A directed edge can also be called a path or walk. Arrow A –&gt; B is therefore different from arrow B –&gt; A.</p>
-
-<p>Endpoints: the edge with vertex A –&gt; B has A and B as endpoints, respectively as start and end of the path/walk.</p>
-
-<p>Isolated vertex: a vertex whose degree is zero, that is, a vertex with no incident edges.</p>
-
-<p>Degree of a vertex: number of its incident edges -in and out-.</p>
-
-<p>Out-degree of vertex A: number of outbound edges / tail ends from A.</p>
-
-<p>In-degree of vertex A: number of incoming edges / head ends to A.</p><empty-line /><p><emphasis>degrees of a vertex diagram</emphasis></p><empty-line /><p>Path: -aka “walk”- path to follow to get from vertex A to vertex B.</p>
-
-<p>3.5. Definition of the Duniter Web of Trust</p>
-
-<p>The Duniter WoTs -one per currency- are simple directed graphs without isolated vertices. The vertices are the members and the edges are the certifications given and received.</p>
-
-<p><emphasis>Directed</emphasis> means that the responsibility of issuing a certification is unique and personal to the certifier. The trust they place in the receiver cannot be imposed in the other direction although in most circumstances both parties equally trust each other.</p>
-
-<p>In addition, all vertices are either currently active members or past-members. Past-member vertices are in a specific ‘deactivated state’ and can no longer issue or receive certifications although the ones already issued or received to/from other members are still considered ‘pending’ to avoid a collapse of the WoT. If these old members don’t come back into the WoT, their pending certifications will eventually expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
-
-<p>To wrap up with old members, after a certain period of time - set in the currency’s parameters - their deactivated vertex is removed from the web and the associated identity is ‘revoked’. The person who owned the account can no longer use this identity but is free to join the web with another one.</p>
-
-<p>Identity : An identity is a set of three pieces of information: a public key, a name and a blockstamp. A blockstamp points to a specific block in the chain. Its main use is to freeze the point in time at which an identity was created and to link this identity to a specific chain and a currency - each currency having its own blockchain.</p>
-
-<p>An identity can be in any one of 5 different status: pending, member, old member, revoked or excluded.</p>
-
-<p>Let’s take a simple example:</p>
-
-<p>    A -&gt; B -&gt; C
-         |
-         \--&gt; D</p>
-
-<p>If, for whatever reason, A were to lose its member status, the web would crumble and all other members would be excluded as a consequence. To avoid this, the certification from A –&gt; B will remain valid until its expiry date, leaving enough time for B to receive certifications from C or D.</p>
-
-<p>Because our WoT doesn’t have any isolated vertices, each new identity created needs to be pulled into the web with all of the certifications it has received, all in the same block. This calls for a temporary ‘buffer’ storage space for pending identities and the certifications they have received. This storage space is called ‘the pool’ of Duniter nodes, which we could also have called the ‘sandbox’ as that’s the name used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other documents and metadata not mentioned here.</p>
-
-<p>3.6. Exploring the rules behind a Duniter Web of Trust</p>
-
-<p>The Duniter WoTs - one per currency - works with a set of eight fundamental rules enforced through eleven different parameters. Ten of these parameters are set within the genesis block, the eleventh one - msPeriod- having being hard-coded in the Ğ1’s code subsequently.</p>
-
-<p>3.6.1. Distance rule and referent members (</p>
-
-<p>stepMax</p>
-
-<p> and</p>
-
-<p>xPercent</p>
-
-<p>)</p>
-
-<p>These two parameters are closely linked and together define the ‘distance rule’. The ‘distance rule’ can only be described after defining what a ‘referent member’ is:</p>
-
-<p>Referent member: member A is said to be ‘referent’ if and only if the total of their degrees are greater than or equal to CEIL-N^-1/stepMax where N is the total number of members. As the size of the web will grow this number will grow too, meaning it will take more certification issuances to become a referent member. The number of certifications needed to become a member shouldn’t change.</p>
-
-<p>Let’s now define the distance rule:</p>
-
-<p>Distance rule: member A is said to observe this rule if and only if for a subset xPercent % of referent members R there exists a path of length less than or equal to stepMax between R and A.</p>
-
-<p>Referent members only exist so that the distance rule can take effect, they have no special privileges over non-referent members. In a perfect web, that is one in which each member has certified all members they legitimately can, all members would be referent members. However, because the web progressively grows in size and because members die and are replaced by new ones, there are always members at any given time t who haven’t yet certified all members they legitimately could. These members would hinder the evolution of the web if they were taken into account in the calculation of the distance rule and the web would effectively stop growing.</p>
-
-<p>Because verifying the application of the distance rule is calculation-greedy, it is only performed when a new identity gets confirmed into the web or an existing member gets renewed. There is an exception to this rule: the distance rule is not observed in the genesis block -when the web is first implemented.</p>
-
-<p>3.6.2. Rule of the minimum number of certifications needed (</p>
-
-<p>sigQty</p>
-
-<p>)</p>
-
-<p>This is the simplest rule, it essentially says that each member must at any given time -meaning in any single block- have received at least sigQty active certifications. If, for whatever reason, member A were to have less than sigQty active certifications in a given block, they would cease to be a member and be required to publish a request for identity renewal.</p>
-
-<p>3.6.3. The membership renewal rule (</p>
-
-<p>msValidity</p>
-
-<p>,</p>
-
-<p>msPeriod</p>
-
-<p> and</p>
-
-<p>msWindow</p>
-
-<p>)</p>
-
-<p>Bear in mind that a membership doesn’t last a lifetime but instead has a lifespan set to msValidity seconds.</p>
-
-<p>Every single member -or old member who hasn’t revoked his identity or been excluded- can request a membership renewal so long as the last request was made more than msPeriod seconds ago. If a member has never requested a renewal, the date of last renewal is equal to the timestamp at which his membership was first created. A new request will be stored in the ‘pool’ for a maximum of msWindow seconds before it’s included in the blockchain. Once again, this can only happen once/if the member meets both the siqQty rule and the distance rule -if these criterion are already matched it’s just a case of waiting for a new block to be mined-.</p>
-
-<p>If a member hasn’t requested a renewal for longer than msValidity seconds, they automatically cease to be a member. From this moment on, the ex-member has another msValidity window to renew their membership. When this period of 2 × msValidity runs out, the membership will expire and this identity will never be available for use again in the web. If the person so desires, they will have to publish new identity and membership documents and find enough certifiers, as any newcomer.</p>
-
-<p>3.6.4. Rule of certification lifespan (</p>
-
-<p>sigValidity</p>
-
-<p>)</p>
-
-<p>All certifications included in the blockchain expire sigValidity seconds after they were issued.</p>
-
-<p>/!\ The issuance and the inclusion of a certification in the blockchain occur at different times. When member A issues a certification at time t1, it gets stored in the pool starting at t1 and only finds its way into the blockchain at t2 when all of the web’s rules are observed. Several weeks can thus go by between t1 and t2!!!</p>
-
-<p>3.6.5. Rule of limited supply of active certifications (</p>
-
-<p>sigStock</p>
-
-<p>)</p>
-
-<p>By ‘active certifications’ we refer to certifications included in the blockchain and that haven’t yet expired.</p>
-
-<p>The total of active certifications issued by any member at any single time must be less than or equal to sigStock. When this threshold is reached the member will have to wait for one of his active certifications to expire before he/she can issue a new one.</p>
-
-<p>3.6.6. Rule of the time period between two certification issuances. (</p>
-
-<p>sigPeriod</p>
-
-<p>)</p>
-
-<p>As soon as a certification issued by member A gets included in the blockchain, they will be unable to issue a new one before another sigPeriod seconds.</p>
-
-<p>3.6.7. Expiry of a certification issuance (</p>
-
-<p>sigWindow</p>
-
-<p>)</p>
-
-<p>When a certification is issued by member A, it will be stored in the ‘pool’ for a maximum of sigWindow seconds. If the certification hasn’t been included in the blockchain by then, it will be cancelled and the member’s sigStock will be repleted by one.</p>
-
-<p>3.6.8. Lifespan of a ‘pending’ identity (</p>
-
-<p>idtyWindow</p>
-
-<p>)</p>
-
-<p>When a new identity is created, it is stored in the ‘pool’ for a maximum of idtyWindow seconds. If the person hasn’t achieved member status by then, the certification will simply be cancelled.</p>
-
-<p>3.7. Details on some of the WoT’s peculiarities at the genesis block</p>
-
-<p>The aforementioned rules can only be enforced with an existing web. They cannot be observed when first creating the web, that is when defining the genesis block.</p>
-
-<p>Only rules 2 and 5 can be observed at the genesis block.</p>
-
-<p>The genesis block has to be manually created by the founding members. In practice this means that there must be a choice on which identities to include on the premise that all of them observe rules 2 and 5. In addition, the genesis block must be signed with the private key of one of these identities.</p>
-
-<p>As soon as the genesis block has been created, the other identities can start mining the blockchain and the member who created block #0 effectively looses the decision power he had at creation.</p>
-
-<p>3.8. Why these rules and application cases in the Ğ1</p>
-
-<p>3.8.1. Distance and maximum size</p>
-
-<p>The distance rule is there to curb the maximum size of a Sybil region as well as that of the monetary community as a whole. The xpercent parameter prevents the creation of a ‘faction’ that could take hold of the blockchain.</p><empty-line /><p><emphasis>Sybil region</emphasis></p>
-
-<p>The Sybil regions are isolated from the rest of the graph in the sense that they can only receive certifications from other ill-intentioned Sybil members. As a consequence, the shortest edge/path between a legitimate member and a Sybil one has to have the attack’s author as an endpoint. The maximum depth the Sybil region can attain is therefore contingent on the distance between the attacking edge-s- and the xpercent% closest referent members, this distance is known as stepAttackers. The maximum size of a Sybil region created by sigQty members depends on the L parameter, defined as L = sigQty/sigStock:</p>
-
-<p>MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)</p>
-
-<p>The maximum size of the Web of Trust is given by the following formula:</p>
-
-<p>WoTmax = (sigStock)*L^(stepMax-1)</p>
-
-<p>However we know for a fact that members will never use all of their available certifications. According to Dunbar<sup>10</sup>, on average, one is able to maintain relationships to around 150 people. Being conservative, we will consider that on average, each person will certify 50 accounts. We can calculate the size of the average web of trust WoTavg :</p>
-
-<p>WoTavg= (50)*(sigQty/50)^(stepMax-1)</p>
-
-<p>Our goal with the Ğ1 is to create a community of about one million members to test the consequences of a libre monetary system. Let’s see how we can tweak the pair of sigQty and stepMax- to reach this size:</p><empty-line /><p><emphasis>Average WoT size graph as a function of sigQty and stepMax</emphasis></p>
-
-<p>The maximum size of a Sybil region grows linearly with sigQty but exponentially with stepMax. Logic has it that we need to keep stepMax as low as possible to ensure sufficient strength to the web. The above graph shows that the lowest value of stepMax for a web of a million members is of 5. This is an order of magnitude and is likely to be much higher in reality, we cannot measure it for sure.</p>
-
-<p>For sigQty we can choose a value of 4 for a web of 1.5 million members or 5 for half a million members. Bear in mind these are gross figures and could be significantly higher, we are talking anywhere between 1 and 10 million in reality. Calculating WOTavg gives us a pretty good idea of how the web would scale bearing in mind that it considers all members are referent members too -which isn’t the case as explained previously-. Hence the maximum size of the web is likely larger, a ballpark figure of half a million is enough for now especially knowing that the smaller sigQty is, the easier it is to launch a Sybil attack -it’s easier to find four accomplices than five-. For security reasons we have settled on five:</p>
-
-<p>stepMax = 5
-sigQty = 5
-sigStock \&gt;= 50</p>
-
-<p>The maximum size of a Sybil region therefore is:</p>
-
-<p>(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))</p>
-
-<p>with sigStock = 50 we have a Sybil region of:</p>
-
-<p>45*(1-10^(5-stepAttackers))/(-9)</p>
-
-<p>A good practice for protecting the web is to maximise stepAttackers. That’s why we decided that referent members in the genesis block had to be at least four steps away from each other.</p>
-
-<p>Another way to keep a Sybil attack at bay, were it slow enough for members to notice it, would be for referent members to ‘stretch’ the web intentionally to limit the growth of the region by ensuring that the attackers’ legitimate certifications received in the first place aren’t renewed. But what if bot accounts were created and certified each other super fast and following all rules, how would we counter that? By introducing a minimum length of time between two certifications!</p>
-
-<p>3.8.2. Time is our friend</p>
-
-<p>To help us deter a Sybil attack, we’ve decided to impose a minimum period of time between any two certifications issued from a single account. This parameter called sigPeriod affords us a greater chance to detect the formation of a ‘hostile’ faction.</p>
-
-<p>Here is a graph showing the evolution of a Sybil region with the variation of sigPeriod. The simulation considers that honest members and attackers both issue a certification each sigPeriod interval, in days:</p><empty-line /><p><emphasis>size of the WoT according to sigPeriod and stepAttackers</emphasis></p>
-
-<p>As we see, there is a strong link between the growth speed of the region and sigPeriod. As evidenced here, we need a sigPeriod high enough in order to ensure that the legitimate web can grow at least as fast as a Sybil region. In addition, the higher sigPeriod is, the more members will exercise their certification power gingerly, the action coming at a higher ‘cost’.</p>
-
-<p>There are numerous advantages to giving sigPeriod a high value and no technical barriers to it, hence our choice of five days.</p>
-
-<p>We could have also gone for one week for the sake of simplicity. However there is an underlying idea behind our choice which was quite simply the pace of today’s life. Certifying someone can be a lengthy process as one needs to make sure they are correctly applying the Ğ1 licence and people nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea to allow one to certify at the end of every working week -five days- instead of a whole calendar one.</p>
-
-<p>3.8.3. Trust me now, trust me forever ? (</p>
-
-<p>sigValidity</p>
-
-<p>,</p>
-
-<p>msValidity</p>
-
-<p>)</p>
-
-<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s Web of Trust:</p>
-
-<p>First of all, some members will pass and those accounts should no longer produce the Universal Dividend.</p>
-
-<p>Secondly it is of the utmost importance that ‘rogue’ accounts can be excluded from the web at some point.</p>
-
-<p>To achieve this, certifications have a limited lifespan. Members need to seek renewal from their peers after sigValidity time. On the other hand, this time can’t be too short that members would spend more time seeking renewal than they would exchanging in the currency. Furthermore, a certification with too short a lifespan would foster careless certifying behaviours. The act of certifying must have a high-enough ‘perceived’ cost to make it feel like an important act. Lastly, we also wanted this lifespan to be easy to remember. Historically speaking, we first settled on the values of sigPeriod and sigStock, meant one could issue all of their certifications in 495 days, one year was therefore not long enough. We deemed three years to be too much and that’s how we agreed on two years in the end.</p>
-
-<p>Thinking that a deceased member could continue producing the UD for two long years without anyone benefitting from it was also something we needed to address. We chose a value of one year for msValidity. The act of renewing every year is done through one of the clients interacting with the blockchain, through a simple click on a button. This parameter is less important than others and is mostly there to ‘prune’ the web of past or inactive members who don’t renew their membership.</p>
-
-<p>3.8.4. Keeping the pools free of information glut (</p>
-
-<p>idtyWindow</p>
-
-<p>,</p>
-
-<p>sigWindow</p>
-
-<p>,</p>
-
-<p>msWindow</p>
-
-<p>)</p>
-
-<p>The pools need to be cleaned up on a regular basis to avoid them clogging up with information and to ensure that machines with less calculating power can still run a Duniter node.</p>
-
-<p>To achieve this, identities with pending membership approval and the corresponding certifications have to remain the shortest time possible in the pool while still having a chance of making it into the blockchain.</p>
-
-<p>For the Ğ1, our opinion was that two months would be enough for all potential certifiers to agree on a specific identity to certify. We also wanted a time period that would be easy enough to remember by all. We settled on two months, and gave this value to all three parameters idtyWindow, sigWindow and msWindow.</p>
-
-<p>3.8.5. Avoiding single members from ‘knowing too many people’ (</p>
-
-<p>sigStock</p>
-
-<p>)</p>
-
-<p>We considered that on average, each person will certify 50 people. However, we know for a fact that some members will use more than 50 certifications. The maximum social network of one individual is around 150 people<sup>11</sup>. Being conservative, we settled on a maximum certification number sigstock of 100.</p><empty-line /><p>
-Since sigStock’s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.</p>
-
-<p>3.8.6. Avoiding locking minorities (</p>
-
-<p>xpercent</p>
-
-<p>)</p>
-
-<p>It’s easy enough to become a referent member, one of the Sybil strategies could therefore be to create a region of referent members. Such a region would grow slower than otherwise but could confer a locking power to its members by using the distance rule. That’s why the distance rule cannot be calculated on 100% of the referent members. Hence the introduction of the xpercent parameter which defines the percentage of referent members needing to be less than five edges -steps- from each other.</p>
-
-<p>This percentage needs to be low enough to prevent the formation of a locking minority -referent Sybil members being too far from legitimate referent members-. On the other hand, it needs to be high enough so as to restrict the maximum size of the Sybil region through the distance rule. The xpercent parameter was one of the hardest to define, therefore we might decide to change its value during the Ğ1 experiment.</p>
-
-<p>We were inspired by the Pareto principle<sup>12</sup>: if at least 20% of members give good density to the web, 80% of the referent members will be five or less steps from any other member -referent or not-. The maximum value for xpercent is therefore 80%, anything above that and the distance rule could be too restrictive for legitimate use cases. With security our top concern, we chose the maximum value of 80%.</p>
-
-<p>3.8.7. Spam protection with (</p>
-
-<p>msPeriod</p>
-
-<p>)</p>
-
-<p>This parameter stands out a bit on its own, as it was added after the genesis block. It is there to protect the Duniter P2P infrastructure against ‘spam’ attacks. We had to think of a strategy against attacks such as high-frequency membership renewal requests -i.e: in every block, every five minutes- or worse still, hundreds of these requests per minute to flood the Duniter nodes. Without such limits, nodes are supposed to address all renewal requests, even in cases where they were last published five minutes ago! The msPeriod parameter was given the same value as idtyWindow, sigWindow and msWindow, i.e. two months.</p>
-
-<p>4. Proof of Work with personal difficulty</p>
-
-<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.</p>
-
-<p>This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each “winning” member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.</p>
-
-<p>Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.</p>
-
-<p>One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an “ecological” PoW ?</p>
-
-<p>4.1. Why do we need Proof of Work ?</p>
-
-<p>Duniter nodes share a database as part of a p2p environment. The proof of work (PoW) allows machines to synchronize with each other. In Duniter’s case, the blockchain is our database, and acts as a ledger keeping a trace of all transactions, status of the WoT and more. How can we let several machines add data (ie: a transaction) at the same time? In addition, how do we settle on how much time has gone by since the blockchain was last updated? Agreement on time is of the utmost importance as we want to create Universal Dividends on a regular basis, and keep track of membership status, both in human time.</p>
-
-<p>Proof-of-work provides a clever solution to both problems:</p><empty-line /><p>Any machine can write into the blockchain (create a new block) but is only authorised to do so if it has previously solved a mathematical equation that require a certain amount of work. The challenge has to be hard enough to prevent two machines to solve it at the same time, ensuring the unicity of a block’s creator.</p>
-
-<p>Solving this challenge takes a certain amount of time, which depends on the calculating power of the whole network. This provides a common ground for defining the needed time reference. A block time is set (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to get an average duration corresponding to this block time.</p>
-
-<p>4.2. Only members can “mine”</p>
-
-<p>One of Duniter’s major differences with other PoW-based cryptocurrencies is that only members are allowed to author blocks. Each block is signed with the member’s private key, allowing the algorithm to determine a personalised difficulty.</p>
-
-<p>This personalised difficulty eliminates the rat-race for the most sophisticated and powerful mining equipment. Another benefit is the fact that no “supercomputer” can take control of the blockchain. Lastly, Duniter implements a rotation in forging members thanks to this personalized difficulty.</p>
-
-<p>This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies. Members can mine with anything from a raspberry pi to a privacy-first internet cube.</p>
-
-<p>4.3. How does it work ?</p>
-
-<p>4.3.1. The hash (aka digest)</p>
-
-<p>Example of a valid hash:</p>
-
-<p>00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</p>
-
-<p>As you can see this hash starts with five zeros which was very hard to achieve and took a lot of work for someone’s computer. Hence the term “proof of work”.</p>
-
-<p>4.3.2. The common difficulty</p>
-
-<p>A common difficulty is needed to settle on a yardstick for our time reference. Its role is to make sure the blockchain moves forward at a steady pace - one block every avgGenTime seconds, avgGenTime being one of the 20 parameters behind the Duniter protocol-.</p>
-
-<p>This difficulty’s initial value can be set to any arbitrary value (70 in Duniter v1.5.x) and then acts as a spring, regulating blocktime creation by increasing itself if the creation interval drops under avgGenTime and vice-versa.</p>
-
-<p>4.3.2.1. How is difficulty applied ?</p>
-
-<p>The numeric value of difficulty is taken from an array of possible hashes out of all possible hashes. In DUBPv13 the hash of a block is its sha256 hexadecimal hash.</p>
-
-<p>To understand the difficulty, we make a euclidiean division of the difficulty by 16.</p>
-
-<p>Here’s an example with a difficulty value of 70 :</p>
-
-<p>70 // 16 = 4 with a remainder of 6.</p>
-
-<p>The valid hashes are the ones starting with four zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation). The valid hashes are then written as starting with : 0000[0-9]. This is a bit different from Bitcoin, where the difficulty is only ruled by the number of zeroes.</p>
-
-<p>4.3.2.2. The Nonce</p>
-
-<p>When a member is forging a new block, his computer freezes the block’s content and changes the Nonce until the hash reaches the required number of zeroes.</p>
-
-<p>The nonce allows us to mine a new block by finding a hash. The hash value allows us to determine the difficulty level of the proof-of-work performed. Examples of possible Nonce values:</p>
-
-<p>10100000112275</p>
-
-<p>10300000288743</p>
-
-<p>10400000008538</p>
-
-<p>10700000079653</p>
-
-<p>10300000070919</p>
-
-<p>In reality the Nonce value follows a pre-determined format akin to XYY00000000000. The Nonce’s value isn’t the number of attempts but rather a value within a set of possible ones. This is how the Nonce is built:</p><empty-line /><p>X is a number assigned to a specific peer. Let’s assume that someone has several nodes each with the same private key, this would lead to possible collisions if this person were to mine the same block with different nodes. Each <strikethrough>block</strikethrough> node ? will therefore have its own unique X to prevent this from happening.</p>
-
-<p>Y is the number of cores of the processor. The Nonce starting with 107[…] belongs to a seven cores processor, while 199[...] could be the proof generated by a 99 cores processor.</p>
-
-<p>The rest of the Nonce, the part that follows after the XYY, is the numerical space for this individual node and is unique to each of the CPU’s core. This space is comprised of eleven digits (00000000000). For the sake of accuracy, we use the term CPU in the wider sense, it can be understood as a bi-CPU for example. We take into consideration the number of cores for the resulting PoW.</p>
-
-<p>4.4. Personalised difficulty</p>
-
-<p>Earlier in this article, we explained that the personalised difficulty is the new and key concept that sets Duniter apart from other PoW-based cryptocurrencies.</p>
-
-<p>Here is how this personalised difficulty is calculated and assigned:</p>
-
-<p>It is determined by a combination of two different constraints with complimentary roles: the exclusion factor and the handicap.</p>
-
-<p>Let powMin be the common difficulty, exFact a member’s exclusion factor and handicap their handicap. This member’s personalised difficulty diff is:</p>
-
-<p>diff = powMin*exFact + handicap</p>
-
-<p>4.4.1. Understanding</p>
-
-<p>exFact</p>
-
-<p>, the exclusion factor</p>
-
-<p>Members who have never produced blocks or haven’t for quite some time are assigned an exclusion factor of 1. Their personalised difficulty is therefore simply the sum of powMin + handicap.</p>
-
-<p>Before reading on, let’s precise the role of this exclusion factor. When a member adds a block to the chain, his exFact jumps up from one to a very high value, to prevent them from forging other blocks immediately after and taking control of the blockchain.</p>
-
-<p>The exclusion factor will then rapidly return to one. This delay is expressed as a number of blocks. It is calculated as a proportion of the number of members forging. In the Ğ1’s case, this proportion is 1/3, meaning that if there are fifteen members currently forging, the member’s exclusion factor will drop down to one after five blocks.</p>
-
-<p>4.4.1.1. What is intended by “the number of members forging” ?</p>
-
-<p>We mean the number of members trying to create the next block. In reality, there is no way to precisely know how many members are calculating at any given time, because it is impossible to view the entire network. But we need this information, whithout which assigning a personalised difficulty is impossible. To achieve this, Duniter looks back at the blockchain and assumes that there is as much members forging as those who have found at least one block in the last blocks in the current window, minus the very last one.</p>
-
-<p>4.4.1.2. Current window</p>
-
-<p>We use the concept of current window. The current window is the number of blocks we look back at to determine how many members are forging. Let’s see how it works:</p><empty-line /><p>issuersFrame is the size of the current window in blocks.</p>
-
-<p>issuersCount the number of members who have calculated at least one block during the current window.</p>
-
-<p>Both issuersFrame and issuersCount are block fields. When first starting a blockchain, the very first block has an issuersFrame=1 and an issuersCount=0. The genesis block is excluded as there are no members in the current window!</p>
-
-<p>From the second block onwards (block #1) we track the variation of issuersCount. The member having mined block #0 enters the current window and in block #1 we will therefore mention issuersCount=1.</p>
-
-<p>issuersFrame then varies as follows:</p>
-
-<p>if issuersCount increases by N (with a maximum step of N = 1), then issuersFrame will increase by one unit over a period of 5N blocks.</p>
-
-<p>Conversely, if issuersCount decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then issuersFrame will decrease by one unit during 5Y blocks.</p>
-
-<p>When such events overlap, issuersFrame evolves as so :</p><empty-line /><p><strong>bloc</strong></p>
-
-<p><strong>event</strong></p>
-
-<p><strong>issuersFrame</strong></p><empty-line /><p>T</p>
-
-<p>Babar writes a block and enters issuersCount</p>
-
-<p>160</p><empty-line /><p>T+1</p>
-
-<p>Celeste leaves issuersCount</p>
-
-<p>160 +1 = 161</p><empty-line /><p>T+2</p>
-
-<p>N/a</p>
-
-<p>161 +1 -1 = 161</p><empty-line /><p>T+3/4/5</p>
-
-<p>N/a</p>
-
-<p>161 +1 -1 = 161</p><empty-line /><p>T+6</p>
-
-<p>N/a</p>
-
-<p>161 -1 = 160</p><empty-line /><p>The calculation can be found under rules BR_G05 and BR_G06 of the DUP protocol.</p>
-
-<p>4.4.1.3. exFact and the personalised difficulty</p>
-
-<p>We explained that exFact spikes immediately after the member has found a block. It decreases then rapidly to 1 after a number of blocks equal to 1/3 * issuersCount. Let’s see precisely how we calculate exFact:</p><empty-line /><p>nbPreviousIssuers is the value of issuersCount at the last block N found by the member.</p>
-
-<p>nbBlocksSince is the number of blocks found by the rest of the network since block N.</p>
-
-<p>percentRot is the number of <emphasis>not excluded</emphasis> peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.</p>
-
-<p>a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]</p>
-
-<p>The FLOOR is a simple truncate function. For exFact to exclude the member, we need :</p>
-
-<p>(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) &gt;= 2</p>
-
-<p>We can see that the member is not excluded if nbBlocksSince is greater than 1/3 of the calculating members. Take as an example nbPreviousIssuers = 6 and nbBlocksSince = 3:</p>
-
-<p>(0.67* 6 / )1 + 3)) = 1.005 -&gt; exFact = 1</p>
-
-<p>However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:</p>
-
-<p>(0.67 * 6 / (1 + 1)) = 2.01 -&gt; exFact = 2</p>
-
-<p>Moreover if the last block was authored by the said member, then:</p>
-
-<p>nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers</p>
-
-<p>ExFact value increases according to the number of members calculating. Thus, if there is enough members calculating, even mining farms would be excluded. We have therefore succeeded in our intent to deter attempts to seize the blockchain and its currency.</p>
-
-<p>However, at any time t, the two-thirds of calculating members all have an exclusion factor of 1, even though they might not all have the same computational power at hand. If the personalised difficulty only took into account the exclusion factor, then only the members with the highest computational power from the remaining third would be able to author new blocks and the other 2/3s would almost always be excluded. Lesser machines wouldn’t stand a chance…</p>
-
-<p>4.4.2. The handicap</p>
-
-<p>The handicap is the second parameter of the personalised difficulty. Its main role is to improve the rotation of forging peers. A higher handicap is assigned to members with higher calculating power, so lesser machines can also compute blocks. As a consequence, there is no incentive on forging with powerful computers. Security can be achieved with less computing power than with pure PoW.</p>
-
-<p>The aim is to handicap the half that has authored most blocks (the most powerful half) to favour the other one. So, the handicap formula will use the median number of blocks authored by peers within the current window.</p><empty-line /><p>nbPersonalBlocksInFrame is the number of blocks authored by a single member within the current window.</p>
-
-<p>medianOfBlocksInFrame is the median number of blocks written by the calculating members during the same timeframe.</p>
-
-<p>a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))</p>
-
-<p>Let’s unwrap the formula:</p>
-
-<p>(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)</p>
-
-<p>is simply the ratio between the number of blocks authored by the peer and the median number of blocks. For example, if a peer has authored 9 blocks in the current window and the median is 5, then the ratio will be (9+1)/5 = 2. The MAX function allows us to ensure that the handicap has a value at least equal to 1.</p>
-
-<p>The Napierian Logarithm of this ratio prevents the handicap from becoming excluding. We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.</p>
-
-<p>If we wanted the handicap to be applied as soon as the median is reached, we would divide it by LN(1). The problem is that we have already set a minimum value of 1 with the MAX function. If we were to divide the ratio by LN(1) all calculating peers would have a handicap \&gt;= 1. In addition, is it really fair to handicap a member who is right on the median?</p>
-
-<p>That’s why we went for 1.189 rather than 1. A member has to be at least 18.9% above the median to be assigned a handicap. 18.9% is actually 16^(1/16), the difficulty factor between two levels of the proof work (hexadecimal hash).</p>
-
-<p>To conclude, you have to remember that :</p>
-
-<p>The handicap is indexed on the logarithm of the ratio to the median,</p>
-
-<p>Handicap is only applied on members whose ratio to the median is greater than the ratio between two levels of the proof-of-work’s difficulty.</p>
-
-<p>Conclusion</p>
-
-<p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.</p>
-
-<p>More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.</p>
-
-<p>The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :</p>
-
-<p>The freedom to choose your currency system: because money should not be imposed.</p>
-
-<p>The freedom to access resources: because we all should have access to economic &amp; monetary resources.</p>
-
-<p>The freedom to estimate and produce value: because value is a purely relative to each individual.</p>
-
-<p>The freedom to trade with the money: because we should not be limited by the avaible money supply.</p>
-
-<p>Those 4 economic freedoms should be understood together, not exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.</p>
-
-<p>Sources :</p>
-
-<p>Relative Theory of Money, S.Laborde, 2010: en.trm.creationmonetaire.info/</p>
-
-<p>Bitcoin Whitepaper, S.Nakamoto, 2008: bitcoin.org/bitcoin.pdf</p>
-
-<p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : lightning.network/lightning-network-paper.pdf</p>
-
-<p>The GNU Privacy Handbook, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335</p>
-
-<p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. cr.yp.to/papers.html#ed25519.</p>
-
-<p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : archive.org/details/PPCoinPaper</p>
-
-<p>Duniter Blockchain Protocol, v13, draft by Elois : git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</p>
-
-<p>The Sibyl Attack, J.R.Douceur: www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992</p><empty-line /><empty-line /><empty-line /><p>Bitcoin Whitepaper, S.Nakamoto, 2008: bitcoin.org/bitcoin.pdf↩</p>
-
-<p>Relative Theory of Money, S.Laborde, 2010: en.trm.creationmonetaire.info/↩</p>
-
-<p>OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335↩</p>
-
-<p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. cr.yp.to/papers.html#ed25519.↩</p>
-
-<p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : archive.org/details/PPCoinPaper↩</p>
-
-<p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : lightning.network/lightning-network-paper.pdf↩</p>
-
-<p>Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf↩</p>
-
-<p>Public key validation on GnuPG manual, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335↩</p>
-
-<p>The Sibyl Attack, J.R.Douceur: www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf↩</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992↩</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992↩</p>
-
-<p>Pareto principle : en.wikipedia.org/wiki/Pareto_principle↩</p><empty-line />
-</section>
-
-</body>
-</FictionBook>
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-<article id="whitepaper" class="content">
-<h1 id="duniter-a-libre-currency-blockchain-generator.">Duniter: A libre currency blockchain generator.</h1>
-<h2 id="abstract">Abstract</h2>
-<p>Many currency principles involve non-equal rights to monetary creation between humans. We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human. This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution. Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process. We use a Web of Trust between living humans for identification. This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.</p>
-<h2 id="introduction">Introduction</h2>
-<p>Duniter is a software to create and manage “libre currencies”. Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :</p>
-<blockquote>
-<p>How should a currency be created to match the principle of equality between all humans, now and between generations ?</p>
-</blockquote>
-<p>The results of this demonstration implies a monetary creation :</p>
-<ul>
-<li>on a regular basis</li>
-<li>for each human being</li>
-<li>which amount has to be reassessed on fixed intervals according to a fixed formula.</li>
-</ul>
-<p>Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :</p>
-<p><br /><span class="math display">$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$</span><br /></p>
-<p>Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.</p>
-<p>The first currency created through Duniter is Ğ1, pronounced “June”. It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.</p>
-<h2 id="state-of-the-art-bitcoin-case">1. State of the art : Bitcoin case</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniter uses the crypto-currency concept introduced by Bitcoin<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a>, which is to use cryptographic tools such as signatures to create trustless digital currencies. Duniter fits this definition, but it has two completely different principles than Bitcoin : the Web of Trust and the Universal Dividend . These differences are on both monetary and technical aspects.</p>
-<h3 id="monetary-creation-a-space-time-asymmetry">1.1. Monetary creation of Bitcoin : a space-time asymmetry</h3>
-<p>Space-time asymmetry refers to the relative access of individuals to newly created money<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a>. Concretely, most existing currencies (c. 2020) are both spatially and temporally asymmetrical for their users. Let's take Bitcoin as an example to understand why.</p>
-<h4 id="spatial-asymmetry">1.1.1. Spatial asymmetry</h4>
-<p>When new Bitcoins are created, only some Bitcoin users (the miners) are given new Bitcoins, while everyone else get nothing. We believe this is the first injustice. However, some might say:</p>
-<blockquote>
-<p>"Miners used their electricity and time to get it!"</p>
-</blockquote>
-<p>... we would answer that this work should not have been rewarded by newly created Bitcoins. New units should be distributed to the whole community. Miners should be rewared another way, but not by money issuance. Of course, Bitcoin cannot create money through Basic Income since Bitcoin users are not strongly identified, and one might benefit from money creation multiple times if they owned several wallets. Duniter gets rid of this problem by identifying its users and creating the same amount of Basic Income to everyone.</p>
-<h4 id="temporal-asymmetry">1.1.2. Temporal-asymmetry</h4>
-<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency), which means ever fewer bitcoins will be created over time until no new BTC are being generated. So, once the first adopters have mined every bitcoin, how will future joiners get Bitcoins? Just like most of us do for Euros or Dollars: to get money, they will have to work for the ones who already own it.</p>
-<p>We believe this is the second injustice. Every member of a monetary community should be equal concerning monetary creation, and get the same relative amount of money over time, even if they are a late adopter. Duniter aims to fix this by making the Universal Dividend (a.k.a. UD) grow by the time according to precise rules, thus making members equal toward money issuance on a half-lifespan.</p>
-<p>Most currencies present one of these two asymmetries, including metal currencies and mutual credit, as exposed in the RTM.</p>
-<h4 id="a-solution">1.1.3. A solution</h4>
-<p>Bitcoin has taught us that it is possible to create a currency system allowing one to both create digital money and to exchange it without a central authority. What we need to change is the way money is issued so we finally have a symmetrical system. We need <strong>Bitcoin + Universal Dividend</strong>. But Universal Dividend implies that the community consists of only identified people. This is where the Web of Trust (WoT) comes into place.</p>
-<p>This concept, introduced by cryptography with the OpenPGP format<a href="#fn3" class="footnote-ref" id="fnref3"><sup>3</sup></a>, allows us to identify people in a decentralized manner. It works as follows: each person creates a personal identity that is linked to its cyptographic certificate. The identity must be confirmed by others members who use their own cryptographic key. It is that simple: people choose who is part of the community and who is not, not a central authority.</p>
-<p>However, Duniter will not use OpenPGP for its cryptographic features: Elliptic Curves<a href="#fn4" class="footnote-ref" id="fnref4"><sup>4</sup></a> will be used instead for the conciseness of its generated keys and its pratical advantages. Duniter has its own Web of Trust principles, that will be exposed later.</p>
-<h3 id="proof-of-work-mining-a-power-race">1.2. Proof-of-Work mining : a power race</h3>
-<p>In Bitcoin Model, the calculation and incentive principles cause a power race : new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers. This leads to a power race an places the control over the currency in the hands of the richest hardware owners. We want to make Duniter blockchain validation much less energy and hardware consuming while keeping a strong level of security. This will be further explained later. A consequence of this choice is the participation of low-end hardware in the Duniter network, leading to a better decentralization of blockchain validation.</p>
-<h4 id="what-about-proof-of-stake">1.2.1 What about Proof of Stake ?</h4>
-<p>Proof of stake consensus algorythm was first introduced in 2012<a href="#fn5" class="footnote-ref" id="fnref5"><sup>5</sup></a>. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a “stake” they would lose in case of cheat.</p>
-<p>At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle. Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.</p>
-<h2 id="duniters-blockchain">2. Duniters Blockchain</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniters Blockchain follows the basic principles of Bitcoins. This is essential for synchronization between peers, as to prevent double-spend attacks. However, Duniters Blockchain will store different informations than Bitcoins.</p>
-<p>The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
-<ul>
-<li>a former transaction (as in Bitcoin)</li>
-<li>a Universal Dividend (specific to Duniter).</li>
-</ul>
-<p>Duniters Web of Trust is also written in the Blockchain. The identity of each member gets registered much like transactions are, with a strong link to the time reference. Thus, the Blockchain is a representation of a space-time frame of reference, where “space” are members of the WoT and “time” the basic blockchain units : the blocks. On each point of time, one can determine which account is legitimate to create the UD, only with a blockchain analysis.</p>
-<h3 id="spam-countermeasures">2.1. Spam countermeasures</h3>
-<p>An issue of most cryptocurrency projects is to prevent the common ledger from growing too much. This would require nodes to have a lot of storage and computing power to be usable. In particular, we don’t want an attacker to be able to make the Blockchain grow too fast. Most projects implement transaction fees as a way to prevent this, making the attacker lose money. We don’t want to introduce this mean since a currency with automatic fees on transactions is no more neutral. Several countermeasuers against such spam attacks are implemented.</p>
-<!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
-<h4 id="minimum-output-amount">2.1.1. Minimum output amount</h4>
-<!-- This has to be implemented in DUBPv13. -->
-<p>Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.</p>
-<h4 id="limited-block-size-and-chainability">2.1.2. Limited block size and chainability</h4>
-<p>The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.</p>
-<p>With the same goal to prevent too many transactions to get registered, while transactions can be “chained” (refer to another transaction in the same block), the chainability of transactions is limited to 5.</p>
-<h3 id="scaling">2.2. Scaling</h3>
-<p>Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :</p>
-<ul>
-<li>Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don’t want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.</li>
-<li>Duniter’s aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.</li>
-</ul>
-<p>However, Duniter has assets that will help if the number of users and transactions grow.</p>
-<h4 id="dynamic-block-size">2.2.1 Dynamic block size</h4>
-<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve. On low use of the blockchain, the maximal block size is 500 bytes. On high use of the blockchain, the maximal block size would be 110% of the average size of the current window blocks(see “personalised difficulty” part for more information). This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :</p>
-<pre><code>block_size &lt; max(500 ; CEIL(1.10 * (average block size))</code></pre>
-<h4 id="lightning-networks">2.2.2. Lightning Networks</h4>
-<p>The Lightning Networks<a href="#fn6" class="footnote-ref" id="fnref6"><sup>6</sup></a> allow almost instant and off-chain transactions. They were first implemented on Lightcoin, and are now on Bitcoin. One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain. The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks. While not available yet, this payment channel might get implemented when needed.</p>
-<h4 id="unit-base">2.2.3. Unit base</h4>
-<p>As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the <code>unitbase</code> is updated each time the UD value reaches 100.00 : it goes from <code>99.99*10^(unitbase)</code> to <code>10.00*10^(unitbase+1)</code>. All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.</p>
-<p>With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.</p>
-<h2 id="duniter-web-of-trust">3. Duniter Web of Trust</h2>
-<h3 id="duniter-wot-basic-principles">3.1. Basic Principles</h3>
-<p>In order to identify “members” accounts - which create monetary units - and other accounts, Duniter uses a Web of Trust. This can be summarized into few principles:</p>
-<ul>
-<li>Each account becomes a member if it received a minimal number of certifications - 5 for Ğ1 currency.</li>
-<li>Only members accounts can send certifications. Certifications have a limited lifespan.</li>
-<li>A certification indicates that the sender accepts the receiver as a legitimate identity.</li>
-</ul>
-<p>The aim of the WoT is to identify a blockchain account to a living human. According to Lauterbach et.al<a href="#fn7" class="footnote-ref" id="fnref7"><sup>7</sup></a>, the strengh of a relationship should be considered when building a vouch system. For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are. A certification represents a strong human relationship : one may certify a close relative, not an acquaintance. Each member has to accept this licence before being included in the WoT. Thus, if a member is part of an attack on the currency, they can be found by mutual relatives. Additional security rules occur to prevent cheat and attacks on a large scale.</p>
-<p>Note that non-members accounts can use the currency, but cannot create money. Non-members accounts can be used by individuals as secondary wallets, or by institutions.</p>
-<p>We were inspired by the OpenPGP Trust system<a href="#fn8" class="footnote-ref" id="fnref8"><sup>8</sup></a>. However, the OpenPGP trust principles aim at defining trust from a particular point of view while Duniter needs to identify humans for the whole community. To achieve this goal, while OpenPGP allows each user to tweak its trust parameters individually, Duniter sets rules in the “genesis” block for the whole community.</p>
-<h3 id="why-do-we-need-a-web-of-trust">3.2. Why do we need a Web of Trust ?</h3>
-<p>There are two reasons we need it :</p>
-<ol type="1">
-<li>To make sure that only one Universal Dividend is produced per member at each specified creation interval. In the Ğ1’s case this interval is set as daily <code>86 400</code> seconds, it is the <em>monetary parameter</em> known as <code>dt</code>.</li>
-<li>To identify the nodes hashing the blocks and assign each a personalised difficulty. This custom difficulty proof of work is there to avoid the blockchain’s validation mechanism becoming too centralised as is the case with many 'non-libre’ cryptocurrencies.</li>
-</ol>
-<blockquote>
-<p><strong>Monetary parameter</strong> : Each currency that use Duniter has its own blockchain whose behaviour is dictated by a set of ‘parameters’ defined in block zero - the so-called genesis block - that can be tweaked to achieve the desired results. At the time of writing the Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21 parameters of which 10 are for the WoT alone. We’ll focus on these 10.</p>
-<p>Suffice to say that in the Ğ1’s case, the DU is created every 24 hours - 86 400 seconds. This interval is set through the time derivative <code>dt</code> parameter and can have a different value in other implementations of the protocol.</p>
-</blockquote>
-<p>We want to make sure that each member can only have one account. As we all know, achieving zero-risk isn’t possible<a href="#fn9" class="footnote-ref" id="fnref9"><sup>9</sup></a>. Our goal is therefore not to create a WoT within which fraud would be absolutely impossible, but instead to discourage it. Here is a rewording of our goal in 4 smaller ones :</p>
-<ol type="1">
-<li>Make the certification process lengthy enough that all members exercise due diligence and are wary of risks.</li>
-<li>Make fraudulent acts as hard as we can to the extent that they become pointless.</li>
-<li>Ensure that any Sybil attacks have a negligible impact on the currency by ensuring that illegitimate double Universal Dividends have no significant bearing on the legitimate monetary mass</li>
-<li>Slow the growth of ‘Sybil regions’ to give enough time for the community to react and isolate the threat.</li>
-</ol>
-<blockquote>
-<p><strong>Sybil attack</strong> : A Sybil attack is an attack perpetrated on a reputation system through the creation of fake identities. A Web of Trust is a specific instance of a Reputation System.</p>
-</blockquote>
-<p>There are plenty of Sybil attack scenarios we can think of and just as many reasons why their perpetrators would want to carry them out. Our objective is that the configuration of the WoT protects both users and its IT backbone infrastructure against these attacks.</p>
-<p>This means that micro-attacks performed by small groups of individuals looking for personal enrichment are of no interest to us. The web’s role isn’t to deter these attacks, this being instead the role of the community. Just like the town you live in is responsible for providing your tap water and electricity but isn’t responsible for any burglaries, etc. Much in the same way, Duniter’s WoT guarantees us all a functional currency, but do not detect small fraud.</p>
-<h3 id="own-certification-system">3.3. The importance of having our own certification system</h3>
-<p>Centralized identification systems can achieve the goal we want. State Identification is an example. However, this has many drawbacks :</p>
-<ul>
-<li>The authority may have arbitrary criteria for identification, for example preventing people without an official state-provided identity or homeless people to be included in the WoT.</li>
-<li>Payment might be required to get identified, thus making the monetary creation not “free”.</li>
-<li>The authority is a point of failure for any attacker.</li>
-</ul>
-<p>It is of the utmost importance that we remain free from any state or corporation. The WoT is an answer to this criterium. To this day we depend only on the Internet and yet, were it to fail, there are already alternatives being tested around the world for a decentralised communication network.</p>
-<h3 id="graph-theory-vocabulary">3.4. A few foundational concepts on graph theory : a bit of vocabulary</h3>
-<ul>
-<li><p><strong>Graph</strong>: set of points -called ‘vertices’- joined by edges -called paths/walks-.</p></li>
-<li><p><strong>Simple graph</strong>: a graph with no loops and with no multiple edges. That is, each edge connects two distinct endpoints and no two edges have the same endpoints. A simple edge is an edge that is not part of a multiple adjacency -of edges-. In many cases, graphs are assumed to be simple unless specified otherwise.</p></li>
-<li><p><strong>Directed graph</strong>: a graph in which the edges have a distinguished direction, from one vertex to another. A directed edge can also be called a path or walk. Arrow A –&gt; B is therefore different from arrow B –&gt; A.</p></li>
-<li><p><strong>Endpoints</strong>: the edge with vertex A –&gt; B has A and B as endpoints, respectively as start and end of the path/walk.</p></li>
-<li><p><strong>Isolated vertex</strong>: a vertex whose degree is zero, that is, a vertex with no incident edges.</p></li>
-<li><p><strong>Degree of a vertex</strong>: number of its incident edges -in and out-.</p></li>
-<li><p><strong>Out-degree of vertex A</strong>: number of outbound edges / tail ends from A.</p></li>
-<li><p><strong>In-degree of vertex A</strong>: number of incoming edges / head ends to A.</p></li>
-</ul>
-<figure>
-<img src="./images/degres.jpg" alt="degrees of a vertex diagram" /><figcaption>degrees of a vertex diagram</figcaption>
-</figure>
-<ul>
-<li><strong>Path</strong>: -aka “walk”- path to follow to get from vertex A to vertex B.</li>
-</ul>
-<h3 id="definition-of-the-duniter-web-of-trust">3.5. Definition of the Duniter Web of Trust</h3>
-<p>The Duniter WoTs -one per currency- are simple directed graphs without isolated vertices. The vertices are the members and the edges are the certifications given and received.</p>
-<p><em>Directed</em> means that the responsibility of issuing a certification is unique and personal to the certifier. The trust they place in the receiver cannot be imposed in the other direction although in most circumstances both parties equally trust each other.</p>
-<p>In addition, all vertices are either currently active members or past-members. Past-member vertices are in a specific ‘deactivated state’ and can no longer issue or receive certifications although the ones already issued or received to/from other members are still considered ‘pending’ to avoid a collapse of the WoT. If these old members don’t come back into the WoT, their pending certifications will eventually expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
-<p>To wrap up with old members, after a certain period of time - set in the currency’s parameters - their deactivated vertex is removed from the web and the associated identity is ‘revoked’. The person who owned the account can no longer use this identity but is free to join the web with another one.</p>
-<blockquote>
-<p><strong>Identity</strong> : An identity is a set of three pieces of information: a public key, a name and a blockstamp. A blockstamp points to a specific block in the chain. Its main use is to freeze the point in time at which an identity was created and to link this identity to a specific chain and a currency - each currency having its own blockchain.</p>
-<p>An identity can be in any one of 5 different status: pending, member, old member, revoked or excluded.</p>
-</blockquote>
-<p>Let’s take a simple example:</p>
-<pre><code>    A -&gt; B -&gt; C
-         |
-         \--&gt; D</code></pre>
-<p>If, for whatever reason, A were to lose its member status, the web would crumble and all other members would be excluded as a consequence. To avoid this, the certification from A –&gt; B will remain valid until its expiry date, leaving enough time for B to receive certifications from C or D.</p>
-<p>Because our WoT doesn’t have any isolated vertices, each new identity created needs to be pulled into the web with all of the certifications it has received, all in the same block. This calls for a temporary ‘buffer’ storage space for <strong>pending</strong> identities and the certifications they have received. This storage space is called ‘the pool’ of Duniter nodes, which we could also have called the ‘sandbox’ as that’s the name used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other documents and metadata not mentioned here.</p>
-<h3 id="exploring-the-rules-behind-duniter-wot">3.6. Exploring the rules behind a Duniter Web of Trust</h3>
-<p>The Duniter WoTs - one per currency - works with a set of eight fundamental rules enforced through eleven different parameters. Ten of these parameters are set within the genesis block, the eleventh one - <code>msPeriod</code>- having being hard-coded in the Ğ1’s code subsequently.</p>
-<h4 id="distance-rule-and-referent-members-stepmax-and-xpercent">3.6.1. Distance rule and referent members (<code>stepMax</code> and <code>xPercent</code>)</h4>
-<p>These two parameters are closely linked and together define the ‘distance rule’. The ‘distance rule’ can only be described after defining what a ‘referent member’ is:</p>
-<blockquote>
-<p><strong>Referent member</strong>: member A is said to be ‘referent’ if and only if the total of their degrees are greater than or equal to <code>CEIL-N^-1/stepMax</code> where N is the total number of members. As the size of the web will grow this number will grow too, meaning it will take more certification issuances to become a referent member. The number of certifications needed to become a member shouldn’t change.</p>
-</blockquote>
-<p>Let’s now define the distance rule:</p>
-<blockquote>
-<p><strong>Distance rule</strong>: member A is said to observe this rule if and only if for a subset xPercent % of referent members R there exists a path of length less than or equal to <code>stepMax</code> between R and A.</p>
-</blockquote>
-<p>Referent members only exist so that the distance rule can take effect, they have no special privileges over non-referent members. In a perfect web, that is one in which each member has certified all members they legitimately can, all members would be referent members. However, because the web progressively grows in size and because members die and are replaced by new ones, there are always members at any given time <code>t</code> who haven’t yet certified all members they legitimately could. These members would hinder the evolution of the web if they were taken into account in the calculation of the distance rule and the web would effectively stop growing.</p>
-<p>Because verifying the application of the distance rule is calculation-greedy, it is only performed when a new identity gets confirmed into the web or an existing member gets renewed. There is an exception to this rule: the distance rule is not observed in the genesis block -when the web is first implemented.</p>
-<h4 id="rule-of-the-minimum-number-of-certifications-needed-sigqty">3.6.2. Rule of the minimum number of certifications needed (<code>sigQty</code>)</h4>
-<p>This is the simplest rule, it essentially says that each member must at any given time -meaning in any single block- have received at least <code>sigQty</code> active certifications. If, for whatever reason, member A were to have less than <code>sigQty</code> active certifications in a given block, they would cease to be a member and be required to publish a request for identity renewal.</p>
-<h4 id="the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">3.6.3. The membership renewal rule (<code>msValidity</code>, <code>msPeriod</code> and <code>msWindow</code>)</h4>
-<p>Bear in mind that a membership doesn’t last a lifetime but instead has a lifespan set to <code>msValidity</code> seconds.</p>
-<p>Every single member -or old member who hasn’t revoked his identity or been excluded- can request a membership renewal so long as the last request was made more than <code>msPeriod</code> seconds ago. If a member has never requested a renewal, the date of last renewal is equal to the timestamp at which his membership was first created. A new request will be stored in the ‘pool’ for a maximum of <code>msWindow</code> seconds before it’s included in the blockchain. Once again, this can only happen once/if the member meets both the <code>siqQty</code> rule and the distance rule -if these criterion are already matched it’s just a case of waiting for a new block to be mined-.</p>
-<p>If a member hasn’t requested a renewal for longer than <code>msValidity</code> seconds, they automatically cease to be a member. From this moment on, the ex-member has another <code>msValidity</code> window to renew their membership. When this period of <code>2 × msValidity</code> runs out, the membership will expire and this identity will never be available for use again in the web. If the person so desires, they will have to publish new identity and membership documents and find enough certifiers, as any newcomer.</p>
-<h4 id="rule-of-certification-lifespan-sigvalidity">3.6.4. Rule of certification lifespan (<code>sigValidity</code>)</h4>
-<p>All certifications included in the blockchain expire <strong>sigValidity</strong> seconds after they were <strong>issued</strong>.</p>
-<blockquote>
-<p>/!\ The issuance and the inclusion of a certification in the blockchain occur at different times. When member A issues a certification at time t1, it gets stored in the pool starting at t1 and only finds its way into the blockchain at t2 when all of the web’s rules are observed. Several weeks can thus go by between t1 and t2!!!</p>
-</blockquote>
-<h4 id="rule-of-limited-supply-of-active-certifications-sigstock">3.6.5. Rule of limited supply of active certifications (<code>sigStock</code>)</h4>
-<p>By ‘active certifications’ we refer to certifications included in the blockchain and that haven’t yet expired.</p>
-<p>The total of active certifications issued by any member at any single time must be less than or equal to <code>sigStock</code>. When this threshold is reached the member will have to wait for one of his active certifications to expire before he/she can issue a new one.</p>
-<h4 id="rule-of-the-time-period-between-two-certification-issuances-sigperiod">3.6.6. Rule of the time period between two certification issuances. (<code>sigPeriod</code>)</h4>
-<p>As soon as a certification issued by member A gets included in the blockchain, they will be unable to issue a new one before another <code>sigPeriod</code> seconds.</p>
-<h4 id="expiry-of-a-certification-issuance-sigwindow">3.6.7. Expiry of a certification issuance (<code>sigWindow</code>)</h4>
-<p>When a certification is issued by member A, it will be stored in the ‘pool’ for a maximum of <code>sigWindow</code> seconds. If the certification hasn’t been included in the blockchain by then, it will be cancelled and the member’s <code>sigStock</code> will be repleted by one.</p>
-<h4 id="lifespan-of-a-pending-identity-idtywindow">3.6.8. Lifespan of a ‘pending’ identity (<code>idtyWindow</code>)</h4>
-<p>When a new identity is created, it is stored in the ‘pool’ for a maximum of <code>idtyWindow</code> seconds. If the person hasn’t achieved member status by then, the certification will simply be cancelled.</p>
-<h3 id="details-on-some-of-the-wots-peculiarities-at-the-genesis-block">3.7. Details on some of the WoT’s peculiarities at the genesis block</h3>
-<p>The aforementioned rules can only be enforced with an existing web. They cannot be observed when first creating the web, that is when defining the genesis block.</p>
-<p>Only rules 2 and 5 can be observed at the genesis block.</p>
-<p>The genesis block has to be manually created by the founding members. In practice this means that there must be a choice on which identities to include on the premise that all of them observe rules 2 and 5. In addition, the genesis block must be signed with the private key of one of these identities.</p>
-<p>As soon as the genesis block has been created, the other identities can start mining the blockchain and the member who created block #0 effectively looses the decision power he had at creation.</p>
-<h3 id="why-these-rules-and-application-cases-in-the-g1">3.8. Why these rules and application cases in the Ğ1</h3>
-<h4 id="distance-and-maximum-size">3.8.1. Distance and maximum size</h4>
-<p>The distance rule is there to curb the maximum size of a Sybil region as well as that of the monetary community as a whole. The <code>xpercent</code> parameter prevents the creation of a ‘faction’ that could take hold of the blockchain.</p>
-<figure>
-<img src="./images/wot-sybil.jpg" alt="Sybil region" /><figcaption>Sybil region</figcaption>
-</figure>
-<p>The Sybil regions are isolated from the rest of the graph in the sense that they can only receive certifications from other ill-intentioned Sybil members. As a consequence, the shortest edge/path between a legitimate member and a Sybil one has to have the attack’s author as an endpoint. The maximum depth the Sybil region can attain is therefore contingent on the distance between the attacking edge-s- and the xpercent% closest referent members, this distance is known as <code>stepAttackers</code>. The maximum size of a Sybil region created by <code>sigQty</code> members depends on the L parameter, defined as <code>L = sigQty/sigStock</code>:</p>
-<pre><code>MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)</code></pre>
-<p>The maximum size of the Web of Trust is given by the following formula:</p>
-<pre><code>WoTmax = (sigStock)*L^(stepMax-1)</code></pre>
-<p>However we know for a fact that members will never use all of their available certifications. According to Dunbar<a href="#fn10" class="footnote-ref" id="fnref10"><sup>10</sup></a>, on average, one is able to maintain relationships to around 150 people. Being conservative, we will consider that on average, each person will certify 50 accounts. We can calculate the size of the average web of trust <code>WoTavg</code> :</p>
-<pre><code>WoTavg= (50)*(sigQty/50)^(stepMax-1)</code></pre>
-<p>Our goal with the Ğ1 is to create a community of about one million members to test the consequences of a libre monetary system. Let’s see how we can tweak the pair of sigQty and stepMax- to reach this size:</p>
-<figure>
-<img src="./images/wot-moy.png" alt="Average WoT size graph as a function of sigQty and stepMax" /><figcaption>Average WoT size graph as a function of sigQty and stepMax</figcaption>
-</figure>
-<p>The maximum size of a Sybil region grows linearly with <code>sigQty</code> but exponentially with <code>stepMax</code>. Logic has it that we need to keep <code>stepMax</code> as low as possible to ensure sufficient strength to the web. The above graph shows that the lowest value of <code>stepMax</code> for a web of a million members is of 5. This is an order of magnitude and is likely to be much higher in reality, we cannot measure it for sure.</p>
-<p>For <code>sigQty</code> we can choose a value of <strong>4</strong> for a web of <strong>1.5 million members</strong> or <strong>5</strong> for <strong>half a million members</strong>. Bear in mind these are gross figures and could be significantly higher, we are talking anywhere between 1 and 10 million in reality. Calculating WOTavg gives us a pretty good idea of how the web would scale bearing in mind that it considers all members are referent members too -which isn’t the case as explained previously-. Hence the maximum size of the web is likely larger, a ballpark figure of half a million is enough for now especially knowing that the smaller <code>sigQty</code> is, the easier it is to launch a Sybil attack -it’s easier to find four accomplices than five-. For security reasons we have settled on five:</p>
-<pre><code>stepMax = 5
-sigQty = 5
-sigStock \&gt;= 50</code></pre>
-<p>The maximum size of a Sybil region therefore is:</p>
-<pre><code>(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))</code></pre>
-<p>with sigStock = 50 we have a Sybil region of:</p>
-<pre><code>45*(1-10^(5-stepAttackers))/(-9)</code></pre>
-<p>A good practice for protecting the web is to maximise <code>stepAttackers</code>. That’s why we decided that referent members in the genesis block had to be at least four steps away from each other.</p>
-<p>Another way to keep a Sybil attack at bay, were it slow enough for members to notice it, would be for referent members to ‘stretch’ the web intentionally to limit the growth of the region by ensuring that the attackers’ legitimate certifications received in the first place aren’t renewed. But what if bot accounts were created and certified each other super fast and following all rules, how would we counter that? By introducing a minimum length of time between two certifications!</p>
-<h4 id="time-is-our-friend">3.8.2. Time is our friend</h4>
-<p>To help us deter a Sybil attack, we’ve decided to impose a minimum period of time between any two certifications issued from a single account. This parameter called <code>sigPeriod</code> affords us a greater chance to detect the formation of a ‘hostile’ faction.</p>
-<p>Here is a graph showing the evolution of a Sybil region with the variation of <code>sigPeriod</code>. The simulation considers that honest members and attackers both issue a certification each <code>sigPeriod</code> interval, in days:</p>
-<figure>
-<img src="./images/impact_sig_period.png" alt="size of the WoT according to sigPeriod and stepAttackers" /><figcaption>size of the WoT according to sigPeriod and stepAttackers</figcaption>
-</figure>
-<p>As we see, there is a strong link between the growth speed of the region and <code>sigPeriod</code>. As evidenced here, we need a <code>sigPeriod</code> high enough in order to ensure that the legitimate web can grow at least as fast as a Sybil region. In addition, the higher <code>sigPeriod</code> is, the more members will exercise their certification power gingerly, the action coming at a higher ‘cost’.</p>
-<p>There are numerous advantages to giving <code>sigPeriod</code> a high value and no technical barriers to it, hence our choice of five days.</p>
-<p>We could have also gone for one week for the sake of simplicity. However there is an underlying idea behind our choice which was quite simply the pace of today’s life. Certifying someone can be a lengthy process as one needs to make sure they are correctly applying the Ğ1 licence and people nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea to allow one to certify at the end of every working week -five days- instead of a whole calendar one.</p>
-<h4 id="trust-me-now-trust-me-forever-sigvalidity-msvalidity">3.8.3. Trust me now, trust me forever ? (<code>sigValidity</code>, <code>msValidity</code>)</h4>
-<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s Web of Trust:</p>
-<ul>
-<li>First of all, some members will pass and those accounts should no longer produce the Universal Dividend.</li>
-<li>Secondly it is of the utmost importance that ‘rogue’ accounts can be excluded from the web at some point.</li>
-</ul>
-<p>To achieve this, certifications have a limited lifespan. Members need to seek renewal from their peers after <code>sigValidity</code> time. On the other hand, this time can’t be too short that members would spend more time seeking renewal than they would exchanging in the currency. Furthermore, a certification with too short a lifespan would foster careless certifying behaviours. The act of certifying must have a high-enough ‘perceived’ cost to make it feel like an important act. Lastly, we also wanted this lifespan to be easy to remember. Historically speaking, we first settled on the values of <code>sigPeriod</code> and <code>sigStock</code>, meant one could issue all of their certifications in 495 days, one year was therefore not long enough. We deemed three years to be too much and that’s how we agreed on two years in the end.</p>
-<p>Thinking that a deceased member could continue producing the UD for two long years without anyone benefitting from it was also something we needed to address. We chose a value of one year for <strong>msValidity</strong>. The act of renewing every year is done through one of the clients interacting with the blockchain, through a simple click on a button. This parameter is less important than others and is mostly there to ‘prune’ the web of past or inactive members who don’t renew their membership.</p>
-<h4 id="keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">3.8.4. Keeping the pools free of information glut (<code>idtyWindow</code>, <code>sigWindow</code>, <code>msWindow</code>)</h4>
-<p>The pools need to be cleaned up on a regular basis to avoid them clogging up with information and to ensure that machines with less calculating power can still run a Duniter node.</p>
-<p>To achieve this, identities with pending membership approval and the corresponding certifications have to remain the shortest time possible in the pool while still having a chance of making it into the blockchain.</p>
-<p>For the Ğ1, our opinion was that two months would be enough for all potential certifiers to agree on a specific identity to certify. We also wanted a time period that would be easy enough to remember by all. We settled on two months, and gave this value to all three parameters <code>idtyWindow</code>, <code>sigWindow</code> and <code>msWindow</code>.</p>
-<h4 id="avoiding-single-members-from-knowing-too-many-people-sigstock">3.8.5. Avoiding single members from ‘knowing too many people’ (<code>sigStock</code>)</h4>
-<p>We considered that on average, each person will certify 50 people. However, we know for a fact that some members will use more than 50 certifications. The maximum social network of one individual is around 150 people<a href="#fn11" class="footnote-ref" id="fnref11"><sup>11</sup></a>. Being conservative, we settled on a maximum certification number <code>sigstock</code> of 100.<br />
-Since <code>sigStock</code>’s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.</p>
-<h4 id="avoiding-locking-minorities-xpercent">3.8.6. Avoiding locking minorities (<code>xpercent</code>)</h4>
-<p>It’s easy enough to become a referent member, one of the Sybil strategies could therefore be to create a region of referent members. Such a region would grow slower than otherwise but could confer a locking power to its members by using the distance rule. That’s why the distance rule cannot be calculated on 100% of the referent members. Hence the introduction of the <code>xpercent</code> parameter which defines the percentage of referent members needing to be less than five edges -steps- from each other.</p>
-<p>This percentage needs to be low enough to prevent the formation of a locking minority -referent Sybil members being too far from legitimate referent members-. On the other hand, it needs to be high enough so as to restrict the maximum size of the Sybil region through the distance rule. The <code>xpercent</code> parameter was one of the hardest to define, therefore we might decide to change its value during the Ğ1 experiment.</p>
-<p>We were inspired by the Pareto principle<a href="#fn12" class="footnote-ref" id="fnref12"><sup>12</sup></a>: if at least 20% of members give good density to the web, 80% of the referent members will be five or less steps from any other member -referent or not-. The maximum value for <code>xpercent</code> is therefore 80%, anything above that and the distance rule could be too restrictive for legitimate use cases. With security our top concern, we chose the maximum value of 80%.</p>
-<h4 id="spam-protection-with-msperiod">3.8.7. Spam protection with (<code>msPeriod</code>)</h4>
-<p>This parameter stands out a bit on its own, as it was added after the genesis block. It is there to protect the Duniter P2P infrastructure against ‘spam’ attacks. We had to think of a strategy against attacks such as high-frequency membership renewal requests -i.e: in every block, every five minutes- or worse still, hundreds of these requests per minute to flood the Duniter nodes. Without such limits, nodes are supposed to address all renewal requests, even in cases where they were last published five minutes ago! The <code>msPeriod</code> parameter was given the same value as <code>idtyWindow</code>, <code>sigWindow</code> and <code>msWindow</code>, i.e. two months.</p>
-<h2 id="proof-of-work-with-personalized-difficulty">4. Proof of Work with personal difficulty</h2>
-<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.</p>
-<p>This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each “winning” member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.</p>
-<p>Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.</p>
-<p>One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an “ecological” PoW ?</p>
-<!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
-<h3 id="why-proof-of-work">4.1. Why do we need Proof of Work ?</h3>
-<p>Duniter nodes share a database as part of a p2p environment. The proof of work (PoW) allows machines to synchronize with each other. In Duniter’s case, the blockchain is our database, and acts as a ledger keeping a trace of all transactions, status of the WoT and more. How can we let several machines add data (ie: a transaction) at the same time? In addition, how do we settle on how much time has gone by since the blockchain was last updated? Agreement on time is of the utmost importance as we want to create Universal Dividends on a regular basis, and keep track of membership status, both in human time.</p>
-<p>Proof-of-work provides a clever solution to both problems:</p>
-<ol type="1">
-<li><p>Any machine can write into the blockchain (create a new block) but is only authorised to do so if it has previously solved a mathematical equation that require a certain amount of work. The challenge has to be hard enough to prevent two machines to solve it at the same time, ensuring the unicity of a block’s creator.</p></li>
-<li><p>Solving this challenge takes a certain amount of time, which depends on the calculating power of the whole network. This provides a common ground for defining the needed time reference. A block time is set (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to get an average duration corresponding to this block time.</p></li>
-</ol>
-<h3 id="only-members-can-mine">4.2. Only members can “mine”</h3>
-<p>One of Duniter’s major differences with other PoW-based cryptocurrencies is that only members are allowed to author blocks. Each block is signed with the member’s private key, allowing the algorithm to determine a personalised difficulty.</p>
-<p>This personalised difficulty eliminates the rat-race for the most sophisticated and powerful mining equipment. Another benefit is the fact that no “supercomputer” can take control of the blockchain. Lastly, Duniter implements a rotation in forging members thanks to this personalized difficulty.</p>
-<p>This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies. Members can mine with anything from a raspberry pi to a privacy-first internet cube.</p>
-<h3 id="how-does-duniter-pow-work">4.3. How does it work ?</h3>
-<h4 id="the-hash">4.3.1. The hash (aka digest)</h4>
-<p>Example of a valid hash:</p>
-<pre><code>00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</code></pre>
-<p>As you can see this hash starts with five zeros which was very hard to achieve and took a lot of work for someone’s computer. Hence the term “proof of work”.</p>
-<h4 id="common-difficulty">4.3.2. The common difficulty</h4>
-<p>A common difficulty is needed to settle on a yardstick for our time reference. Its role is to make sure the blockchain moves forward at a steady pace - one block every <code>avgGenTime</code> seconds, <code>avgGenTime</code> being one of the 20 parameters behind the Duniter protocol-.</p>
-<p>This difficulty’s initial value can be set to any arbitrary value (<code>70</code> in Duniter <code>v1.5.x</code>) and then acts as a spring, regulating blocktime creation by increasing itself if the creation interval drops under <code>avgGenTime</code> and vice-versa.</p>
-<h5 id="how-is-difficulty-applied">4.3.2.1. How is difficulty applied ?</h5>
-<p>The numeric value of difficulty is taken from an array of possible hashes out of all possible hashes. In DUBPv13 the hash of a block is its sha256 hexadecimal hash.</p>
-<p>To understand the difficulty, we make a euclidiean division of the difficulty by 16.</p>
-<p>Here’s an example with a difficulty value of 70 :</p>
-<pre><code>70 // 16 = 4 with a remainder of 6. </code></pre>
-<p>The valid hashes are the ones starting with four zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation). The valid hashes are then written as starting with : <code>0000[0-9]</code>. This is a bit different from Bitcoin, where the difficulty is only ruled by the number of zeroes.</p>
-<h5 id="the-nonce">4.3.2.2. The Nonce</h5>
-<p>When a member is forging a new block, his computer freezes the block’s content and changes the Nonce until the hash reaches the required number of zeroes.</p>
-<p>The nonce allows us to mine a new block by finding a hash. The hash value allows us to determine the difficulty level of the proof-of-work performed. Examples of possible Nonce values:</p>
-<ul>
-<li>10100000112275</li>
-<li>10300000288743</li>
-<li>10400000008538</li>
-<li>10700000079653</li>
-<li>10300000070919</li>
-</ul>
-<p>In reality the <code>Nonce</code> value follows a pre-determined format akin to <code>XYY00000000000</code>. The Nonce’s value isn’t the number of attempts but rather a value within a set of possible ones. This is how the Nonce is built:</p>
-<ul>
-<li><p>X is a number assigned to a specific peer. Let’s assume that someone has several nodes each with the same private key, this would lead to possible collisions if this person were to mine the same block with different nodes. Each <del>block</del> <strong>node ?</strong> will therefore have its own unique X to prevent this from happening.</p></li>
-<li><p>Y is the number of cores of the processor. The Nonce starting with <code>107[…]</code> belongs to a seven cores processor, while <code>199[...]</code> could be the proof generated by a 99 cores processor.</p></li>
-</ul>
-<p>The rest of the Nonce, the part that follows after the XYY, is the numerical space for this individual node and is unique to each of the CPU’s core. This space is comprised of eleven digits (<code>00000000000</code>). For the sake of accuracy, we use the term CPU in the wider sense, it can be understood as a bi-CPU for example. We take into consideration the number of cores for the resulting PoW.</p>
-<h3 id="personalised-difficulty">4.4. Personalised difficulty</h3>
-<p>Earlier in this article, we explained that the personalised difficulty is the new and key concept that sets Duniter apart from other PoW-based cryptocurrencies.</p>
-<p>Here is how this personalised difficulty is calculated and assigned:</p>
-<p>It is determined by a combination of two different constraints with complimentary roles: the <strong>exclusion factor</strong> and the <strong>handicap</strong>.</p>
-<p>Let <code>powMin</code> be the common difficulty, <code>exFact</code> a member’s exclusion factor and <code>handicap</code> their handicap. This member’s personalised difficulty <code>diff</code> is:</p>
-<pre><code>diff = powMin*exFact + handicap</code></pre>
-<h4 id="the-exclusion-factor">4.4.1. Understanding <code>exFact</code>, the exclusion factor</h4>
-<p>Members who have never produced blocks or haven’t for quite some time are assigned an exclusion factor of <code>1</code>. Their personalised difficulty is therefore simply the sum of <code>powMin + handicap</code>.</p>
-<p>Before reading on, let’s precise the role of this exclusion factor. When a member adds a block to the chain, his <code>exFact</code> jumps up from one to a very high value, to prevent them from forging other blocks immediately after and taking control of the blockchain.</p>
-<p>The exclusion factor will then rapidly return to one. This delay is expressed as a number of blocks. It is calculated as a proportion of the number of members forging. In the Ğ1’s case, this proportion is 1/3, meaning that if there are fifteen members currently forging, the member’s exclusion factor will drop down to one after five blocks.</p>
-<h5 id="what-is-intended-by-the-number-of-members-forging">4.4.1.1. What is intended by “the number of members forging” ?</h5>
-<p>We mean the number of members trying to create the next block. In reality, there is no way to precisely know how many members are calculating at any given time, because it is impossible to view the entire network. But we need this information, whithout which assigning a personalised difficulty is impossible. To achieve this, Duniter looks back at the blockchain and assumes that there is as much members forging as those who have found at least one block in the last blocks in the current window, minus the very last one.</p>
-<h5 id="current-window">4.4.1.2. Current window</h5>
-<p>We use the concept of <strong>current window</strong>. The current window is the number of blocks we look back at to determine how many members are forging. Let’s see how it works:</p>
-<ul>
-<li><p><code>issuersFrame</code> is the size of the current window in blocks.</p></li>
-<li><p><code>issuersCount</code> the number of members who have calculated at least one block during the current window.</p></li>
-</ul>
-<p>Both <code>issuersFrame</code> and <code>issuersCount</code> are block fields. When first starting a blockchain, the very first block has an <code>issuersFrame=1</code> and an <code>issuersCount=0</code>. The genesis block is excluded as there are no members in the current window!</p>
-<p>From the second block onwards (block #1) we track the variation of <code>issuersCount</code>. The member having mined block #0 enters the current window and in block #1 we will therefore mention <code>issuersCount=1</code>.</p>
-<p><code>issuersFrame</code> then varies as follows:</p>
-<ul>
-<li>if <code>issuersCount</code> increases by N (with a maximum step of N = 1), then <code>issuersFrame</code> will increase by one unit over a period of 5N blocks.</li>
-<li>Conversely, if <code>issuersCount</code> decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then <code>issuersFrame</code> will decrease by one unit during 5Y blocks.</li>
-<li>When such events overlap, <code>issuersFrame</code> evolves as so :</li>
-</ul>
-<table>
-<thead>
-<tr class="header">
-<th>bloc</th>
-<th>event</th>
-<th>issuersFrame</th>
-</tr>
-</thead>
-<tbody>
-<tr class="odd">
-<td>T</td>
-<td>Babar writes a block and enters issuersCount</td>
-<td>160</td>
-</tr>
-<tr class="even">
-<td>T+1</td>
-<td>Celeste leaves issuersCount</td>
-<td>160 +1 = 161</td>
-</tr>
-<tr class="odd">
-<td>T+2</td>
-<td>N/a</td>
-<td>161 +1 -1 = 161</td>
-</tr>
-<tr class="even">
-<td>T+3/4/5</td>
-<td>N/a</td>
-<td>161 +1 -1 = 161</td>
-</tr>
-<tr class="odd">
-<td>T+6</td>
-<td>N/a</td>
-<td>161 -1 = 160</td>
-</tr>
-</tbody>
-</table>
-<p>The calculation can be found under rules <a href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe">BR_G05</a> and <a href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar">BR_G06</a> of the DUP protocol.</p>
-<h5 id="exfact-and-the-personalised-difficulty">4.4.1.3. exFact and the personalised difficulty</h5>
-<p>We explained that <code>exFact</code> spikes immediately after the member has found a block. It decreases then rapidly to <code>1</code> after a number of blocks equal to <code>1/3 * issuersCount</code>. Let’s see precisely how we calculate <code>exFact</code>:</p>
-<ul>
-<li><p><code>nbPreviousIssuers</code> is the value of issuersCount at the last block <code>N</code> found by the member.</p></li>
-<li><p><code>nbBlocksSince</code> is the number of blocks found by the rest of the network since block <code>N</code>.</p></li>
-<li><p><code>percentRot</code> is the number of <em>not excluded</em> peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.</p></li>
-</ul>
-<pre><code>a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]</code></pre>
-<p>The FLOOR is a simple truncate function. For <code>exFact</code> to exclude the member, we need :</p>
-<pre><code>(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) &gt;= 2</code></pre>
-<p>We can see that the member is not excluded if <code>nbBlocksSince</code> is greater than 1/3 of the calculating members. Take as an example <code>nbPreviousIssuers = 6</code> and <code>nbBlocksSince = 3</code>:</p>
-<pre><code>(0.67* 6 / )1 + 3)) = 1.005 -&gt; exFact = 1</code></pre>
-<p>However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:</p>
-<pre><code>(0.67 * 6 / (1 + 1)) = 2.01 -&gt; exFact = 2</code></pre>
-<p>Moreover if the last block was authored by the said member, then:</p>
-<pre><code>nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers</code></pre>
-<p>ExFact value increases according to the number of members calculating. Thus, if there is enough members calculating, even mining farms would be excluded. We have therefore succeeded in our intent to deter attempts to seize the blockchain and its currency.</p>
-<p>However, at any time <code>t</code>, the two-thirds of calculating members all have an exclusion factor of <code>1</code>, even though they might not all have the same computational power at hand. If the personalised difficulty only took into account the exclusion factor, then only the members with the highest computational power from the remaining third would be able to author new blocks and the other 2/3s would almost always be excluded. Lesser machines wouldn’t stand a chance…</p>
-<h4 id="the-handicap">4.4.2. The handicap</h4>
-<p>The handicap is the second parameter of the personalised difficulty. Its main role is to improve the rotation of forging peers. A higher handicap is assigned to members with higher calculating power, so lesser machines can also compute blocks. As a consequence, there is no incentive on forging with powerful computers. Security can be achieved with less computing power than with pure PoW.</p>
-<p>The aim is to handicap the half that has authored most blocks (the most powerful half) to favour the other one. So, the handicap formula will use the median number of blocks authored by peers within the current window.</p>
-<ul>
-<li><p><code>nbPersonalBlocksInFrame</code> is the number of blocks authored by a single member within the current window.</p></li>
-<li><p><code>medianOfBlocksInFrame</code> is the median number of blocks written by the calculating members during the same timeframe.</p></li>
-</ul>
-<pre><code>a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))</code></pre>
-<p>Let’s unwrap the formula:</p>
-<pre><code>(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)</code></pre>
-<p>is simply the ratio between the number of blocks authored by the peer and the median number of blocks. For example, if a peer has authored <code>9</code> blocks in the current window and the median is <code>5</code>, then the ratio will be <code>(9+1)/5 = 2</code>. The MAX function allows us to ensure that the handicap has a value at least equal to <code>1</code>.</p>
-<p>The Napierian Logarithm of this ratio prevents the handicap from becoming excluding. We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.</p>
-<p>If we wanted the handicap to be applied as soon as the median is reached, we would divide it by <code>LN(1)</code>. The problem is that we have already set a minimum value of <code>1</code> with the MAX function. If we were to divide the ratio by <code>LN(1)</code> all calculating peers would have a handicap <code>\&gt;= 1</code>. In addition, is it really fair to handicap a member who is right on the median?</p>
-<p>That’s why we went for <code>1.189</code> rather than <code>1</code>. A member has to be at least <code>18.9%</code> above the median to be assigned a handicap. 18.9% is actually 16^(1/16), the difficulty factor between two levels of the proof work (hexadecimal hash).</p>
-<p>To conclude, you have to remember that :</p>
-<ul>
-<li>The handicap is indexed on the logarithm of the ratio to the median,</li>
-<li>Handicap is only applied on members whose ratio to the median is greater than the ratio between two levels of the proof-of-work’s difficulty.</li>
-</ul>
-<h2 id="conclusion">Conclusion</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.</p>
-<p>More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.</p>
-<p>The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :</p>
-<ul>
-<li>The freedom to choose your currency system: because money should not be imposed.</li>
-<li>The freedom to access resources: because we all should have access to economic &amp; monetary resources.</li>
-<li>The freedom to estimate and produce value: because value is a purely relative to each individual.</li>
-<li>The freedom to trade with the money: because we should not be limited by the avaible money supply.</li>
-</ul>
-<p>Those 4 economic freedoms should be understood together, not exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.</p>
-<h2 id="sources">Sources :</h2>
-<ul>
-<li>Relative Theory of Money, S.Laborde, 2010: <a href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></li>
-<li>Bitcoin Whitepaper, S.Nakamoto, 2008: <a href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></li>
-<li>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : <a href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></li>
-<li>The GNU Privacy Handbook, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></li>
-<li>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. <a href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</li>
-<li>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : <a href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></li>
-<li>Duniter Blockchain Protocol, v13, draft by Elois : <a href="https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md">git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</a></li>
-<li>The Sibyl Attack, J.R.Douceur: <a href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></li>
-<li>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992</li>
-</ul>
-</article>
-</main>
-</body>
-</html>
-<section class="footnotes">
-<hr />
-<ol>
-<li id="fn1"><p>Bitcoin Whitepaper, S.Nakamoto, 2008: <a href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a><a href="#fnref1" class="footnote-back">↩</a></p></li>
-<li id="fn2"><p>Relative Theory of Money, S.Laborde, 2010: <a href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a><a href="#fnref2" class="footnote-back">↩</a></p></li>
-<li id="fn3"><p>OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a><a href="#fnref3" class="footnote-back">↩</a></p></li>
-<li id="fn4"><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. <a href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.<a href="#fnref4" class="footnote-back">↩</a></p></li>
-<li id="fn5"><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : <a href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a><a href="#fnref5" class="footnote-back">↩</a></p></li>
-<li id="fn6"><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : <a href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a><a href="#fnref6" class="footnote-back">↩</a></p></li>
-<li id="fn7"><p>Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: <a href="http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf">snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf</a><a href="#fnref7" class="footnote-back">↩</a></p></li>
-<li id="fn8"><p>Public key validation on GnuPG manual, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a><a href="#fnref8" class="footnote-back">↩</a></p></li>
-<li id="fn9"><p>The Sibyl Attack, J.R.Douceur: <a href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a><a href="#fnref9" class="footnote-back">↩</a></p></li>
-<li id="fn10"><p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992<a href="#fnref10" class="footnote-back">↩</a></p></li>
-<li id="fn11"><p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992<a href="#fnref11" class="footnote-back">↩</a></p></li>
-<li id="fn12"><p>Pareto principle : <a href="https://en.wikipedia.org/wiki/Pareto_principle">en.wikipedia.org/wiki/Pareto_principle</a><a href="#fnref12" class="footnote-back">↩</a></p></li>
-</ol>
-</section>
diff --git a/build/whitepaper_en.md b/build/whitepaper_en.md
deleted file mode 100644
index a73c873832445b1546c4eea5abb7272cdaca8674..0000000000000000000000000000000000000000
--- a/build/whitepaper_en.md
+++ /dev/null
@@ -1,1178 +0,0 @@
-Duniter: A libre currency blockchain generator.
-=======================================
-
-## Abstract {#abstract}
-
-Many currency principles involve non-equal rights to monetary creation between humans.
-We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human.
-This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution.
-Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process.
-We use a Web of Trust between living humans for identification.
-This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.
-
-
-
-## Introduction {#introduction}
-
-Duniter is a software to create and manage "libre currencies". Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :
-
-> How should a currency be created to match the principle of equality between all humans, now and between generations ?
-
-The results of this demonstration implies a monetary creation :
-
-* on a regular basis
-* for each human being
-* which amount has to be reassessed on fixed intervals according to a fixed formula.
-
-Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :
-
-$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$
-
-
-Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.
-
-The first currency created through Duniter is Ğ1, pronounced "June". It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.
-
-
-## 1. State of the art : Bitcoin case {#state-of-the-art-bitcoin-case}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter uses the crypto-currency concept introduced by Bitcoin[^BTC_whitepaper], which is
-to use cryptographic tools such as signatures to create trustless digital
-currencies. Duniter fits this definition, but it has two completely
-different principles than Bitcoin : the Web of Trust and the Universal
-Dividend . These differences are on both monetary and technical aspects.
-
-[^BTC_whitepaper]: Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-
-### 1.1. Monetary creation of Bitcoin : a space-time asymmetry {#monetary-creation-a-space-time-asymmetry}
-
-Space-time asymmetry refers to the relative access of individuals to
-newly created money[^RTM]. Concretely, most existing currencies (c. 2020) are
-both spatially and temporally asymmetrical for their users. Let\'s take
-Bitcoin as an example to understand why.
-
-[^RTM]: Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-
-#### 1.1.1. Spatial asymmetry {#spatial-asymmetry}
-
-When new Bitcoins are created, only some Bitcoin users (the miners)
-are given new Bitcoins, while everyone else get nothing. We believe
-this is the first injustice. However, some might say:
-
-> \"Miners used their electricity and time to get it!\"
-
-\... we would answer that this work should not have been rewarded by
-newly created Bitcoins. New units should be distributed to the whole
-community. Miners should be rewared another way, but not by
-money issuance. Of course, Bitcoin cannot create money through Basic
-Income since Bitcoin users are not strongly identified, and one might
-benefit from money creation multiple times if they owned several wallets.
-Duniter gets rid of this problem by identifying its users and
-creating the same amount of Basic Income to everyone.
-
-#### 1.1.2. Temporal-asymmetry {#temporal-asymmetry}
-
-Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
-which means ever fewer bitcoins will be created over time until no new BTC are
-being generated. So, once the first adopters have mined every bitcoin,
-how will future joiners get Bitcoins? Just like most of us do for Euros or
-Dollars: to get money, they will have to work for the ones who already own it.
-
-We believe this is the second injustice. Every member of a
-monetary community should be equal concerning monetary creation, and get
-the same relative amount of money over time, even if they are a late
-adopter. Duniter aims to fix this by making the Universal Dividend
-(a.k.a. UD) grow by the time according to precise rules, thus making
-members equal toward money issuance on a half-lifespan.
-
-Most currencies present one of these two asymmetries, including metal currencies
-and mutual credit, as exposed in the RTM.
-
-#### 1.1.3. A solution {#a-solution}
-
-Bitcoin has taught us that it is possible to create a currency system
-allowing one to both create digital money and to exchange it without a
-central authority. What we need to change is the way money is issued
-so we finally have a symmetrical system. We need **Bitcoin + Universal
-Dividend**. But Universal Dividend implies that the community consists
-of only identified people. This is where the Web of Trust (WoT) comes
-into place.
-
-This concept, introduced by cryptography with the OpenPGP format[^OpenPGP],
-allows us to identify people in a decentralized manner. It works as
-follows: each person creates a personal identity that is linked to its
-cyptographic certificate. The identity must be confirmed by others
-members who use their own cryptographic key. It is that simple: people
-choose who is part of the community and who is not, not a central
-authority.
-
-[^OpenPGP]: OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-However, Duniter will not use OpenPGP for its cryptographic features:
-Elliptic Curves[^Elliptic] will be used instead for the conciseness of its
-generated keys and its pratical advantages. Duniter has its own Web 
-of Trust principles, that will be exposed later.
-
-[^Elliptic]: High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-
-### 1.2. Proof-of-Work mining : a power race {#proof-of-work-mining-a-power-race}
-
-In Bitcoin Model, the calculation and incentive principles cause a power race :
-new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers.
-This leads to a power race an places the control over the currency in the hands of the richest hardware owners.
-We want to make Duniter blockchain validation much less energy and hardware consuming while 
-keeping a strong level of security. This will be further explained later. A consequence of 
-this choice is the participation of low-end hardware in the Duniter network,
-leading to a better decentralization of blockchain validation.
-
-#### 1.2.1 What about Proof of Stake ? {#what-about-proof-of-stake}
-
-Proof of stake consensus algorythm was first introduced in 2012[^PPCoin]. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a "stake" they would lose in case of cheat.
-
-[^PPCoin]: PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-
-At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle.
-Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead 
-to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.
-
-## 2. Duniters Blockchain {#duniters-blockchain}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-
-Duniters Blockchain follows the basic principles of Bitcoins. 
-This is essential for synchronization between peers, as to prevent double-spend attacks. 
-However, Duniters Blockchain will store different informations than Bitcoins. 
-
-The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:
-
-* a former transaction (as in Bitcoin)
-* a Universal Dividend (specific to Duniter).
-
-Duniters Web of Trust is also written in the Blockchain. The identity of each
-member gets registered much like transactions are, with a strong link to the
-time reference. Thus, the Blockchain is a representation of a space-time frame
-of reference, where "space" are members of the WoT and "time" the basic blockchain
-units : the blocks. On each point of time, one can determine which account is
-legitimate to create the UD, only with a blockchain analysis.
-
-
-### 2.1. Spam countermeasures {#spam-countermeasures}
-
-
-An issue of most cryptocurrency projects is to prevent the common ledger from
-growing too much. This would require nodes to have a lot of storage and computing
-power to be usable. In particular, we don't want an attacker to be able to make the
-Blockchain grow too fast. Most projects implement transaction fees as a way to prevent
-this, making the attacker lose money. We don't want to introduce this mean since a
-currency with automatic fees on transactions is no more neutral. Several
-countermeasuers against such spam attacks are implemented.
-
-<!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
-
-#### 2.1.1. Minimum output amount {#minimum-output-amount}
-
-<!-- This has to be implemented in DUBPv13. -->
-
-Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.
-
-#### 2.1.2. Limited block size and chainability {#limited-block-size-and-chainability}
-
-The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.
-
-With the same goal to prevent too many transactions to get registered, while transactions can be "chained" (refer to another transaction in the same block), the chainability of transactions is limited to 5.
-
-
-### 2.2. Scaling {#scaling}
-
-Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :
-
-* Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don't want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.
-* Duniter's aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.
-
-However, Duniter has assets that will help if the number of users and transactions grow.
-
-#### 2.2.1 Dynamic block size {#dynamic-block-size}
-
-While Bitcoin has a fixed block size, Duniters blocks size can evolve. 
-On low use of the blockchain, the maximal block size is 500 bytes. 
-On high use of the blockchain, the maximal block size would be 110% of the
-average size of the current window blocks(see "personalised difficulty" part for more information).
-This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :
-
-```
-block_size < max(500 ; CEIL(1.10 * (average block size))
-```
-
-#### 2.2.2. Lightning Networks {#lightning-networks}
-
-The Lightning Networks[^Lightning] allow almost instant and off-chain transactions.
-They were first implemented on Lightcoin, and are now on Bitcoin.
-One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain.
-The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks.
-While not available yet, this payment channel might get implemented when needed.
-
-[^Lightning]: The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-
-#### 2.2.3. Unit base {#unit-base}
-
-As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the `unitbase` is updated each time the UD value reaches 100.00 : it goes from `99.99*10^(unitbase)` to `10.00*10^(unitbase+1)`. All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.
-
-With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.
-
-## 3. Duniter Web of Trust
-
-
-### 3.1. Basic Principles {#duniter-wot-basic-principles}
-
-In order to identify "members" accounts - which create monetary units -
-and other accounts, Duniter uses a Web of Trust. This can be summarized
-into few principles:
-
--   Each account becomes a member if it received a minimal number of
-    certifications - 5 for Ğ1 currency.
--   Only members accounts can send certifications. Certifications have a
-    limited lifespan.
--   A certification indicates that the sender accepts the receiver as a
-    legitimate identity.
-
-The aim of the WoT is to identify a blockchain account to a living
-human. According to Lauterbach et.al[^Couchsurf], the strengh of a relationship should be considered when building a vouch system.
-For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are.
-A certification represents a strong human relationship : one may certify a close relative, not an acquaintance.
-Each member has to accept this licence before being included in the WoT.
-Thus, if a member is part of an attack on the currency, they can be found by mutual relatives.
-Additional security rules occur to prevent cheat and attacks on a large scale.
-
-[^Couchsurf]: Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: [snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf](http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf)
-
-Note that non-members accounts can use the currency, but cannot create
-money. Non-members accounts can be used by individuals as secondary wallets, or by
-institutions.
-
-We were inspired by the OpenPGP Trust system[^OpenPGP_Trust]. However, the OpenPGP
-trust principles aim at defining trust from a particular point of view while Duniter needs to
-identify humans for the whole community. To achieve this goal, while OpenPGP allows each
-user to tweak its trust parameters individually, Duniter sets rules in the "genesis" block for the whole community. 
-
-[^OpenPGP_Trust]: Public key validation on GnuPG manual, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-### 3.2. Why do we need a Web of Trust ? {#why-do-we-need-a-web-of-trust}
-
-There are two reasons we need it :
-
-1.  To make sure that only one Universal Dividend is produced per member
-    at each specified creation interval. In the Ğ1's case this interval
-    is set as daily `86 400` seconds, it is the *monetary parameter*
-    known as `dt`.
-2.  To identify the nodes hashing the blocks and assign each a
-    personalised difficulty. This custom difficulty proof of work is
-    there to avoid the blockchain's validation mechanism becoming too
-    centralised as is the case with many \'non-libre' cryptocurrencies.
-
-> **Monetary parameter** : Each currency that use Duniter has its own blockchain whose behaviour is
-> dictated by a set of 'parameters' defined in block zero - the so-called
-> genesis block - that can be tweaked to achieve the desired results. At
-> the time of writing the Whitepaper, the Duniter Blockchain Protocol
-> (DUBP) has a total of 21 parameters of which 10 are for the WoT alone.
-> We'll focus on these 10.
-> 
-> Suffice to say that in the Ğ1's case, the DU is created every 24 hours -
-> 86 400 seconds. This interval is set through the time derivative `dt`
-> parameter and can have a different value in other implementations of the
-> protocol.
-
-We want to make sure that each member can only have one account. As we
-all know, achieving zero-risk isn't possible[^Sybil_Attack].
-Our goal is therefore not to create a WoT within which fraud
-would be absolutely impossible, but instead to discourage it. Here is a
-rewording of our goal in 4 smaller ones :
-
-1.  Make the certification process lengthy enough that all members
-    exercise due diligence and are wary of risks.
-2.  Make fraudulent acts as hard as we can to the extent that they
-    become pointless.
-3.  Ensure that any Sybil attacks have a negligible impact on the
-    currency by ensuring that illegitimate double Universal Dividends
-    have no significant bearing on the legitimate monetary mass
-4.  Slow the growth of 'Sybil regions' to give enough time for the
-    community to react and isolate the threat.
-    
-[^Sybil_Attack]: The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-
-> **Sybil attack** : A Sybil attack is an attack perpetrated on a
-> reputation system through the creation of fake identities. A Web of
-> Trust is a specific instance of a Reputation System. 
-
-There are plenty of Sybil attack scenarios we can think of and just as
-many reasons why their perpetrators would want to carry them out. Our
-objective is that the configuration of the WoT protects both users and
-its IT backbone infrastructure against these attacks.
-
-This means that micro-attacks performed by small groups of individuals
-looking for personal enrichment are of no interest to us. The web's role
-isn't to deter these attacks, this being instead the role of the
-community. Just like the town you live in is responsible for providing
-your tap water and electricity but isn't responsible for any burglaries,
-etc. Much in the same way, Duniter's WoT guarantees us all a functional
-currency, but do not detect small fraud.
-
-### 3.3. The importance of having our own certification system {#own-certification-system}
-
-Centralized identification systems can achieve the goal we want. State
-Identification is an example. However, this has many drawbacks :
-
-* The authority may have arbitrary criteria for identification, for example
-preventing people without an official state-provided identity or
-homeless people to be included in the WoT.
-* Payment might be required
-to get identified, thus making the monetary creation not "free".
-* The authority is a point of failure for any attacker.
-
-It is of the utmost importance that we remain free from any state or
-corporation. The WoT is an answer to this criterium. To this day we
-depend only on the Internet and yet, were it to fail, there are already
-alternatives being tested around the world for a decentralised communication network.
-
-### 3.4. A few foundational concepts on graph theory : a bit of vocabulary {#graph-theory-vocabulary}
-
--   **Graph**: set of points -called 'vertices'- joined by edges -called
-    paths/walks-.
-
--   **Simple graph**: a graph with no loops and with no multiple edges.
-    That is, each edge connects two distinct endpoints and no two edges
-    have the same endpoints. A simple edge is an edge that is not part
-    of a multiple adjacency -of edges-. In many cases, graphs are
-    assumed to be simple unless specified otherwise.
-    
--   **Directed graph**: a graph in which the edges have a distinguished
-    direction, from one vertex to another. A directed edge can also be
-    called a path or walk.
-    Arrow A --\> B is therefore different from arrow B --\> A.
-
--   **Endpoints**: the edge with vertex A --\> B has A and B as
-    endpoints, respectively as start and end of the path/walk.
-
--   **Isolated vertex**: a vertex whose degree is zero, that is, a
-    vertex with no incident edges.
-
--   **Degree of a vertex**: number of its incident edges -in and out-.
-
--   **Out-degree of vertex A**: number of outbound edges / tail ends
-    from A.
-
--   **In-degree of vertex A**: number of incoming edges / head ends
-    to A.
-
-![degrees of a vertex diagram](./images/degres.jpg)
-
--   **Path**: -aka "walk"- path to follow to get from vertex A to
-    vertex B.
-
-### 3.5. Definition of the Duniter Web of Trust {#definition-of-the-duniter-web-of-trust}
-
-The Duniter WoTs -one per currency- are simple directed graphs without
-isolated vertices. The vertices are the members and the edges are the
-certifications given and received.
-
-*Directed* means that the responsibility of issuing a certification is
-unique and personal to the certifier. The trust they place in the
-receiver cannot be imposed in the other direction although in most
-circumstances both parties equally trust each other.
-
-In addition, all vertices are either currently active members or
-past-members. Past-member vertices are in a specific 'deactivated state'
-and can no longer issue or receive certifications although the ones
-already issued or received to/from other members are still considered
-'pending' to avoid a collapse of the WoT. If these old members don't
-come back into the WoT, their pending certifications will eventually
-expire and they will switch from 'deactivated' to 'isolated' vertices.
-
-To wrap up with old members, after a certain period of time - set in the
-currency's parameters - their deactivated vertex is removed from the web
-and the associated identity is 'revoked'. The person who owned the
-account can no longer use this identity but is free to join the web with
-another one.
-
-> **Identity** : An identity is a set of three pieces of information: a public key, a
-> name and a blockstamp. A blockstamp points to a specific block in the
-> chain. Its main use is to freeze the point in time at which an identity
-> was created and to link this identity to a specific chain and a currency
-> - each currency having its own blockchain.
-> 
-> An identity can be in any one of 5 different status: pending, member,
-> old member, revoked or excluded.
-
-Let's take a simple example:
-
-```
-    A -> B -> C
-         |
-         \--> D
-```
-
-If, for whatever reason, A were to lose its member status, the web would
-crumble and all other members would be excluded as a consequence. To
-avoid this, the certification from A --\> B will remain valid until its
-expiry date, leaving enough time for B to receive certifications from C
-or D.
-
-Because our WoT doesn't have any isolated vertices, each new identity
-created needs to be pulled into the web with all of the certifications
-it has received, all in the same block. This calls for a temporary
-'buffer' storage space for **pending** identities and the certifications
-they have received. This storage space is called 'the pool' of Duniter
-nodes, which we could also have called the 'sandbox' as that's the name
-used in Duniter's code. Duniter nodes inclued other 'pools' for other
-documents and metadata not mentioned here.
-
-### 3.6. Exploring the rules behind a Duniter Web of Trust {#exploring-the-rules-behind-duniter-wot}
-
-The Duniter WoTs - one per currency - works with a set of eight
-fundamental rules enforced through eleven different parameters. Ten of
-these parameters are set within the genesis block, the eleventh one -
-`msPeriod`- having being hard-coded in the Ğ1's code subsequently.
-
-#### 3.6.1. Distance rule and referent members (`stepMax` and `xPercent`) {#distance-rule-and-referent-members-stepmax-and-xpercent}
-
-These two parameters are closely linked and together define the
-'distance rule'. The 'distance rule' can only be described after
-defining what a 'referent member' is:
-
-> **Referent member**: member A is said to be 'referent' if and only if
-> the total of their degrees are greater than or equal to
-> `CEIL-N^-1/stepMax` where N is the total number of members. As the
-> size of the web will grow this number will grow too, meaning it will
-> take more certification issuances to become a referent member. The
-> number of certifications needed to become a member shouldn't change.
-
-Let's now define the distance rule:
-
-> **Distance rule**: member A is said to observe this rule if and only
-> if for a subset xPercent % of referent members R there exists a path
-> of length less than or equal to `stepMax` between R and A.
-
-Referent members only exist so that the distance rule can take effect,
-they have no special privileges over non-referent members. In a perfect
-web, that is one in which each member has certified all members they
-legitimately can, all members would be referent members. However,
-because the web progressively grows in size and because members die and
-are replaced by new ones, there are always members at any given time `t`
-who haven't yet certified all members they legitimately could. These
-members would hinder the evolution of the web if they were taken into
-account in the calculation of the distance rule and the web would
-effectively stop growing.
-
-Because verifying the application of the distance rule is
-calculation-greedy, it is only performed when a new identity gets
-confirmed into the web or an existing member gets renewed. There is an
-exception to this rule: the distance rule is not observed in the genesis
-block -when the web is first implemented.
-
-#### 3.6.2. Rule of the minimum number of certifications needed (`sigQty`) {#rule-of-the-minimum-number-of-certifications-needed-sigqty}
-
-This is the simplest rule, it essentially says that each member must at
-any given time -meaning in any single block- have received at least
-`sigQty` active certifications. If, for whatever reason, member A were
-to have less than `sigQty` active certifications in a given block, they
-would cease to be a member and be required to publish a request for
-identity renewal.
-
-#### 3.6.3. The membership renewal rule (`msValidity`, `msPeriod` and `msWindow`) {#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow}
-
-Bear in mind that a membership doesn't last a lifetime but instead has a
-lifespan set to `msValidity` seconds.
-
-Every single member -or old member who hasn't revoked his identity or
-been excluded- can request a membership renewal so long as the last
-request was made more than `msPeriod` seconds ago. If a member has never
-requested a renewal, the date of last renewal is equal to the timestamp
-at which his membership was first created. A new request will be stored
-in the 'pool' for a maximum of `msWindow` seconds before it's included
-in the blockchain. Once again, this can only happen once/if the member
-meets both the `siqQty` rule and the distance rule -if these criterion
-are already matched it's just a case of waiting for a new block to be
-mined-.
-
-If a member hasn't requested a renewal for longer than `msValidity`
-seconds, they automatically cease to be a member. From this moment on,
-the ex-member has another `msValidity` window to renew their membership.
-When this period of `2 × msValidity` runs out, the membership will
-expire and this identity will never be available for use again in the
-web. If the person so desires, they will have to publish new identity
-and membership documents and find enough certifiers, as any newcomer.
-
-#### 3.6.4. Rule of certification lifespan (`sigValidity`) {#rule-of-certification-lifespan-sigvalidity}
-
-All certifications included in the blockchain expire **sigValidity**
-seconds after they were **issued**.
-
-> /!\\ The issuance and the inclusion of a certification in the
-> blockchain occur at different times. When member A issues a
-> certification at time t1, it gets stored in the pool starting at t1
-> and only finds its way into the blockchain at t2 when all of the web's
-> rules are observed. Several weeks can thus go by between t1 and t2!!!
-
-#### 3.6.5. Rule of limited supply of active certifications (`sigStock`) {#rule-of-limited-supply-of-active-certifications-sigstock}
-
-By 'active certifications' we refer to certifications included in the
-blockchain and that haven't yet expired.
-
-The total of active certifications issued by any member at any single
-time must be less than or equal to `sigStock`. When this threshold is
-reached the member will have to wait for one of his active
-certifications to expire before he/she can issue a new one.
-
-#### 3.6.6. Rule of the time period between two certification issuances. (`sigPeriod`) {#rule-of-the-time-period-between-two-certification-issuances-sigperiod}
-
-As soon as a certification issued by member A gets included in the
-blockchain, they will be unable to issue a new one before another
-`sigPeriod` seconds.
-
-#### 3.6.7. Expiry of a certification issuance (`sigWindow`) {#expiry-of-a-certification-issuance-sigwindow}
-
-When a certification is issued by member A, it will be stored in the
-'pool' for a maximum of `sigWindow` seconds. If the certification hasn't
-been included in the blockchain by then, it will be cancelled and the
-member's `sigStock` will be repleted by one.
-
-#### 3.6.8. Lifespan of a 'pending' identity (`idtyWindow`) {#lifespan-of-a-pending-identity-idtywindow}
-
-When a new identity is created, it is stored in the 'pool' for a maximum
-of `idtyWindow` seconds. If the person hasn't achieved member status by
-then, the certification will simply be cancelled.
-
-### 3.7. Details on some of the WoT's peculiarities at the genesis block {#details-on-some-of-the-wots-peculiarities-at-the-genesis-block}
-
-The aforementioned rules can only be enforced with an existing web. They
-cannot be observed when first creating the web, that is when defining
-the genesis block.
-
-Only rules 2 and 5 can be observed at the genesis block.
-
-The genesis block has to be manually created by the founding members. In
-practice this means that there must be a choice on which identities to
-include on the premise that all of them observe rules 2 and 5. In
-addition, the genesis block must be signed with the private key of one
-of these identities.
-
-As soon as the genesis block has been created, the other identities can
-start mining the blockchain and the member who created block \#0
-effectively looses the decision power he had at creation.
-
-### 3.8. Why these rules and application cases in the Ğ1 {#why-these-rules-and-application-cases-in-the-g1}
-
-#### 3.8.1. Distance and maximum size {#distance-and-maximum-size}
-
-The distance rule is there to curb the maximum size of a Sybil region as
-well as that of the monetary community as a whole. The `xpercent`
-parameter prevents the creation of a 'faction' that could take hold of
-the blockchain.
-
-![Sybil region](./images/wot-sybil.jpg)
-
-The Sybil regions are isolated from the rest of the graph in the sense
-that they can only receive certifications from other ill-intentioned
-Sybil members. As a consequence, the shortest edge/path between a
-legitimate member and a Sybil one has to have the attack's author as an
-endpoint. The maximum depth the Sybil region can attain is therefore
-contingent on the distance between the attacking edge-s- and the
-xpercent% closest referent members, this distance is known as
-`stepAttackers`. The maximum size of a Sybil region created by `sigQty`
-members depends on the L parameter, defined as `L = sigQty/sigStock`:
-
-```
-MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)
-```
-
-The maximum size of the Web of Trust is given by the following formula:
-
-```
-WoTmax = (sigStock)*L^(stepMax-1)
-```
-
-However we know for a fact that members will never use all of their
-available certifications. 
-According to Dunbar[^Dunbar], on average, one is able to maintain relationships to around 150 people.
-Being conservative, we will consider that on average, each person will certify 50 accounts. 
-We can calculate the size of the average web of trust `WoTavg` :
-
-```
-WoTavg= (50)*(sigQty/50)^(stepMax-1)
-```
-
-[^Dunbar]: Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
-
-
-Our goal with the Ğ1 is to create a community of about one million
-members to test the consequences of a libre monetary system. Let's see
-how we can tweak the pair of sigQty and stepMax- to reach this size:
-
-![Average WoT size graph as a function of sigQty and stepMax](./images/wot-moy.png)
-
-The maximum size of a Sybil region grows linearly with `sigQty` but
-exponentially with `stepMax`. Logic has it that we need to keep
-`stepMax` as low as possible to ensure sufficient strength to the web.
-The above graph shows that the lowest value of `stepMax` for a web of a
-million members is of 5. This is an order of magnitude and is likely to
-be much higher in reality, we cannot measure it for sure.
-
-For `sigQty` we can choose a value of **4** for a web of **1.5 million
-members** or **5** for **half a million members**. Bear in mind these
-are gross figures and could be significantly higher, we are talking
-anywhere between 1 and 10 million in reality. Calculating WOTavg gives
-us a pretty good idea of how the web would scale bearing in mind that it
-considers all members are referent members too -which isn't the case as
-explained previously-. Hence the maximum size of the web is likely
-larger, a ballpark figure of half a million is enough for now especially
-knowing that the smaller `sigQty` is, the easier it is to launch a Sybil
-attack -it's easier to find four accomplices than five-. For security
-reasons we have settled on five:
-
-```
-stepMax = 5
-sigQty = 5
-sigStock \>= 50
-```
-
-The maximum size of a Sybil region therefore is:
-
-```
-(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))
-```
-
-with sigStock = 50 we have a Sybil region of:
-
-```
-45*(1-10^(5-stepAttackers))/(-9)
-```
-
-A good practice for protecting the web is to maximise `stepAttackers`.
-That's why we decided that referent members in the genesis block had to
-be at least four steps away from each other.
-
-Another way to keep a Sybil attack at bay, were it slow enough for
-members to notice it, would be for referent members to 'stretch' the web
-intentionally to limit the growth of the region by ensuring that the
-attackers' legitimate certifications received in the first place aren't
-renewed. But what if bot accounts were created and certified each other
-super fast and following all rules, how would we counter that? By
-introducing a minimum length of time between two certifications!
-
-#### 3.8.2. Time is our friend {#time-is-our-friend}
-
-To help us deter a Sybil attack, we've decided to impose a minimum
-period of time between any two certifications issued from a single
-account. This parameter called `sigPeriod` affords us a greater chance
-to detect the formation of a 'hostile' faction.
-
-Here is a graph showing the evolution of a Sybil region with the
-variation of `sigPeriod`. The simulation considers that honest members 
-and attackers both issue a certification each `sigPeriod` interval, in days:
-
-![size of the WoT according to sigPeriod and stepAttackers](./images/impact_sig_period.png)
-
-As we see, there is a strong link between the
-growth speed of the region and `sigPeriod`. As evidenced here, we need a
-`sigPeriod` high enough in order to ensure that the legitimate web can
-grow at least as fast as a Sybil region. In addition, the higher
-`sigPeriod` is, the more members will exercise their certification power
-gingerly, the action coming at a higher 'cost'.
-
-There are numerous advantages to giving `sigPeriod` a high value and no
-technical barriers to it, hence our choice of five days.
-
-We could have also gone for one week for the sake of simplicity. However
-there is an underlying idea behind our choice which was quite simply the
-pace of today's life. Certifying someone can be a lengthy process as one
-needs to make sure they are correctly applying the Ğ1 licence and people
-nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
-to allow one to certify at the end of every working week -five days-
-instead of a whole calendar one.
-
-#### 3.8.3. Trust me now, trust me forever ? (`sigValidity`, `msValidity`) {#trust-me-now-trust-me-forever-sigvalidity-msvalidity}
-
-There would be two main drawbacks to a lifetime membership in the Ğ1's
-Web of Trust:
-
--   First of all, some members will pass and those accounts should no
-    longer produce the Universal Dividend.
--   Secondly it is of the utmost importance that 'rogue' accounts can be
-    excluded from the web at some point.
-
-To achieve this, certifications have a limited lifespan. Members need to
-seek renewal from their peers after `sigValidity` time. On the other
-hand, this time can't be too short that members would spend more time
-seeking renewal than they would exchanging in the currency. Furthermore,
-a certification with too short a lifespan would foster careless
-certifying behaviours. The act of certifying must have a high-enough
-'perceived' cost to make it feel like an important act. Lastly, we also
-wanted this lifespan to be easy to remember. Historically speaking, we
-first settled on the values of `sigPeriod` and `sigStock`, meant one
-could issue all of their certifications in 495 days, one year was
-therefore not long enough. We deemed three years to be too much and
-that's how we agreed on two years in the end.
-
-Thinking that a deceased member could continue producing the UD for two
-long years without anyone benefitting from it was also something we
-needed to address. We chose a value of one year for **msValidity**. The
-act of renewing every year is done through one of the clients
-interacting with the blockchain, through a simple click on a button.
-This parameter is less important than others and is mostly there to
-'prune' the web of past or inactive members who don't renew their
-membership.
-
-#### 3.8.4. Keeping the pools free of information glut (`idtyWindow`, `sigWindow`, `msWindow`) {#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow}
-
-The pools need to be cleaned up on a regular basis to avoid them
-clogging up with information and to ensure that machines with less
-calculating power can still run a Duniter node.
-
-To achieve this, identities with pending membership approval and the
-corresponding certifications have to remain the shortest time possible
-in the pool while still having a chance of making it into the
-blockchain.
-
-For the Ğ1, our opinion was that two months would be enough for all
-potential certifiers to agree on a specific identity to certify. We also
-wanted a time period that would be easy enough to remember by all. We
-settled on two months, and gave this value to all three parameters
-`idtyWindow`, `sigWindow` and `msWindow`.
-
-#### 3.8.5. Avoiding single members from 'knowing too many people' (`sigStock`) {#avoiding-single-members-from-knowing-too-many-people-sigstock}
-
-We considered that on average, each person will certify 50 people. 
-However, we know for a fact that some members will use more than 50 certifications.
-The maximum social network of one individual is around 150 people[^Dunbar].
-Being conservative, we settled on a maximum certification number `sigstock` of 100.  
-Since `sigStock`'s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.
-
-#### 3.8.6. Avoiding locking minorities (`xpercent`) {#avoiding-locking-minorities-xpercent}
-
-It's easy enough to become a referent member, one of the Sybil
-strategies could therefore be to create a region of referent members.
-Such a region would grow slower than otherwise but could confer a
-locking power to its members by using the distance rule. That's why the
-distance rule cannot be calculated on 100% of the referent members.
-Hence the introduction of the `xpercent` parameter which defines the
-percentage of referent members needing to be less than five edges
--steps- from each other.
-
-This percentage needs to be low enough to prevent the formation of a
-locking minority -referent Sybil members being too far from legitimate
-referent members-. On the other hand, it needs to be high enough so as
-to restrict the maximum size of the Sybil region through the distance
-rule. The `xpercent` parameter was one of the hardest to define,
-therefore we might decide to change its value during the Ğ1 experiment.
-
-We were inspired by the Pareto
-principle[^Pareto]: if at least
-20% of members give good density to the web, 80% of the referent members
-will be five or less steps from any other member -referent or not-. The
-maximum value for `xpercent` is therefore 80%, anything above that and
-the distance rule could be too restrictive for legitimate use cases.
-With security our top concern, we chose the maximum value of 80%.
-
-[^Pareto]: Pareto principle : [en.wikipedia.org/wiki/Pareto_principle](https://en.wikipedia.org/wiki/Pareto_principle)
-
-#### 3.8.7. Spam protection with (`msPeriod`) {#spam-protection-with-msperiod}
-
-This parameter stands out a bit on its own, as it was added after the
-genesis block. It is there to protect the Duniter P2P infrastructure
-against 'spam' attacks. We had to think of a strategy against attacks
-such as high-frequency membership renewal requests -i.e: in every block,
-every five minutes- or worse still, hundreds of these requests per
-minute to flood the Duniter nodes. Without such limits, nodes are
-supposed to address all renewal requests, even in cases where they were
-last published five minutes ago! The `msPeriod` parameter was given the
-same value as `idtyWindow`, `sigWindow` and `msWindow`, i.e. two months.
-
-
-## 4. Proof of Work with personal difficulty {#proof-of-work-with-personalized-difficulty}
-
-As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.
-
-This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each "winning" member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.
-
-Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.
-
-One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an "ecological" PoW ?
-
-
-
-<!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
-
-### 4.1. Why do we need Proof of Work ? {#why-proof-of-work}
-
-Duniter nodes share a database as part of a p2p environment. The proof of
-work (PoW) allows machines to synchronize with each other. In Duniter's case, the blockchain is
-our database, and acts as a ledger keeping
-a trace of all transactions, status of the WoT and more. 
-How can we let several machines add data (ie: a transaction) at
-the same time? In addition, how do we settle on how much time has gone
-by since the blockchain was last updated? Agreement on time is of the utmost importance
-as we want to create Universal Dividends on a regular basis, and keep track
-of membership status, both in human time.
-
-
-Proof-of-work provides a clever solution to both problems:
-
-1. Any machine can write into the blockchain (create a new block) but is only
-authorised to do so if it has previously solved a mathematical equation
-that require a certain amount of work. The challenge has to
-be hard enough to prevent two machines to solve it at the same time,
-ensuring the unicity of a block's creator.
-
-2. Solving this challenge
-takes a certain amount of time, which depends on the calculating power
-of the whole network. This provides a common ground for defining
-the needed time reference. A block time is set (ie: 1 block = 5 min) and 
-Duniter adapts the challenge difficulty to get an average duration 
-corresponding to this block time.
-
-### 4.2. Only members can "mine" {#only-members-can-mine}
-
-One of Duniter's major differences with other PoW-based cryptocurrencies
-is that only members are allowed to author blocks. Each block is signed
-with the member's private key, allowing the algorithm to determine a
-personalised difficulty.
-
-This personalised difficulty eliminates the rat-race for the most
-sophisticated and powerful mining equipment. Another benefit is the fact
-that no "supercomputer" can take control of the blockchain. Lastly, Duniter 
-implements a rotation in forging members thanks to this personalized difficulty.
-
-This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies.
-Members can mine with anything from a raspberry pi to a privacy-first
-internet cube.
-
-### 4.3. How does it work ? {#how-does-duniter-pow-work}
-
-#### 4.3.1. The hash (aka digest) {#the-hash}
-
-Example of a valid hash:
-
-```
-00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653
-```
-
-As you can see this hash starts with five zeros which was very hard to
-achieve and took a lot of work for someone's computer. Hence the term
-"proof of work".
-
-#### 4.3.2. The common difficulty {#common-difficulty}
-
-A common difficulty is needed to settle on a yardstick for our time reference.
-Its role is to make sure the blockchain moves forward
-at a steady pace - one block every `avgGenTime` seconds, `avgGenTime`
-being one of the 20 parameters behind the Duniter protocol-. 
-
-This difficulty's initial value can be set to any arbitrary value (`70` in
-Duniter `v1.5.x`) and then acts as a spring, regulating blocktime
-creation by increasing itself if the creation interval drops under
-`avgGenTime` and vice-versa.
-
-##### 4.3.2.1. How is difficulty applied ? {#how-is-difficulty-applied}
-
-The numeric value of difficulty is taken from an array of possible
-hashes out of all possible hashes. In DUBPv13 the hash
-of a block is its sha256 hexadecimal hash.
-
-To understand the difficulty, we make a euclidiean division of the
-difficulty by 16.
-
-Here's an example with a difficulty value of 70 : 
-
-```
-70 // 16 = 4 with a remainder of 6. 
-```
-
-The valid hashes are the ones starting with four
-zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation).
-The valid hashes are then written as starting with : `0000[0-9]`. 
-This is a bit different from Bitcoin, 
-where the difficulty is only ruled by the number of zeroes.
-
-##### 4.3.2.2. The Nonce {#the-nonce}
-
-When a member is forging a new
-block, his computer freezes the block's content and changes the Nonce
-until the hash reaches the required number of zeroes. 
-
-The nonce allows us to mine a new block by finding a hash. The
-hash value allows us to determine the difficulty level of the
-proof-of-work performed. Examples of possible Nonce values:
-
--   10100000112275
--   10300000288743
--   10400000008538
--   10700000079653
--   10300000070919
-
-In reality the `Nonce` value follows a pre-determined format akin to
-`XYY00000000000`. The Nonce's value isn't the number of attempts but
-rather a value within a set of possible ones. This is how the Nonce is
-built:
-
--   X is a number assigned to a specific peer. Let's assume that someone
-    has several nodes each with the same private key, this would lead to
-    possible collisions if this person were to mine the same block with
-    different nodes. Each ~~block~~ **node ?** will therefore have its own unique X to
-    prevent this from happening.
-
--   Y is the number of cores of the processor. The Nonce starting with
-    `107[…]` belongs to a seven cores processor, while `199[...]` could
-    be the proof generated by a 99 cores processor.
-
-The rest of the Nonce, the part that follows after the XYY, is the
-numerical space for this individual node and is unique to each of the
-CPU's core. This space is comprised of eleven digits (`00000000000`).
-For the sake of accuracy, we use the term CPU in the wider sense, it can
-be understood as a bi-CPU for example. We take into consideration the
-number of cores for the resulting PoW.
-
-### 4.4. Personalised difficulty {#personalised-difficulty}
-
-Earlier in this article, we explained that the personalised difficulty
-is the new and key concept that sets Duniter apart from other
-PoW-based cryptocurrencies.
-
-Here is how this personalised difficulty is calculated and assigned:
-
-It is determined by a combination of two different constraints with
-complimentary roles: the **exclusion factor** and the **handicap**.
-
-Let `powMin` be the common difficulty, `exFact` a member's exclusion
-factor and `handicap` their handicap. This member's personalised
-difficulty `diff` is:
-
-```
-diff = powMin*exFact + handicap
-```
-
-#### 4.4.1. Understanding `exFact`, the exclusion factor {#the-exclusion-factor}
-
-Members who have never produced blocks or haven't for quite some time
-are assigned an exclusion factor of `1`. Their personalised difficulty
-is therefore simply the sum of `powMin + handicap`.
-
-Before reading on, let's precise the role of this exclusion factor.
-When a member adds a block to the chain, his `exFact` jumps up from one to
-a very high value, to prevent them from forging other blocks
-immediately after and taking control of the blockchain.
-
-The exclusion factor will then rapidly return to one. 
-This delay is expressed as a number of blocks. It is calculated as a
-proportion of the number of members forging. In the Ğ1's case, this
-proportion is 1/3, meaning that if there are fifteen members currently
-forging, the member's exclusion factor will drop down to one after five
-blocks.
-
-##### 4.4.1.1. What is intended by "the number of members forging" ?
-
-We mean the number of members trying to create the next block. 
-In reality, there is no way to precisely know how
-many members are calculating at any given time, because it is impossible
-to view the entire network. But we need this information, whithout which 
-assigning a personalised difficulty is impossible. 
-To achieve this, Duniter looks back at the blockchain and assumes that there is as much 
-members forging as those who have found at least one block
-in the last blocks in the current window, minus the very last one.
-
-##### 4.4.1.2. Current window
-
-We use the concept of **current window**. The current window is the number of blocks we look back at to determine how many members are forging.
-Let's see how it works: 
-
-* `issuersFrame` is the size of the
-current window in blocks.
-
-* `issuersCount` the number of members who
-have calculated at least one block during the current window. 
-
-Both `issuersFrame` and `issuersCount` are block fields. When first
-starting a blockchain, the very first block has an `issuersFrame=1` and
-an `issuersCount=0`. The genesis block is excluded as there are no members in the current
-window!
-
-From the second block onwards (block \#1) we track the variation of
-`issuersCount`. The member having mined block \#0 enters the current
-window and in block \#1 we will therefore mention `issuersCount=1`.
-
-
-`issuersFrame` then varies as follows: 
-
-* if `issuersCount` increases by N (with a maximum step of N = 1), then `issuersFrame` will increase by one unit over a period of 5N blocks. 
-* Conversely, if `issuersCount` decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then `issuersFrame` will decrease by one unit during 5Y blocks. 
-* When such events overlap, `issuersFrame` evolves as so :
-
-| bloc | event | issuersFrame|
-|---|---|---|
-| T | Babar writes a block and enters issuersCount | 160 |
-| T+1 | Celeste leaves issuersCount | 160 +1 = 161 |
-| T+2 | N/a | 161 +1 -1 = 161 |
-| T+3/4/5 | N/a | 161 +1 -1 = 161 |
-| T+6 | N/a | 161 -1 = 160 |
-
-
-The calculation can be found under rules
-[BR\_G05](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe)
-and
-[BR\_G06](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar)
-of the DUP protocol.
-
-##### 4.4.1.3. exFact and the personalised difficulty {#exfact-and-the-personalised-difficulty}
-
-We explained that `exFact` spikes immediately after the member has
-found a block. It decreases then rapidly to `1` after a number of 
-blocks equal to `1/3 * issuersCount`. Let's see precisely
-how we calculate `exFact`:
-
-* `nbPreviousIssuers` is the value of issuersCount at the
-last block `N` found by the member.
-
-* `nbBlocksSince` is the number of blocks
-found by the rest of the network since block `N`.
-
-* `percentRot` is the number of *not excluded* peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.
-
-```
-a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]
-```
-
-The FLOOR is a simple truncate function. For `exFact` to exclude the
-member, we need :
-
-```
-(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) >= 2
-```
-
-We can see that the member is not excluded if `nbBlocksSince` is greater than 1/3 of
-the calculating members. Take as an example `nbPreviousIssuers = 6` and `nbBlocksSince = 3`:
-
-```
-(0.67* 6 / )1 + 3)) = 1.005 -> exFact = 1
-```
-
-However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:
-
-```
-(0.67 * 6 / (1 + 1)) = 2.01 -> exFact = 2
-```
-
-Moreover if the last block was authored by the said member, then:
-```
-nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers
-```
-
-ExFact value increases according to the number of
-members calculating. Thus, if there is enough members calculating, even 
-mining farms would be excluded. We have therefore
-succeeded in our intent to deter attempts to seize the blockchain and
-its currency.
-
-
-However, at any time `t`, the two-thirds of
-calculating members all have an exclusion factor of `1`, even though
-they might not all have the same computational power at hand. If the
-personalised difficulty only took into account the exclusion factor, then
-only the members with the highest computational power from the remaining
-third would be able to author new blocks and the other 2/3s would almost
-always be excluded. Lesser machines wouldn't stand a
-chance...
-
-#### 4.4.2. The handicap {#the-handicap}
-
-The handicap is the second parameter of the personalised difficulty. Its
-main role is to improve the rotation of forging peers. 
-A higher handicap is assigned to members with higher calculating
-power, so lesser machines can also compute blocks. As a consequence, 
-there is no incentive on forging with powerful computers. 
-Security can be achieved with less computing power than with pure PoW.
-
-The aim is to handicap the half that has
-authored most blocks (the most powerful half) to favour the other one.
-So, the handicap formula will use the median number of blocks authored by peers within the current window.
-
-* `nbPersonalBlocksInFrame` is the number of blocks authored by a
-single member within the current window.
-
-* `medianOfBlocksInFrame` is the
-median number of blocks written by the calculating members during the
-same timeframe.
-
-```
-a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))
-```
-
-Let's unwrap the formula:
-
-```
-(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)
-``` 
-
-is simply the
-ratio between the number of blocks authored by the peer and the median
-number of blocks. For example, if a peer has authored `9`
-blocks in the current window and the median is `5`, then the ratio
-will be `(9+1)/5 = 2`. The MAX function allows us to ensure that
-the handicap has a value at least equal to `1`.
-
-The Napierian Logarithm of this ratio prevents the handicap from becoming excluding.
-We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.
-
-If we wanted the handicap to be applied as soon as the median is reached,
-we would divide it by `LN(1)`. The problem is that we have already set
-a minimum value of `1` with the MAX function. If we were to divide
-the ratio by `LN(1)` all calculating peers would have a handicap `\>=
-1`. In addition, is it really fair to handicap a member who is right on
-the median?
-
-That's why we went for `1.189` rather than `1`. A member has to
-be at least `18.9%` above the median to be assigned a handicap.
-18.9% is actually 16\^(1/16), the difficulty
-factor between two levels of the proof work (hexadecimal hash).
-
-To conclude, you have to remember that :
-
-* The handicap is indexed on the logarithm of the ratio to the median,
-* Handicap is only applied on members whose ratio to the median is greater than the ratio between two
-levels of the proof-of-work's difficulty.
-
-
-
-## Conclusion {#conclusion}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter's Blockchain can be compared to Bitcoin's : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.
-
-More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.
-
-The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :
-
-
-* The freedom to choose your currency system: because money should not be imposed.
-* The freedom to access resources: because we all should have access to economic & monetary resources.
-* The freedom to estimate and produce value: because value is a purely relative to each individual.
-* The freedom to trade with the money: because we should not be limited by the avaible money supply.
-
-
-Those 4 economic freedoms should be understood together, not exclusively. Plus, "freedom" has to be understood as "non-nuisance". So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.
-
-## Sources : {#sources}
-
-* Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-* Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-* The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-* The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-* High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-* PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-* Duniter Blockchain Protocol, v13, draft by Elois : [git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md](https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md)
-* The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-* Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
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-            <book-title>whitepaper fr</book-title>
-            
-            <lang>fr</lang>
-            
-            
-            
-        </title-info>
-        <document-info>
-            <author><first-name></first-name><last-name>Inconnu(e)</last-name></author>
-            <program-used>calibre 3.46.0</program-used>
-            <date>5.5.2020</date>
-            <id>e13c9ea4-7536-44c5-8117-25f915c2e2da</id>
-            <version>1.0</version>
-        </document-info>
-        <publish-info>
-            
-            
-            
-        </publish-info>
-    </description>
-<body>
-<section>
-<empty-line /><p>Duniter: A libre currency blockchain generator.</p>
-
-<p>Abstract</p>
-
-<p>Many currency principles involve non-equal rights to monetary creation between humans. We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human. This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution. Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process. We use a Web of Trust between living humans for identification. This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.</p>
-
-<p>Introduction</p>
-
-<p>Duniter is a software to create and manage “libre currencies”. Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :</p>
-
-<p>How should a currency be created to match the principle of equality between all humans, now and between generations ?</p>
-
-<p>The results of this demonstration implies a monetary creation :</p>
-
-<p>on a regular basis</p>
-
-<p>for each human being</p>
-
-<p>which amount has to be reassessed on fixed intervals according to a fixed formula.</p>
-
-<p>Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :</p>
-
-<p>$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$</p>
-
-<p>Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.</p>
-
-<p>The first currency created through Duniter is Ğ1, pronounced “June”. It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.</p>
-
-<p>1. State of the art : Bitcoin case</p>
-
-<p>Duniter uses the crypto-currency concept introduced by Bitcoin<sup>1</sup>, which is to use cryptographic tools such as signatures to create trustless digital currencies. Duniter fits this definition, but it has two completely different principles than Bitcoin : the Web of Trust and the Universal Dividend . These differences are on both monetary and technical aspects.</p>
-
-<p>1.1. Monetary creation of Bitcoin : a space-time asymmetry</p>
-
-<p>Space-time asymmetry refers to the relative access of individuals to newly created money<sup>2</sup>. Concretely, most existing currencies (c. 2020) are both spatially and temporally asymmetrical for their users. Let's take Bitcoin as an example to understand why.</p>
-
-<p>1.1.1. Spatial asymmetry</p>
-
-<p>When new Bitcoins are created, only some Bitcoin users (the miners) are given new Bitcoins, while everyone else get nothing. We believe this is the first injustice. However, some might say:</p>
-
-<p>"Miners used their electricity and time to get it!"</p>
-
-<p>... we would answer that this work should not have been rewarded by newly created Bitcoins. New units should be distributed to the whole community. Miners should be rewared another way, but not by money issuance. Of course, Bitcoin cannot create money through Basic Income since Bitcoin users are not strongly identified, and one might benefit from money creation multiple times if they owned several wallets. Duniter gets rid of this problem by identifying its users and creating the same amount of Basic Income to everyone.</p>
-
-<p>1.1.2. Temporal-asymmetry</p>
-
-<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency), which means ever fewer bitcoins will be created over time until no new BTC are being generated. So, once the first adopters have mined every bitcoin, how will future joiners get Bitcoins? Just like most of us do for Euros or Dollars: to get money, they will have to work for the ones who already own it.</p>
-
-<p>We believe this is the second injustice. Every member of a monetary community should be equal concerning monetary creation, and get the same relative amount of money over time, even if they are a late adopter. Duniter aims to fix this by making the Universal Dividend (a.k.a. UD) grow by the time according to precise rules, thus making members equal toward money issuance on a half-lifespan.</p>
-
-<p>Most currencies present one of these two asymmetries, including metal currencies and mutual credit, as exposed in the RTM.</p>
-
-<p>1.1.3. A solution</p>
-
-<p>Bitcoin has taught us that it is possible to create a currency system allowing one to both create digital money and to exchange it without a central authority. What we need to change is the way money is issued so we finally have a symmetrical system. We need Bitcoin + Universal Dividend. But Universal Dividend implies that the community consists of only identified people. This is where the Web of Trust (WoT) comes into place.</p>
-
-<p>This concept, introduced by cryptography with the OpenPGP format<sup>3</sup>, allows us to identify people in a decentralized manner. It works as follows: each person creates a personal identity that is linked to its cyptographic certificate. The identity must be confirmed by others members who use their own cryptographic key. It is that simple: people choose who is part of the community and who is not, not a central authority.</p>
-
-<p>However, Duniter will not use OpenPGP for its cryptographic features: Elliptic Curves<sup>4</sup> will be used instead for the conciseness of its generated keys and its pratical advantages. Duniter has its own Web of Trust principles, that will be exposed later.</p>
-
-<p>1.2. Proof-of-Work mining : a power race</p>
-
-<p>In Bitcoin Model, the calculation and incentive principles cause a power race : new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers. This leads to a power race an places the control over the currency in the hands of the richest hardware owners. We want to make Duniter blockchain validation much less energy and hardware consuming while keeping a strong level of security. This will be further explained later. A consequence of this choice is the participation of low-end hardware in the Duniter network, leading to a better decentralization of blockchain validation.</p>
-
-<p>1.2.1 What about Proof of Stake ?</p>
-
-<p>Proof of stake consensus algorythm was first introduced in 2012<sup>5</sup>. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a “stake” they would lose in case of cheat.</p>
-
-<p>At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle. Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.</p>
-
-<p>2. Duniters Blockchain</p>
-
-<p>Duniters Blockchain follows the basic principles of Bitcoins. This is essential for synchronization between peers, as to prevent double-spend attacks. However, Duniters Blockchain will store different informations than Bitcoins.</p>
-
-<p>The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
-
-<p>a former transaction (as in Bitcoin)</p>
-
-<p>a Universal Dividend (specific to Duniter).</p>
-
-<p>Duniters Web of Trust is also written in the Blockchain. The identity of each member gets registered much like transactions are, with a strong link to the time reference. Thus, the Blockchain is a representation of a space-time frame of reference, where “space” are members of the WoT and “time” the basic blockchain units : the blocks. On each point of time, one can determine which account is legitimate to create the UD, only with a blockchain analysis.</p>
-
-<p>2.1. Spam countermeasures</p>
-
-<p>An issue of most cryptocurrency projects is to prevent the common ledger from growing too much. This would require nodes to have a lot of storage and computing power to be usable. In particular, we don’t want an attacker to be able to make the Blockchain grow too fast. Most projects implement transaction fees as a way to prevent this, making the attacker lose money. We don’t want to introduce this mean since a currency with automatic fees on transactions is no more neutral. Several countermeasuers against such spam attacks are implemented.</p>
-
-<p>2.1.1. Minimum output amount</p>
-
-<p>Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.</p>
-
-<p>2.1.2. Limited block size and chainability</p>
-
-<p>The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.</p>
-
-<p>With the same goal to prevent too many transactions to get registered, while transactions can be “chained” (refer to another transaction in the same block), the chainability of transactions is limited to 5.</p>
-
-<p>2.2. Scaling</p>
-
-<p>Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :</p>
-
-<p>Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don’t want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.</p>
-
-<p>Duniter’s aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.</p>
-
-<p>However, Duniter has assets that will help if the number of users and transactions grow.</p>
-
-<p>2.2.1 Dynamic block size</p>
-
-<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve. On low use of the blockchain, the maximal block size is 500 bytes. On high use of the blockchain, the maximal block size would be 110% of the average size of the current window blocks(see “personalised difficulty” part for more information). This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :</p>
-
-<p>block_size &lt; max(500 ; CEIL(1.10 * (average block size))</p>
-
-<p>2.2.2. Lightning Networks</p>
-
-<p>The Lightning Networks<sup>6</sup> allow almost instant and off-chain transactions. They were first implemented on Lightcoin, and are now on Bitcoin. One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain. The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks. While not available yet, this payment channel might get implemented when needed.</p>
-
-<p>2.2.3. Unit base</p>
-
-<p>As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the unitbase is updated each time the UD value reaches 100.00 : it goes from 99.99*10^(unitbase) to 10.00*10^(unitbase+1). All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.</p>
-
-<p>With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.</p>
-
-<p>3. Duniter Web of Trust</p>
-
-<p>3.1. Basic Principles</p>
-
-<p>In order to identify “members” accounts - which create monetary units - and other accounts, Duniter uses a Web of Trust. This can be summarized into few principles:</p>
-
-<p>Each account becomes a member if it received a minimal number of certifications - 5 for Ğ1 currency.</p>
-
-<p>Only members accounts can send certifications. Certifications have a limited lifespan.</p>
-
-<p>A certification indicates that the sender accepts the receiver as a legitimate identity.</p>
-
-<p>The aim of the WoT is to identify a blockchain account to a living human. According to Lauterbach et.al<sup>7</sup>, the strengh of a relationship should be considered when building a vouch system. For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are. A certification represents a strong human relationship : one may certify a close relative, not an acquaintance. Each member has to accept this licence before being included in the WoT. Thus, if a member is part of an attack on the currency, they can be found by mutual relatives. Additional security rules occur to prevent cheat and attacks on a large scale.</p>
-
-<p>Note that non-members accounts can use the currency, but cannot create money. Non-members accounts can be used by individuals as secondary wallets, or by institutions.</p>
-
-<p>We were inspired by the OpenPGP Trust system<sup>8</sup>. However, the OpenPGP trust principles aim at defining trust from a particular point of view while Duniter needs to identify humans for the whole community. To achieve this goal, while OpenPGP allows each user to tweak its trust parameters individually, Duniter sets rules in the “genesis” block for the whole community.</p>
-
-<p>3.2. Why do we need a Web of Trust ?</p>
-
-<p>There are two reasons we need it :</p>
-
-<p>To make sure that only one Universal Dividend is produced per member at each specified creation interval. In the Ğ1’s case this interval is set as daily 86 400 seconds, it is the <emphasis>monetary parameter</emphasis> known as dt.</p>
-
-<p>To identify the nodes hashing the blocks and assign each a personalised difficulty. This custom difficulty proof of work is there to avoid the blockchain’s validation mechanism becoming too centralised as is the case with many 'non-libre’ cryptocurrencies.</p><empty-line /><p>Monetary parameter : Each currency that use Duniter has its own blockchain whose behaviour is dictated by a set of ‘parameters’ defined in block zero - the so-called genesis block - that can be tweaked to achieve the desired results. At the time of writing the Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21 parameters of which 10 are for the WoT alone. We’ll focus on these 10.</p>
-
-<p>Suffice to say that in the Ğ1’s case, the DU is created every 24 hours - 86 400 seconds. This interval is set through the time derivative dt parameter and can have a different value in other implementations of the protocol.</p>
-
-<p>We want to make sure that each member can only have one account. As we all know, achieving zero-risk isn’t possible<sup>9</sup>. Our goal is therefore not to create a WoT within which fraud would be absolutely impossible, but instead to discourage it. Here is a rewording of our goal in 4 smaller ones :</p>
-
-<p>Make the certification process lengthy enough that all members exercise due diligence and are wary of risks.</p>
-
-<p>Make fraudulent acts as hard as we can to the extent that they become pointless.</p>
-
-<p>Ensure that any Sybil attacks have a negligible impact on the currency by ensuring that illegitimate double Universal Dividends have no significant bearing on the legitimate monetary mass</p>
-
-<p>Slow the growth of ‘Sybil regions’ to give enough time for the community to react and isolate the threat.</p><empty-line /><p>Sybil attack : A Sybil attack is an attack perpetrated on a reputation system through the creation of fake identities. A Web of Trust is a specific instance of a Reputation System.</p>
-
-<p>There are plenty of Sybil attack scenarios we can think of and just as many reasons why their perpetrators would want to carry them out. Our objective is that the configuration of the WoT protects both users and its IT backbone infrastructure against these attacks.</p>
-
-<p>This means that micro-attacks performed by small groups of individuals looking for personal enrichment are of no interest to us. The web’s role isn’t to deter these attacks, this being instead the role of the community. Just like the town you live in is responsible for providing your tap water and electricity but isn’t responsible for any burglaries, etc. Much in the same way, Duniter’s WoT guarantees us all a functional currency, but do not detect small fraud.</p>
-
-<p>3.3. The importance of having our own certification system</p>
-
-<p>Centralized identification systems can achieve the goal we want. State Identification is an example. However, this has many drawbacks :</p>
-
-<p>The authority may have arbitrary criteria for identification, for example preventing people without an official state-provided identity or homeless people to be included in the WoT.</p>
-
-<p>Payment might be required to get identified, thus making the monetary creation not “free”.</p>
-
-<p>The authority is a point of failure for any attacker.</p>
-
-<p>It is of the utmost importance that we remain free from any state or corporation. The WoT is an answer to this criterium. To this day we depend only on the Internet and yet, were it to fail, there are already alternatives being tested around the world for a decentralised communication network.</p>
-
-<p>3.4. A few foundational concepts on graph theory : a bit of vocabulary</p><empty-line /><p>Graph: set of points -called ‘vertices’- joined by edges -called paths/walks-.</p>
-
-<p>Simple graph: a graph with no loops and with no multiple edges. That is, each edge connects two distinct endpoints and no two edges have the same endpoints. A simple edge is an edge that is not part of a multiple adjacency -of edges-. In many cases, graphs are assumed to be simple unless specified otherwise.</p>
-
-<p>Directed graph: a graph in which the edges have a distinguished direction, from one vertex to another. A directed edge can also be called a path or walk. Arrow A –&gt; B is therefore different from arrow B –&gt; A.</p>
-
-<p>Endpoints: the edge with vertex A –&gt; B has A and B as endpoints, respectively as start and end of the path/walk.</p>
-
-<p>Isolated vertex: a vertex whose degree is zero, that is, a vertex with no incident edges.</p>
-
-<p>Degree of a vertex: number of its incident edges -in and out-.</p>
-
-<p>Out-degree of vertex A: number of outbound edges / tail ends from A.</p>
-
-<p>In-degree of vertex A: number of incoming edges / head ends to A.</p><empty-line /><p><emphasis>degrees of a vertex diagram</emphasis></p><empty-line /><p>Path: -aka “walk”- path to follow to get from vertex A to vertex B.</p>
-
-<p>3.5. Definition of the Duniter Web of Trust</p>
-
-<p>The Duniter WoTs -one per currency- are simple directed graphs without isolated vertices. The vertices are the members and the edges are the certifications given and received.</p>
-
-<p><emphasis>Directed</emphasis> means that the responsibility of issuing a certification is unique and personal to the certifier. The trust they place in the receiver cannot be imposed in the other direction although in most circumstances both parties equally trust each other.</p>
-
-<p>In addition, all vertices are either currently active members or past-members. Past-member vertices are in a specific ‘deactivated state’ and can no longer issue or receive certifications although the ones already issued or received to/from other members are still considered ‘pending’ to avoid a collapse of the WoT. If these old members don’t come back into the WoT, their pending certifications will eventually expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
-
-<p>To wrap up with old members, after a certain period of time - set in the currency’s parameters - their deactivated vertex is removed from the web and the associated identity is ‘revoked’. The person who owned the account can no longer use this identity but is free to join the web with another one.</p>
-
-<p>Identity : An identity is a set of three pieces of information: a public key, a name and a blockstamp. A blockstamp points to a specific block in the chain. Its main use is to freeze the point in time at which an identity was created and to link this identity to a specific chain and a currency - each currency having its own blockchain.</p>
-
-<p>An identity can be in any one of 5 different status: pending, member, old member, revoked or excluded.</p>
-
-<p>Let’s take a simple example:</p>
-
-<p>    A -&gt; B -&gt; C
-         |
-         \--&gt; D</p>
-
-<p>If, for whatever reason, A were to lose its member status, the web would crumble and all other members would be excluded as a consequence. To avoid this, the certification from A –&gt; B will remain valid until its expiry date, leaving enough time for B to receive certifications from C or D.</p>
-
-<p>Because our WoT doesn’t have any isolated vertices, each new identity created needs to be pulled into the web with all of the certifications it has received, all in the same block. This calls for a temporary ‘buffer’ storage space for pending identities and the certifications they have received. This storage space is called ‘the pool’ of Duniter nodes, which we could also have called the ‘sandbox’ as that’s the name used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other documents and metadata not mentioned here.</p>
-
-<p>3.6. Exploring the rules behind a Duniter Web of Trust</p>
-
-<p>The Duniter WoTs - one per currency - works with a set of eight fundamental rules enforced through eleven different parameters. Ten of these parameters are set within the genesis block, the eleventh one - msPeriod- having being hard-coded in the Ğ1’s code subsequently.</p>
-
-<p>3.6.1. Distance rule and referent members (</p>
-
-<p>stepMax</p>
-
-<p> and</p>
-
-<p>xPercent</p>
-
-<p>)</p>
-
-<p>These two parameters are closely linked and together define the ‘distance rule’. The ‘distance rule’ can only be described after defining what a ‘referent member’ is:</p>
-
-<p>Referent member: member A is said to be ‘referent’ if and only if the total of their degrees are greater than or equal to CEIL-N^-1/stepMax where N is the total number of members. As the size of the web will grow this number will grow too, meaning it will take more certification issuances to become a referent member. The number of certifications needed to become a member shouldn’t change.</p>
-
-<p>Let’s now define the distance rule:</p>
-
-<p>Distance rule: member A is said to observe this rule if and only if for a subset xPercent % of referent members R there exists a path of length less than or equal to stepMax between R and A.</p>
-
-<p>Referent members only exist so that the distance rule can take effect, they have no special privileges over non-referent members. In a perfect web, that is one in which each member has certified all members they legitimately can, all members would be referent members. However, because the web progressively grows in size and because members die and are replaced by new ones, there are always members at any given time t who haven’t yet certified all members they legitimately could. These members would hinder the evolution of the web if they were taken into account in the calculation of the distance rule and the web would effectively stop growing.</p>
-
-<p>Because verifying the application of the distance rule is calculation-greedy, it is only performed when a new identity gets confirmed into the web or an existing member gets renewed. There is an exception to this rule: the distance rule is not observed in the genesis block -when the web is first implemented.</p>
-
-<p>3.6.2. Rule of the minimum number of certifications needed (</p>
-
-<p>sigQty</p>
-
-<p>)</p>
-
-<p>This is the simplest rule, it essentially says that each member must at any given time -meaning in any single block- have received at least sigQty active certifications. If, for whatever reason, member A were to have less than sigQty active certifications in a given block, they would cease to be a member and be required to publish a request for identity renewal.</p>
-
-<p>3.6.3. The membership renewal rule (</p>
-
-<p>msValidity</p>
-
-<p>,</p>
-
-<p>msPeriod</p>
-
-<p> and</p>
-
-<p>msWindow</p>
-
-<p>)</p>
-
-<p>Bear in mind that a membership doesn’t last a lifetime but instead has a lifespan set to msValidity seconds.</p>
-
-<p>Every single member -or old member who hasn’t revoked his identity or been excluded- can request a membership renewal so long as the last request was made more than msPeriod seconds ago. If a member has never requested a renewal, the date of last renewal is equal to the timestamp at which his membership was first created. A new request will be stored in the ‘pool’ for a maximum of msWindow seconds before it’s included in the blockchain. Once again, this can only happen once/if the member meets both the siqQty rule and the distance rule -if these criterion are already matched it’s just a case of waiting for a new block to be mined-.</p>
-
-<p>If a member hasn’t requested a renewal for longer than msValidity seconds, they automatically cease to be a member. From this moment on, the ex-member has another msValidity window to renew their membership. When this period of 2 × msValidity runs out, the membership will expire and this identity will never be available for use again in the web. If the person so desires, they will have to publish new identity and membership documents and find enough certifiers, as any newcomer.</p>
-
-<p>3.6.4. Rule of certification lifespan (</p>
-
-<p>sigValidity</p>
-
-<p>)</p>
-
-<p>All certifications included in the blockchain expire sigValidity seconds after they were issued.</p>
-
-<p>/!\ The issuance and the inclusion of a certification in the blockchain occur at different times. When member A issues a certification at time t1, it gets stored in the pool starting at t1 and only finds its way into the blockchain at t2 when all of the web’s rules are observed. Several weeks can thus go by between t1 and t2!!!</p>
-
-<p>3.6.5. Rule of limited supply of active certifications (</p>
-
-<p>sigStock</p>
-
-<p>)</p>
-
-<p>By ‘active certifications’ we refer to certifications included in the blockchain and that haven’t yet expired.</p>
-
-<p>The total of active certifications issued by any member at any single time must be less than or equal to sigStock. When this threshold is reached the member will have to wait for one of his active certifications to expire before he/she can issue a new one.</p>
-
-<p>3.6.6. Rule of the time period between two certification issuances. (</p>
-
-<p>sigPeriod</p>
-
-<p>)</p>
-
-<p>As soon as a certification issued by member A gets included in the blockchain, they will be unable to issue a new one before another sigPeriod seconds.</p>
-
-<p>3.6.7. Expiry of a certification issuance (</p>
-
-<p>sigWindow</p>
-
-<p>)</p>
-
-<p>When a certification is issued by member A, it will be stored in the ‘pool’ for a maximum of sigWindow seconds. If the certification hasn’t been included in the blockchain by then, it will be cancelled and the member’s sigStock will be repleted by one.</p>
-
-<p>3.6.8. Lifespan of a ‘pending’ identity (</p>
-
-<p>idtyWindow</p>
-
-<p>)</p>
-
-<p>When a new identity is created, it is stored in the ‘pool’ for a maximum of idtyWindow seconds. If the person hasn’t achieved member status by then, the certification will simply be cancelled.</p>
-
-<p>3.7. Details on some of the WoT’s peculiarities at the genesis block</p>
-
-<p>The aforementioned rules can only be enforced with an existing web. They cannot be observed when first creating the web, that is when defining the genesis block.</p>
-
-<p>Only rules 2 and 5 can be observed at the genesis block.</p>
-
-<p>The genesis block has to be manually created by the founding members. In practice this means that there must be a choice on which identities to include on the premise that all of them observe rules 2 and 5. In addition, the genesis block must be signed with the private key of one of these identities.</p>
-
-<p>As soon as the genesis block has been created, the other identities can start mining the blockchain and the member who created block #0 effectively looses the decision power he had at creation.</p>
-
-<p>3.8. Why these rules and application cases in the Ğ1</p>
-
-<p>3.8.1. Distance and maximum size</p>
-
-<p>The distance rule is there to curb the maximum size of a Sybil region as well as that of the monetary community as a whole. The xpercent parameter prevents the creation of a ‘faction’ that could take hold of the blockchain.</p><empty-line /><p><emphasis>Sybil region</emphasis></p>
-
-<p>The Sybil regions are isolated from the rest of the graph in the sense that they can only receive certifications from other ill-intentioned Sybil members. As a consequence, the shortest edge/path between a legitimate member and a Sybil one has to have the attack’s author as an endpoint. The maximum depth the Sybil region can attain is therefore contingent on the distance between the attacking edge-s- and the xpercent% closest referent members, this distance is known as stepAttackers. The maximum size of a Sybil region created by sigQty members depends on the L parameter, defined as L = sigQty/sigStock:</p>
-
-<p>MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)</p>
-
-<p>The maximum size of the Web of Trust is given by the following formula:</p>
-
-<p>WoTmax = (sigStock)*L^(stepMax-1)</p>
-
-<p>However we know for a fact that members will never use all of their available certifications. According to Dunbar<sup>10</sup>, on average, one is able to maintain relationships to around 150 people. Being conservative, we will consider that on average, each person will certify 50 accounts. We can calculate the size of the average web of trust WoTavg :</p>
-
-<p>WoTavg= (50)*(sigQty/50)^(stepMax-1)</p>
-
-<p>Our goal with the Ğ1 is to create a community of about one million members to test the consequences of a libre monetary system. Let’s see how we can tweak the pair of sigQty and stepMax- to reach this size:</p><empty-line /><p><emphasis>Average WoT size graph as a function of sigQty and stepMax</emphasis></p>
-
-<p>The maximum size of a Sybil region grows linearly with sigQty but exponentially with stepMax. Logic has it that we need to keep stepMax as low as possible to ensure sufficient strength to the web. The above graph shows that the lowest value of stepMax for a web of a million members is of 5. This is an order of magnitude and is likely to be much higher in reality, we cannot measure it for sure.</p>
-
-<p>For sigQty we can choose a value of 4 for a web of 1.5 million members or 5 for half a million members. Bear in mind these are gross figures and could be significantly higher, we are talking anywhere between 1 and 10 million in reality. Calculating WOTavg gives us a pretty good idea of how the web would scale bearing in mind that it considers all members are referent members too -which isn’t the case as explained previously-. Hence the maximum size of the web is likely larger, a ballpark figure of half a million is enough for now especially knowing that the smaller sigQty is, the easier it is to launch a Sybil attack -it’s easier to find four accomplices than five-. For security reasons we have settled on five:</p>
-
-<p>stepMax = 5
-sigQty = 5
-sigStock \&gt;= 50</p>
-
-<p>The maximum size of a Sybil region therefore is:</p>
-
-<p>(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))</p>
-
-<p>with sigStock = 50 we have a Sybil region of:</p>
-
-<p>45*(1-10^(5-stepAttackers))/(-9)</p>
-
-<p>A good practice for protecting the web is to maximise stepAttackers. That’s why we decided that referent members in the genesis block had to be at least four steps away from each other.</p>
-
-<p>Another way to keep a Sybil attack at bay, were it slow enough for members to notice it, would be for referent members to ‘stretch’ the web intentionally to limit the growth of the region by ensuring that the attackers’ legitimate certifications received in the first place aren’t renewed. But what if bot accounts were created and certified each other super fast and following all rules, how would we counter that? By introducing a minimum length of time between two certifications!</p>
-
-<p>3.8.2. Time is our friend</p>
-
-<p>To help us deter a Sybil attack, we’ve decided to impose a minimum period of time between any two certifications issued from a single account. This parameter called sigPeriod affords us a greater chance to detect the formation of a ‘hostile’ faction.</p>
-
-<p>Here is a graph showing the evolution of a Sybil region with the variation of sigPeriod. The simulation considers that honest members and attackers both issue a certification each sigPeriod interval, in days:</p><empty-line /><p><emphasis>size of the WoT according to sigPeriod and stepAttackers</emphasis></p>
-
-<p>As we see, there is a strong link between the growth speed of the region and sigPeriod. As evidenced here, we need a sigPeriod high enough in order to ensure that the legitimate web can grow at least as fast as a Sybil region. In addition, the higher sigPeriod is, the more members will exercise their certification power gingerly, the action coming at a higher ‘cost’.</p>
-
-<p>There are numerous advantages to giving sigPeriod a high value and no technical barriers to it, hence our choice of five days.</p>
-
-<p>We could have also gone for one week for the sake of simplicity. However there is an underlying idea behind our choice which was quite simply the pace of today’s life. Certifying someone can be a lengthy process as one needs to make sure they are correctly applying the Ğ1 licence and people nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea to allow one to certify at the end of every working week -five days- instead of a whole calendar one.</p>
-
-<p>3.8.3. Trust me now, trust me forever ? (</p>
-
-<p>sigValidity</p>
-
-<p>,</p>
-
-<p>msValidity</p>
-
-<p>)</p>
-
-<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s Web of Trust:</p>
-
-<p>First of all, some members will pass and those accounts should no longer produce the Universal Dividend.</p>
-
-<p>Secondly it is of the utmost importance that ‘rogue’ accounts can be excluded from the web at some point.</p>
-
-<p>To achieve this, certifications have a limited lifespan. Members need to seek renewal from their peers after sigValidity time. On the other hand, this time can’t be too short that members would spend more time seeking renewal than they would exchanging in the currency. Furthermore, a certification with too short a lifespan would foster careless certifying behaviours. The act of certifying must have a high-enough ‘perceived’ cost to make it feel like an important act. Lastly, we also wanted this lifespan to be easy to remember. Historically speaking, we first settled on the values of sigPeriod and sigStock, meant one could issue all of their certifications in 495 days, one year was therefore not long enough. We deemed three years to be too much and that’s how we agreed on two years in the end.</p>
-
-<p>Thinking that a deceased member could continue producing the UD for two long years without anyone benefitting from it was also something we needed to address. We chose a value of one year for msValidity. The act of renewing every year is done through one of the clients interacting with the blockchain, through a simple click on a button. This parameter is less important than others and is mostly there to ‘prune’ the web of past or inactive members who don’t renew their membership.</p>
-
-<p>3.8.4. Keeping the pools free of information glut (</p>
-
-<p>idtyWindow</p>
-
-<p>,</p>
-
-<p>sigWindow</p>
-
-<p>,</p>
-
-<p>msWindow</p>
-
-<p>)</p>
-
-<p>The pools need to be cleaned up on a regular basis to avoid them clogging up with information and to ensure that machines with less calculating power can still run a Duniter node.</p>
-
-<p>To achieve this, identities with pending membership approval and the corresponding certifications have to remain the shortest time possible in the pool while still having a chance of making it into the blockchain.</p>
-
-<p>For the Ğ1, our opinion was that two months would be enough for all potential certifiers to agree on a specific identity to certify. We also wanted a time period that would be easy enough to remember by all. We settled on two months, and gave this value to all three parameters idtyWindow, sigWindow and msWindow.</p>
-
-<p>3.8.5. Avoiding single members from ‘knowing too many people’ (</p>
-
-<p>sigStock</p>
-
-<p>)</p>
-
-<p>We considered that on average, each person will certify 50 people. However, we know for a fact that some members will use more than 50 certifications. The maximum social network of one individual is around 150 people<sup>11</sup>. Being conservative, we settled on a maximum certification number sigstock of 100. Since sigStock’s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.</p>
-
-<p>3.8.6. Avoiding locking minorities (</p>
-
-<p>xpercent</p>
-
-<p>)</p>
-
-<p>It’s easy enough to become a referent member, one of the Sybil strategies could therefore be to create a region of referent members. Such a region would grow slower than otherwise but could confer a locking power to its members by using the distance rule. That’s why the distance rule cannot be calculated on 100% of the referent members. Hence the introduction of the xpercent parameter which defines the percentage of referent members needing to be less than five edges -steps- from each other.</p>
-
-<p>This percentage needs to be low enough to prevent the formation of a locking minority -referent Sybil members being too far from legitimate referent members-. On the other hand, it needs to be high enough so as to restrict the maximum size of the Sybil region through the distance rule. The xpercent parameter was one of the hardest to define, therefore we might decide to change its value during the Ğ1 experiment.</p>
-
-<p>We were inspired by the Pareto principle<sup>12</sup>: if at least 20% of members give good density to the web, 80% of the referent members will be five or less steps from any other member -referent or not-. The maximum value for xpercent is therefore 80%, anything above that and the distance rule could be too restrictive for legitimate use cases. With security our top concern, we chose the maximum value of 80%.</p>
-
-<p>3.8.7. Spam protection with (</p>
-
-<p>msPeriod</p>
-
-<p>)</p>
-
-<p>This parameter stands out a bit on its own, as it was added after the genesis block. It is there to protect the Duniter P2P infrastructure against ‘spam’ attacks. We had to think of a strategy against attacks such as high-frequency membership renewal requests -i.e: in every block, every five minutes- or worse still, hundreds of these requests per minute to flood the Duniter nodes. Without such limits, nodes are supposed to address all renewal requests, even in cases where they were last published five minutes ago! The msPeriod parameter was given the same value as idtyWindow, sigWindow and msWindow, i.e. two months.</p>
-
-<p>4. Proof of Work with personal difficulty</p>
-
-<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.</p>
-
-<p>This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each “winning” member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.</p>
-
-<p>Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.</p>
-
-<p>One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an “ecological” PoW ?</p>
-
-<p>4.1. Why do we need Proof of Work ?</p>
-
-<p>Duniter nodes share a database as part of a p2p environment. The proof of work (PoW) allows machines to synchronize with each other. In Duniter’s case, the blockchain is our database, and acts as a ledger keeping a trace of all transactions, status of the WoT and more. How can we let several machines add data (ie: a transaction) at the same time? In addition, how do we settle on how much time has gone by since the blockchain was last updated? Agreement on time is of the utmost importance as we want to create Universal Dividends on a regular basis, and keep track of membership status, both in human time.</p>
-
-<p>Proof-of-work provides a clever solution to both problems:</p><empty-line /><p>Any machine can write into the blockchain (create a new block) but is only authorised to do so if it has previously solved a mathematical equation that require a certain amount of work. The challenge has to be hard enough to prevent two machines to solve it at the same time, ensuring the unicity of a block’s creator.</p>
-
-<p>Solving this challenge takes a certain amount of time, which depends on the calculating power of the whole network. This provides a common ground for defining the needed time reference. A block time is set (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to get an average duration corresponding to this block time.</p>
-
-<p>4.2. Only members can “mine”</p>
-
-<p>One of Duniter’s major differences with other PoW-based cryptocurrencies is that only members are allowed to author blocks. Each block is signed with the member’s private key, allowing the algorithm to determine a personalised difficulty.</p>
-
-<p>This personalised difficulty eliminates the rat-race for the most sophisticated and powerful mining equipment. Another benefit is the fact that no “supercomputer” can take control of the blockchain. Lastly, Duniter implements a rotation in forging members thanks to this personalized difficulty.</p>
-
-<p>This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies. Members can mine with anything from a raspberry pi to a privacy-first internet cube.</p>
-
-<p>4.3. How does it work ?</p>
-
-<p>4.3.1. The hash (aka digest)</p>
-
-<p>Example of a valid hash:</p>
-
-<p>00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</p>
-
-<p>As you can see this hash starts with five zeros which was very hard to achieve and took a lot of work for someone’s computer. Hence the term “proof of work”.</p>
-
-<p>4.3.2. The common difficulty</p>
-
-<p>A common difficulty is needed to settle on a yardstick for our time reference. Its role is to make sure the blockchain moves forward at a steady pace - one block every avgGenTime seconds, avgGenTime being one of the 20 parameters behind the Duniter protocol-.</p>
-
-<p>This difficulty’s initial value can be set to any arbitrary value (70 in Duniter v1.5.x) and then acts as a spring, regulating blocktime creation by increasing itself if the creation interval drops under avgGenTime and vice-versa.</p>
-
-<p>4.3.2.1. How is difficulty applied ?</p>
-
-<p>The numeric value of difficulty is taken from an array of possible hashes out of all possible hashes. In DUBPv13 the hash of a block is its sha256 hexadecimal hash.</p>
-
-<p>To understand the difficulty, we make a euclidiean division of the difficulty by 16.</p>
-
-<p>Here’s an example with a difficulty value of 70 :</p>
-
-<p>70 // 16 = 4 with a remainder of 6.</p>
-
-<p>The valid hashes are the ones starting with four zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation). The valid hashes are then written as starting with : 0000[0-9]. This is a bit different from Bitcoin, where the difficulty is only ruled by the number of zeroes.</p>
-
-<p>4.3.2.2. The Nonce</p>
-
-<p>When a member is forging a new block, his computer freezes the block’s content and changes the Nonce until the hash reaches the required number of zeroes.</p>
-
-<p>The nonce allows us to mine a new block by finding a hash. The hash value allows us to determine the difficulty level of the proof-of-work performed. Examples of possible Nonce values:</p>
-
-<p>10100000112275</p>
-
-<p>10300000288743</p>
-
-<p>10400000008538</p>
-
-<p>10700000079653</p>
-
-<p>10300000070919</p>
-
-<p>In reality the Nonce value follows a pre-determined format akin to XYY00000000000. The Nonce’s value isn’t the number of attempts but rather a value within a set of possible ones. This is how the Nonce is built:</p><empty-line /><p>X is a number assigned to a specific peer. Let’s assume that someone has several nodes each with the same private key, this would lead to possible collisions if this person were to mine the same block with different nodes. Each <strikethrough>block</strikethrough> node ? will therefore have its own unique X to prevent this from happening.</p>
-
-<p>Y is the number of cores of the processor. The Nonce starting with 107[…] belongs to a seven cores processor, while 199[...] could be the proof generated by a 99 cores processor.</p>
-
-<p>The rest of the Nonce, the part that follows after the XYY, is the numerical space for this individual node and is unique to each of the CPU’s core. This space is comprised of eleven digits (00000000000). For the sake of accuracy, we use the term CPU in the wider sense, it can be understood as a bi-CPU for example. We take into consideration the number of cores for the resulting PoW.</p>
-
-<p>4.4. Personalised difficulty</p>
-
-<p>Earlier in this article, we explained that the personalised difficulty is the new and key concept that sets Duniter apart from other PoW-based cryptocurrencies.</p>
-
-<p>Here is how this personalised difficulty is calculated and assigned:</p>
-
-<p>It is determined by a combination of two different constraints with complimentary roles: the exclusion factor and the handicap.</p>
-
-<p>Let powMin be the common difficulty, exFact a member’s exclusion factor and handicap their handicap. This member’s personalised difficulty diff is:</p>
-
-<p>diff = powMin*exFact + handicap</p>
-
-<p>4.4.1. Understanding</p>
-
-<p>exFact</p>
-
-<p>, the exclusion factor</p>
-
-<p>Members who have never produced blocks or haven’t for quite some time are assigned an exclusion factor of 1. Their personalised difficulty is therefore simply the sum of powMin + handicap.</p>
-
-<p>Before reading on, let’s precise the role of this exclusion factor. When a member adds a block to the chain, his exFact jumps up from one to a very high value, to prevent them from forging other blocks immediately after and taking control of the blockchain.</p>
-
-<p>The exclusion factor will then rapidly return to one. This delay is expressed as a number of blocks. It is calculated as a proportion of the number of members forging. In the Ğ1’s case, this proportion is 1/3, meaning that if there are fifteen members currently forging, the member’s exclusion factor will drop down to one after five blocks.</p>
-
-<p>4.4.1.1. What is intended by “the number of members forging” ?</p>
-
-<p>We mean the number of members trying to create the next block. In reality, there is no way to precisely know how many members are calculating at any given time, because it is impossible to view the entire network. But we need this information, whithout which assigning a personalised difficulty is impossible. To achieve this, Duniter looks back at the blockchain and assumes that there is as much members forging as those who have found at least one block in the last blocks in the current window, minus the very last one.</p>
-
-<p>4.4.1.2. Current window</p>
-
-<p>We use the concept of current window. The current window is the number of blocks we look back at to determine how many members are forging. Let’s see how it works:</p><empty-line /><p>issuersFrame is the size of the current window in blocks.</p>
-
-<p>issuersCount the number of members who have calculated at least one block during the current window.</p>
-
-<p>Both issuersFrame and issuersCount are block fields. When first starting a blockchain, the very first block has an issuersFrame=1 and an issuersCount=0. The genesis block is excluded as there are no members in the current window!</p>
-
-<p>From the second block onwards (block #1) we track the variation of issuersCount. The member having mined block #0 enters the current window and in block #1 we will therefore mention issuersCount=1.</p>
-
-<p>issuersFrame then varies as follows:</p>
-
-<p>if issuersCount increases by N (with a maximum step of N = 1), then issuersFrame will increase by one unit over a period of 5N blocks.</p>
-
-<p>Conversely, if issuersCount decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then issuersFrame will decrease by one unit during 5Y blocks.</p>
-
-<p>When such events overlap, issuersFrame evolves as so :</p><empty-line /><p><strong>bloc</strong></p>
-
-<p><strong>event</strong></p>
-
-<p><strong>issuersFrame</strong></p><empty-line /><p>T</p>
-
-<p>Babar writes a block and enters issuersCount</p>
-
-<p>160</p><empty-line /><p>T+1</p>
-
-<p>Celeste leaves issuersCount</p>
-
-<p>160 +1 = 161</p><empty-line /><p>T+2</p>
-
-<p>N/a</p>
-
-<p>161 +1 -1 = 161</p><empty-line /><p>T+3/4/5</p>
-
-<p>N/a</p>
-
-<p>161 +1 -1 = 161</p><empty-line /><p>T+6</p>
-
-<p>N/a</p>
-
-<p>161 -1 = 160</p><empty-line /><p>The calculation can be found under rules BR_G05 and BR_G06 of the DUP protocol.</p>
-
-<p>4.4.1.3. exFact and the personalised difficulty</p>
-
-<p>We explained that exFact spikes immediately after the member has found a block. It decreases then rapidly to 1 after a number of blocks equal to 1/3 * issuersCount. Let’s see precisely how we calculate exFact:</p><empty-line /><p>nbPreviousIssuers is the value of issuersCount at the last block N found by the member.</p>
-
-<p>nbBlocksSince is the number of blocks found by the rest of the network since block N.</p>
-
-<p>percentRot is the number of <emphasis>not excluded</emphasis> peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.</p>
-
-<p>a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]</p>
-
-<p>The FLOOR is a simple truncate function. For exFact to exclude the member, we need :</p>
-
-<p>(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) &gt;= 2</p>
-
-<p>We can see that the member is not excluded if nbBlocksSince is greater than 1/3 of the calculating members. Take as an example nbPreviousIssuers = 6 and nbBlocksSince = 3:</p>
-
-<p>(0.67* 6 / )1 + 3)) = 1.005 -&gt; exFact = 1</p>
-
-<p>However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:</p>
-
-<p>(0.67 * 6 / (1 + 1)) = 2.01 -&gt; exFact = 2</p>
-
-<p>Moreover if the last block was authored by the said member, then:</p>
-
-<p>nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers</p>
-
-<p>ExFact value increases according to the number of members calculating. Thus, if there is enough members calculating, even mining farms would be excluded. We have therefore succeeded in our intent to deter attempts to seize the blockchain and its currency.</p>
-
-<p>However, at any time t, the two-thirds of calculating members all have an exclusion factor of 1, even though they might not all have the same computational power at hand. If the personalised difficulty only took into account the exclusion factor, then only the members with the highest computational power from the remaining third would be able to author new blocks and the other 2/3s would almost always be excluded. Lesser machines wouldn’t stand a chance…</p>
-
-<p>4.4.2. The handicap</p>
-
-<p>The handicap is the second parameter of the personalised difficulty. Its main role is to improve the rotation of forging peers. A higher handicap is assigned to members with higher calculating power, so lesser machines can also compute blocks. As a consequence, there is no incentive on forging with powerful computers. Security can be achieved with less computing power than with pure PoW.</p>
-
-<p>The aim is to handicap the half that has authored most blocks (the most powerful half) to favour the other one. So, the handicap formula will use the median number of blocks authored by peers within the current window.</p><empty-line /><p>nbPersonalBlocksInFrame is the number of blocks authored by a single member within the current window.</p>
-
-<p>medianOfBlocksInFrame is the median number of blocks written by the calculating members during the same timeframe.</p>
-
-<p>a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))</p>
-
-<p>Let’s unwrap the formula:</p>
-
-<p>(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)</p>
-
-<p>is simply the ratio between the number of blocks authored by the peer and the median number of blocks. For example, if a peer has authored 9 blocks in the current window and the median is 5, then the ratio will be (9+1)/5 = 2. The MAX function allows us to ensure that the handicap has a value at least equal to 1.</p>
-
-<p>The Napierian Logarithm of this ratio prevents the handicap from becoming excluding. We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.</p>
-
-<p>If we wanted the handicap to be applied as soon as the median is reached, we would divide it by LN(1). The problem is that we have already set a minimum value of 1 with the MAX function. If we were to divide the ratio by LN(1) all calculating peers would have a handicap \&gt;= 1. In addition, is it really fair to handicap a member who is right on the median?</p>
-
-<p>That’s why we went for 1.189 rather than 1. A member has to be at least 18.9% above the median to be assigned a handicap. 18.9% is actually 16^(1/16), the difficulty factor between two levels of the proof work (hexadecimal hash).</p>
-
-<p>To conclude, you have to remember that :</p>
-
-<p>The handicap is indexed on the logarithm of the ratio to the median,</p>
-
-<p>Handicap is only applied on members whose ratio to the median is greater than the ratio between two levels of the proof-of-work’s difficulty.</p>
-
-<p>Conclusion</p>
-
-<p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.</p>
-
-<p>More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.</p>
-
-<p>The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :</p>
-
-<p>The freedom to choose your currency system: because money should not be imposed.</p>
-
-<p>The freedom to access resources: because we all should have access to economic &amp; monetary resources.</p>
-
-<p>The freedom to estimate and produce value: because value is a purely relative to each individual.</p>
-
-<p>The freedom to trade with the money: because we should not be limited by the avaible money supply.</p>
-
-<p>Those 4 economic freedoms should be understood together, not exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.</p>
-
-<p>Sources :</p>
-
-<p>Relative Theory of Money, S.Laborde, 2010: en.trm.creationmonetaire.info/</p>
-
-<p>Bitcoin Whitepaper, S.Nakamoto, 2008: bitcoin.org/bitcoin.pdf</p>
-
-<p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : lightning.network/lightning-network-paper.pdf</p>
-
-<p>The GNU Privacy Handbook, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335</p>
-
-<p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. cr.yp.to/papers.html#ed25519.</p>
-
-<p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : archive.org/details/PPCoinPaper</p>
-
-<p>Duniter Blockchain Protocol, v13, draft by Elois : git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</p>
-
-<p>The Sibyl Attack, J.R.Douceur: www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992</p><empty-line /><empty-line /><empty-line /><p>Bitcoin Whitepaper, S.Nakamoto, 2008: bitcoin.org/bitcoin.pdf↩</p>
-
-<p>Relative Theory of Money, S.Laborde, 2010: en.trm.creationmonetaire.info/↩</p>
-
-<p>OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335↩</p>
-
-<p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. cr.yp.to/papers.html#ed25519.↩</p>
-
-<p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : archive.org/details/PPCoinPaper↩</p>
-
-<p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : lightning.network/lightning-network-paper.pdf↩</p>
-
-<p>Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf↩</p>
-
-<p>Public key validation on GnuPG manual, M.Ashley, 1999 : www.gnupg.org/gph/en/manual.html#AEN335↩</p>
-
-<p>The Sibyl Attack, J.R.Douceur: www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf↩</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992↩</p>
-
-<p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992↩</p>
-
-<p>Pareto principle : en.wikipedia.org/wiki/Pareto_principle↩</p><empty-line />
-</section>
-
-</body>
-</FictionBook>
\ No newline at end of file
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-<article id="whitepaper" class="content">
-<h1 id="duniter-a-libre-currency-blockchain-generator.">Duniter: A libre currency blockchain generator.</h1>
-<h2 id="abstract">Abstract</h2>
-<p>Many currency principles involve non-equal rights to monetary creation between humans. We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human. This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution. Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process. We use a Web of Trust between living humans for identification. This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.</p>
-<h2 id="introduction">Introduction</h2>
-<p>Duniter is a software to create and manage “libre currencies”. Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :</p>
-<blockquote>
-<p>How should a currency be created to match the principle of equality between all humans, now and between generations ?</p>
-</blockquote>
-<p>The results of this demonstration implies a monetary creation :</p>
-<ul>
-<li>on a regular basis</li>
-<li>for each human being</li>
-<li>which amount has to be reassessed on fixed intervals according to a fixed formula.</li>
-</ul>
-<p>Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :</p>
-<pre><code>$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$</code></pre>
-<p>Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.</p>
-<p>The first currency created through Duniter is Ğ1, pronounced “June”. It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.</p>
-<h2 id="state-of-the-art-bitcoin-case">1. State of the art : Bitcoin case</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniter uses the crypto-currency concept introduced by Bitcoin<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a>, which is to use cryptographic tools such as signatures to create trustless digital currencies. Duniter fits this definition, but it has two completely different principles than Bitcoin : the Web of Trust and the Universal Dividend . These differences are on both monetary and technical aspects.</p>
-<h3 id="monetary-creation-a-space-time-asymmetry">1.1. Monetary creation of Bitcoin : a space-time asymmetry</h3>
-<p>Space-time asymmetry refers to the relative access of individuals to newly created money<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a>. Concretely, most existing currencies (c. 2020) are both spatially and temporally asymmetrical for their users. Let's take Bitcoin as an example to understand why.</p>
-<h4 id="spatial-asymmetry">1.1.1. Spatial asymmetry</h4>
-<p>When new Bitcoins are created, only some Bitcoin users (the miners) are given new Bitcoins, while everyone else get nothing. We believe this is the first injustice. However, some might say:</p>
-<blockquote>
-<p>"Miners used their electricity and time to get it!"</p>
-</blockquote>
-<p>... we would answer that this work should not have been rewarded by newly created Bitcoins. New units should be distributed to the whole community. Miners should be rewared another way, but not by money issuance. Of course, Bitcoin cannot create money through Basic Income since Bitcoin users are not strongly identified, and one might benefit from money creation multiple times if they owned several wallets. Duniter gets rid of this problem by identifying its users and creating the same amount of Basic Income to everyone.</p>
-<h4 id="temporal-asymmetry">1.1.2. Temporal-asymmetry</h4>
-<p>Bitcoin has an absolute limit of 21 million BTC (its unit of currency), which means ever fewer bitcoins will be created over time until no new BTC are being generated. So, once the first adopters have mined every bitcoin, how will future joiners get Bitcoins? Just like most of us do for Euros or Dollars: to get money, they will have to work for the ones who already own it.</p>
-<p>We believe this is the second injustice. Every member of a monetary community should be equal concerning monetary creation, and get the same relative amount of money over time, even if they are a late adopter. Duniter aims to fix this by making the Universal Dividend (a.k.a. UD) grow by the time according to precise rules, thus making members equal toward money issuance on a half-lifespan.</p>
-<p>Most currencies present one of these two asymmetries, including metal currencies and mutual credit, as exposed in the RTM.</p>
-<h4 id="a-solution">1.1.3. A solution</h4>
-<p>Bitcoin has taught us that it is possible to create a currency system allowing one to both create digital money and to exchange it without a central authority. What we need to change is the way money is issued so we finally have a symmetrical system. We need <strong>Bitcoin + Universal Dividend</strong>. But Universal Dividend implies that the community consists of only identified people. This is where the Web of Trust (WoT) comes into place.</p>
-<p>This concept, introduced by cryptography with the OpenPGP format<a href="#fn3" class="footnote-ref" id="fnref3"><sup>3</sup></a>, allows us to identify people in a decentralized manner. It works as follows: each person creates a personal identity that is linked to its cyptographic certificate. The identity must be confirmed by others members who use their own cryptographic key. It is that simple: people choose who is part of the community and who is not, not a central authority.</p>
-<p>However, Duniter will not use OpenPGP for its cryptographic features: Elliptic Curves<a href="#fn4" class="footnote-ref" id="fnref4"><sup>4</sup></a> will be used instead for the conciseness of its generated keys and its pratical advantages. Duniter has its own Web of Trust principles, that will be exposed later.</p>
-<h3 id="proof-of-work-mining-a-power-race">1.2. Proof-of-Work mining : a power race</h3>
-<p>In Bitcoin Model, the calculation and incentive principles cause a power race : new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers. This leads to a power race an places the control over the currency in the hands of the richest hardware owners. We want to make Duniter blockchain validation much less energy and hardware consuming while keeping a strong level of security. This will be further explained later. A consequence of this choice is the participation of low-end hardware in the Duniter network, leading to a better decentralization of blockchain validation.</p>
-<h4 id="what-about-proof-of-stake">1.2.1 What about Proof of Stake ?</h4>
-<p>Proof of stake consensus algorythm was first introduced in 2012<a href="#fn5" class="footnote-ref" id="fnref5"><sup>5</sup></a>. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a “stake” they would lose in case of cheat.</p>
-<p>At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle. Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.</p>
-<h2 id="duniters-blockchain">2. Duniters Blockchain</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniters Blockchain follows the basic principles of Bitcoins. This is essential for synchronization between peers, as to prevent double-spend attacks. However, Duniters Blockchain will store different informations than Bitcoins.</p>
-<p>The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:</p>
-<ul>
-<li>a former transaction (as in Bitcoin)</li>
-<li>a Universal Dividend (specific to Duniter).</li>
-</ul>
-<p>Duniters Web of Trust is also written in the Blockchain. The identity of each member gets registered much like transactions are, with a strong link to the time reference. Thus, the Blockchain is a representation of a space-time frame of reference, where “space” are members of the WoT and “time” the basic blockchain units : the blocks. On each point of time, one can determine which account is legitimate to create the UD, only with a blockchain analysis.</p>
-<h3 id="spam-countermeasures">2.1. Spam countermeasures</h3>
-<p>An issue of most cryptocurrency projects is to prevent the common ledger from growing too much. This would require nodes to have a lot of storage and computing power to be usable. In particular, we don’t want an attacker to be able to make the Blockchain grow too fast. Most projects implement transaction fees as a way to prevent this, making the attacker lose money. We don’t want to introduce this mean since a currency with automatic fees on transactions is no more neutral. Several countermeasuers against such spam attacks are implemented.</p>
-<!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
-<h4 id="minimum-output-amount">2.1.1. Minimum output amount</h4>
-<!-- This has to be implemented in DUBPv13. -->
-<p>Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.</p>
-<h4 id="limited-block-size-and-chainability">2.1.2. Limited block size and chainability</h4>
-<p>The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.</p>
-<p>With the same goal to prevent too many transactions to get registered, while transactions can be “chained” (refer to another transaction in the same block), the chainability of transactions is limited to 5.</p>
-<h3 id="scaling">2.2. Scaling</h3>
-<p>Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :</p>
-<ul>
-<li>Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don’t want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.</li>
-<li>Duniter’s aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.</li>
-</ul>
-<p>However, Duniter has assets that will help if the number of users and transactions grow.</p>
-<h4 id="dynamic-block-size">2.2.1 Dynamic block size</h4>
-<p>While Bitcoin has a fixed block size, Duniters blocks size can evolve. On low use of the blockchain, the maximal block size is 500 bytes. On high use of the blockchain, the maximal block size would be 110% of the average size of the current window blocks(see “personalised difficulty” part for more information). This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :</p>
-<pre><code>block_size &lt; max(500 ; CEIL(1.10 * (average block size))</code></pre>
-<h4 id="lightning-networks">2.2.2. Lightning Networks</h4>
-<p>The Lightning Networks<a href="#fn6" class="footnote-ref" id="fnref6"><sup>6</sup></a> allow almost instant and off-chain transactions. They were first implemented on Lightcoin, and are now on Bitcoin. One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain. The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks. While not available yet, this payment channel might get implemented when needed.</p>
-<h4 id="unit-base">2.2.3. Unit base</h4>
-<p>As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the <code>unitbase</code> is updated each time the UD value reaches 100.00 : it goes from <code>99.99*10^(unitbase)</code> to <code>10.00*10^(unitbase+1)</code>. All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.</p>
-<p>With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.</p>
-<h2 id="duniter-web-of-trust">3. Duniter Web of Trust</h2>
-<h3 id="duniter-wot-basic-principles">3.1. Basic Principles</h3>
-<p>In order to identify “members” accounts - which create monetary units - and other accounts, Duniter uses a Web of Trust. This can be summarized into few principles:</p>
-<ul>
-<li>Each account becomes a member if it received a minimal number of certifications - 5 for Ğ1 currency.</li>
-<li>Only members accounts can send certifications. Certifications have a limited lifespan.</li>
-<li>A certification indicates that the sender accepts the receiver as a legitimate identity.</li>
-</ul>
-<p>The aim of the WoT is to identify a blockchain account to a living human. According to Lauterbach et.al<a href="#fn7" class="footnote-ref" id="fnref7"><sup>7</sup></a>, the strengh of a relationship should be considered when building a vouch system. For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are. A certification represents a strong human relationship : one may certify a close relative, not an acquaintance. Each member has to accept this licence before being included in the WoT. Thus, if a member is part of an attack on the currency, they can be found by mutual relatives. Additional security rules occur to prevent cheat and attacks on a large scale.</p>
-<p>Note that non-members accounts can use the currency, but cannot create money. Non-members accounts can be used by individuals as secondary wallets, or by institutions.</p>
-<p>We were inspired by the OpenPGP Trust system<a href="#fn8" class="footnote-ref" id="fnref8"><sup>8</sup></a>. However, the OpenPGP trust principles aim at defining trust from a particular point of view while Duniter needs to identify humans for the whole community. To achieve this goal, while OpenPGP allows each user to tweak its trust parameters individually, Duniter sets rules in the “genesis” block for the whole community.</p>
-<h3 id="why-do-we-need-a-web-of-trust">3.2. Why do we need a Web of Trust ?</h3>
-<p>There are two reasons we need it :</p>
-<ol type="1">
-<li>To make sure that only one Universal Dividend is produced per member at each specified creation interval. In the Ğ1’s case this interval is set as daily <code>86 400</code> seconds, it is the <em>monetary parameter</em> known as <code>dt</code>.</li>
-<li>To identify the nodes hashing the blocks and assign each a personalised difficulty. This custom difficulty proof of work is there to avoid the blockchain’s validation mechanism becoming too centralised as is the case with many 'non-libre’ cryptocurrencies.</li>
-</ol>
-<blockquote>
-<p><strong>Monetary parameter</strong> : Each currency that use Duniter has its own blockchain whose behaviour is dictated by a set of ‘parameters’ defined in block zero - the so-called genesis block - that can be tweaked to achieve the desired results. At the time of writing the Whitepaper, the Duniter Blockchain Protocol (DUBP) has a total of 21 parameters of which 10 are for the WoT alone. We’ll focus on these 10.</p>
-<p>Suffice to say that in the Ğ1’s case, the DU is created every 24 hours - 86 400 seconds. This interval is set through the time derivative <code>dt</code> parameter and can have a different value in other implementations of the protocol.</p>
-</blockquote>
-<p>We want to make sure that each member can only have one account. As we all know, achieving zero-risk isn’t possible<a href="#fn9" class="footnote-ref" id="fnref9"><sup>9</sup></a>. Our goal is therefore not to create a WoT within which fraud would be absolutely impossible, but instead to discourage it. Here is a rewording of our goal in 4 smaller ones :</p>
-<ol type="1">
-<li>Make the certification process lengthy enough that all members exercise due diligence and are wary of risks.</li>
-<li>Make fraudulent acts as hard as we can to the extent that they become pointless.</li>
-<li>Ensure that any Sybil attacks have a negligible impact on the currency by ensuring that illegitimate double Universal Dividends have no significant bearing on the legitimate monetary mass</li>
-<li>Slow the growth of ‘Sybil regions’ to give enough time for the community to react and isolate the threat.</li>
-</ol>
-<blockquote>
-<p><strong>Sybil attack</strong> : A Sybil attack is an attack perpetrated on a reputation system through the creation of fake identities. A Web of Trust is a specific instance of a Reputation System.</p>
-</blockquote>
-<p>There are plenty of Sybil attack scenarios we can think of and just as many reasons why their perpetrators would want to carry them out. Our objective is that the configuration of the WoT protects both users and its IT backbone infrastructure against these attacks.</p>
-<p>This means that micro-attacks performed by small groups of individuals looking for personal enrichment are of no interest to us. The web’s role isn’t to deter these attacks, this being instead the role of the community. Just like the town you live in is responsible for providing your tap water and electricity but isn’t responsible for any burglaries, etc. Much in the same way, Duniter’s WoT guarantees us all a functional currency, but do not detect small fraud.</p>
-<h3 id="own-certification-system">3.3. The importance of having our own certification system</h3>
-<p>Centralized identification systems can achieve the goal we want. State Identification is an example. However, this has many drawbacks :</p>
-<ul>
-<li>The authority may have arbitrary criteria for identification, for example preventing people without an official state-provided identity or homeless people to be included in the WoT.</li>
-<li>Payment might be required to get identified, thus making the monetary creation not “free”.</li>
-<li>The authority is a point of failure for any attacker.</li>
-</ul>
-<p>It is of the utmost importance that we remain free from any state or corporation. The WoT is an answer to this criterium. To this day we depend only on the Internet and yet, were it to fail, there are already alternatives being tested around the world for a decentralised communication network.</p>
-<h3 id="graph-theory-vocabulary">3.4. A few foundational concepts on graph theory : a bit of vocabulary</h3>
-<ul>
-<li><p><strong>Graph</strong>: set of points -called ‘vertices’- joined by edges -called paths/walks-.</p></li>
-<li><p><strong>Simple graph</strong>: a graph with no loops and with no multiple edges. That is, each edge connects two distinct endpoints and no two edges have the same endpoints. A simple edge is an edge that is not part of a multiple adjacency -of edges-. In many cases, graphs are assumed to be simple unless specified otherwise.</p></li>
-<li><p><strong>Directed graph</strong>: a graph in which the edges have a distinguished direction, from one vertex to another. A directed edge can also be called a path or walk. Arrow A –&gt; B is therefore different from arrow B –&gt; A.</p></li>
-<li><p><strong>Endpoints</strong>: the edge with vertex A –&gt; B has A and B as endpoints, respectively as start and end of the path/walk.</p></li>
-<li><p><strong>Isolated vertex</strong>: a vertex whose degree is zero, that is, a vertex with no incident edges.</p></li>
-<li><p><strong>Degree of a vertex</strong>: number of its incident edges -in and out-.</p></li>
-<li><p><strong>Out-degree of vertex A</strong>: number of outbound edges / tail ends from A.</p></li>
-<li><p><strong>In-degree of vertex A</strong>: number of incoming edges / head ends to A.</p></li>
-</ul>
-<figure>
-<img src="./images/degres.jpg" alt="degrees of a vertex diagram" /><figcaption>degrees of a vertex diagram</figcaption>
-</figure>
-<ul>
-<li><strong>Path</strong>: -aka “walk”- path to follow to get from vertex A to vertex B.</li>
-</ul>
-<h3 id="definition-of-the-duniter-web-of-trust">3.5. Definition of the Duniter Web of Trust</h3>
-<p>The Duniter WoTs -one per currency- are simple directed graphs without isolated vertices. The vertices are the members and the edges are the certifications given and received.</p>
-<p><em>Directed</em> means that the responsibility of issuing a certification is unique and personal to the certifier. The trust they place in the receiver cannot be imposed in the other direction although in most circumstances both parties equally trust each other.</p>
-<p>In addition, all vertices are either currently active members or past-members. Past-member vertices are in a specific ‘deactivated state’ and can no longer issue or receive certifications although the ones already issued or received to/from other members are still considered ‘pending’ to avoid a collapse of the WoT. If these old members don’t come back into the WoT, their pending certifications will eventually expire and they will switch from ‘deactivated’ to ‘isolated’ vertices.</p>
-<p>To wrap up with old members, after a certain period of time - set in the currency’s parameters - their deactivated vertex is removed from the web and the associated identity is ‘revoked’. The person who owned the account can no longer use this identity but is free to join the web with another one.</p>
-<blockquote>
-<p><strong>Identity</strong> : An identity is a set of three pieces of information: a public key, a name and a blockstamp. A blockstamp points to a specific block in the chain. Its main use is to freeze the point in time at which an identity was created and to link this identity to a specific chain and a currency - each currency having its own blockchain.</p>
-<p>An identity can be in any one of 5 different status: pending, member, old member, revoked or excluded.</p>
-</blockquote>
-<p>Let’s take a simple example:</p>
-<pre><code>    A -&gt; B -&gt; C
-         |
-         \--&gt; D</code></pre>
-<p>If, for whatever reason, A were to lose its member status, the web would crumble and all other members would be excluded as a consequence. To avoid this, the certification from A –&gt; B will remain valid until its expiry date, leaving enough time for B to receive certifications from C or D.</p>
-<p>Because our WoT doesn’t have any isolated vertices, each new identity created needs to be pulled into the web with all of the certifications it has received, all in the same block. This calls for a temporary ‘buffer’ storage space for <strong>pending</strong> identities and the certifications they have received. This storage space is called ‘the pool’ of Duniter nodes, which we could also have called the ‘sandbox’ as that’s the name used in Duniter’s code. Duniter nodes inclued other ‘pools’ for other documents and metadata not mentioned here.</p>
-<h3 id="exploring-the-rules-behind-duniter-wot">3.6. Exploring the rules behind a Duniter Web of Trust</h3>
-<p>The Duniter WoTs - one per currency - works with a set of eight fundamental rules enforced through eleven different parameters. Ten of these parameters are set within the genesis block, the eleventh one - <code>msPeriod</code>- having being hard-coded in the Ğ1’s code subsequently.</p>
-<h4 id="distance-rule-and-referent-members-stepmax-and-xpercent">3.6.1. Distance rule and referent members (<code>stepMax</code> and <code>xPercent</code>)</h4>
-<p>These two parameters are closely linked and together define the ‘distance rule’. The ‘distance rule’ can only be described after defining what a ‘referent member’ is:</p>
-<blockquote>
-<p><strong>Referent member</strong>: member A is said to be ‘referent’ if and only if the total of their degrees are greater than or equal to <code>CEIL-N^-1/stepMax</code> where N is the total number of members. As the size of the web will grow this number will grow too, meaning it will take more certification issuances to become a referent member. The number of certifications needed to become a member shouldn’t change.</p>
-</blockquote>
-<p>Let’s now define the distance rule:</p>
-<blockquote>
-<p><strong>Distance rule</strong>: member A is said to observe this rule if and only if for a subset xPercent % of referent members R there exists a path of length less than or equal to <code>stepMax</code> between R and A.</p>
-</blockquote>
-<p>Referent members only exist so that the distance rule can take effect, they have no special privileges over non-referent members. In a perfect web, that is one in which each member has certified all members they legitimately can, all members would be referent members. However, because the web progressively grows in size and because members die and are replaced by new ones, there are always members at any given time <code>t</code> who haven’t yet certified all members they legitimately could. These members would hinder the evolution of the web if they were taken into account in the calculation of the distance rule and the web would effectively stop growing.</p>
-<p>Because verifying the application of the distance rule is calculation-greedy, it is only performed when a new identity gets confirmed into the web or an existing member gets renewed. There is an exception to this rule: the distance rule is not observed in the genesis block -when the web is first implemented.</p>
-<h4 id="rule-of-the-minimum-number-of-certifications-needed-sigqty">3.6.2. Rule of the minimum number of certifications needed (<code>sigQty</code>)</h4>
-<p>This is the simplest rule, it essentially says that each member must at any given time -meaning in any single block- have received at least <code>sigQty</code> active certifications. If, for whatever reason, member A were to have less than <code>sigQty</code> active certifications in a given block, they would cease to be a member and be required to publish a request for identity renewal.</p>
-<h4 id="the-membership-renewal-rule-msvalidity-msperiod-and-mswindow">3.6.3. The membership renewal rule (<code>msValidity</code>, <code>msPeriod</code> and <code>msWindow</code>)</h4>
-<p>Bear in mind that a membership doesn’t last a lifetime but instead has a lifespan set to <code>msValidity</code> seconds.</p>
-<p>Every single member -or old member who hasn’t revoked his identity or been excluded- can request a membership renewal so long as the last request was made more than <code>msPeriod</code> seconds ago. If a member has never requested a renewal, the date of last renewal is equal to the timestamp at which his membership was first created. A new request will be stored in the ‘pool’ for a maximum of <code>msWindow</code> seconds before it’s included in the blockchain. Once again, this can only happen once/if the member meets both the <code>siqQty</code> rule and the distance rule -if these criterion are already matched it’s just a case of waiting for a new block to be mined-.</p>
-<p>If a member hasn’t requested a renewal for longer than <code>msValidity</code> seconds, they automatically cease to be a member. From this moment on, the ex-member has another <code>msValidity</code> window to renew their membership. When this period of <code>2 × msValidity</code> runs out, the membership will expire and this identity will never be available for use again in the web. If the person so desires, they will have to publish new identity and membership documents and find enough certifiers, as any newcomer.</p>
-<h4 id="rule-of-certification-lifespan-sigvalidity">3.6.4. Rule of certification lifespan (<code>sigValidity</code>)</h4>
-<p>All certifications included in the blockchain expire <strong>sigValidity</strong> seconds after they were <strong>issued</strong>.</p>
-<blockquote>
-<p>/!\ The issuance and the inclusion of a certification in the blockchain occur at different times. When member A issues a certification at time t1, it gets stored in the pool starting at t1 and only finds its way into the blockchain at t2 when all of the web’s rules are observed. Several weeks can thus go by between t1 and t2!!!</p>
-</blockquote>
-<h4 id="rule-of-limited-supply-of-active-certifications-sigstock">3.6.5. Rule of limited supply of active certifications (<code>sigStock</code>)</h4>
-<p>By ‘active certifications’ we refer to certifications included in the blockchain and that haven’t yet expired.</p>
-<p>The total of active certifications issued by any member at any single time must be less than or equal to <code>sigStock</code>. When this threshold is reached the member will have to wait for one of his active certifications to expire before he/she can issue a new one.</p>
-<h4 id="rule-of-the-time-period-between-two-certification-issuances-sigperiod">3.6.6. Rule of the time period between two certification issuances. (<code>sigPeriod</code>)</h4>
-<p>As soon as a certification issued by member A gets included in the blockchain, they will be unable to issue a new one before another <code>sigPeriod</code> seconds.</p>
-<h4 id="expiry-of-a-certification-issuance-sigwindow">3.6.7. Expiry of a certification issuance (<code>sigWindow</code>)</h4>
-<p>When a certification is issued by member A, it will be stored in the ‘pool’ for a maximum of <code>sigWindow</code> seconds. If the certification hasn’t been included in the blockchain by then, it will be cancelled and the member’s <code>sigStock</code> will be repleted by one.</p>
-<h4 id="lifespan-of-a-pending-identity-idtywindow">3.6.8. Lifespan of a ‘pending’ identity (<code>idtyWindow</code>)</h4>
-<p>When a new identity is created, it is stored in the ‘pool’ for a maximum of <code>idtyWindow</code> seconds. If the person hasn’t achieved member status by then, the certification will simply be cancelled.</p>
-<h3 id="details-on-some-of-the-wots-peculiarities-at-the-genesis-block">3.7. Details on some of the WoT’s peculiarities at the genesis block</h3>
-<p>The aforementioned rules can only be enforced with an existing web. They cannot be observed when first creating the web, that is when defining the genesis block.</p>
-<p>Only rules 2 and 5 can be observed at the genesis block.</p>
-<p>The genesis block has to be manually created by the founding members. In practice this means that there must be a choice on which identities to include on the premise that all of them observe rules 2 and 5. In addition, the genesis block must be signed with the private key of one of these identities.</p>
-<p>As soon as the genesis block has been created, the other identities can start mining the blockchain and the member who created block #0 effectively looses the decision power he had at creation.</p>
-<h3 id="why-these-rules-and-application-cases-in-the-g1">3.8. Why these rules and application cases in the Ğ1</h3>
-<h4 id="distance-and-maximum-size">3.8.1. Distance and maximum size</h4>
-<p>The distance rule is there to curb the maximum size of a Sybil region as well as that of the monetary community as a whole. The <code>xpercent</code> parameter prevents the creation of a ‘faction’ that could take hold of the blockchain.</p>
-<figure>
-<img src="./images/wot-sybil.jpg" alt="Sybil region" /><figcaption>Sybil region</figcaption>
-</figure>
-<p>The Sybil regions are isolated from the rest of the graph in the sense that they can only receive certifications from other ill-intentioned Sybil members. As a consequence, the shortest edge/path between a legitimate member and a Sybil one has to have the attack’s author as an endpoint. The maximum depth the Sybil region can attain is therefore contingent on the distance between the attacking edge-s- and the xpercent% closest referent members, this distance is known as <code>stepAttackers</code>. The maximum size of a Sybil region created by <code>sigQty</code> members depends on the L parameter, defined as <code>L = sigQty/sigStock</code>:</p>
-<pre><code>MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)</code></pre>
-<p>The maximum size of the Web of Trust is given by the following formula:</p>
-<pre><code>WoTmax = (sigStock)*L^(stepMax-1)</code></pre>
-<p>However we know for a fact that members will never use all of their available certifications. According to Dunbar<a href="#fn10" class="footnote-ref" id="fnref10"><sup>10</sup></a>, on average, one is able to maintain relationships to around 150 people. Being conservative, we will consider that on average, each person will certify 50 accounts. We can calculate the size of the average web of trust <code>WoTavg</code> :</p>
-<pre><code>WoTavg= (50)*(sigQty/50)^(stepMax-1)</code></pre>
-<p>Our goal with the Ğ1 is to create a community of about one million members to test the consequences of a libre monetary system. Let’s see how we can tweak the pair of sigQty and stepMax- to reach this size:</p>
-<figure>
-<img src="./images/wot-moy.png" alt="Average WoT size graph as a function of sigQty and stepMax" /><figcaption>Average WoT size graph as a function of sigQty and stepMax</figcaption>
-</figure>
-<p>The maximum size of a Sybil region grows linearly with <code>sigQty</code> but exponentially with <code>stepMax</code>. Logic has it that we need to keep <code>stepMax</code> as low as possible to ensure sufficient strength to the web. The above graph shows that the lowest value of <code>stepMax</code> for a web of a million members is of 5. This is an order of magnitude and is likely to be much higher in reality, we cannot measure it for sure.</p>
-<p>For <code>sigQty</code> we can choose a value of <strong>4</strong> for a web of <strong>1.5 million members</strong> or <strong>5</strong> for <strong>half a million members</strong>. Bear in mind these are gross figures and could be significantly higher, we are talking anywhere between 1 and 10 million in reality. Calculating WOTavg gives us a pretty good idea of how the web would scale bearing in mind that it considers all members are referent members too -which isn’t the case as explained previously-. Hence the maximum size of the web is likely larger, a ballpark figure of half a million is enough for now especially knowing that the smaller <code>sigQty</code> is, the easier it is to launch a Sybil attack -it’s easier to find four accomplices than five-. For security reasons we have settled on five:</p>
-<pre><code>stepMax = 5
-sigQty = 5
-sigStock \&gt;= 50</code></pre>
-<p>The maximum size of a Sybil region therefore is:</p>
-<pre><code>(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))</code></pre>
-<p>with sigStock = 50 we have a Sybil region of:</p>
-<pre><code>45*(1-10^(5-stepAttackers))/(-9)</code></pre>
-<p>A good practice for protecting the web is to maximise <code>stepAttackers</code>. That’s why we decided that referent members in the genesis block had to be at least four steps away from each other.</p>
-<p>Another way to keep a Sybil attack at bay, were it slow enough for members to notice it, would be for referent members to ‘stretch’ the web intentionally to limit the growth of the region by ensuring that the attackers’ legitimate certifications received in the first place aren’t renewed. But what if bot accounts were created and certified each other super fast and following all rules, how would we counter that? By introducing a minimum length of time between two certifications!</p>
-<h4 id="time-is-our-friend">3.8.2. Time is our friend</h4>
-<p>To help us deter a Sybil attack, we’ve decided to impose a minimum period of time between any two certifications issued from a single account. This parameter called <code>sigPeriod</code> affords us a greater chance to detect the formation of a ‘hostile’ faction.</p>
-<p>Here is a graph showing the evolution of a Sybil region with the variation of <code>sigPeriod</code>. The simulation considers that honest members and attackers both issue a certification each <code>sigPeriod</code> interval, in days:</p>
-<figure>
-<img src="./images/impact_sig_period.png" alt="size of the WoT according to sigPeriod and stepAttackers" /><figcaption>size of the WoT according to sigPeriod and stepAttackers</figcaption>
-</figure>
-<p>As we see, there is a strong link between the growth speed of the region and <code>sigPeriod</code>. As evidenced here, we need a <code>sigPeriod</code> high enough in order to ensure that the legitimate web can grow at least as fast as a Sybil region. In addition, the higher <code>sigPeriod</code> is, the more members will exercise their certification power gingerly, the action coming at a higher ‘cost’.</p>
-<p>There are numerous advantages to giving <code>sigPeriod</code> a high value and no technical barriers to it, hence our choice of five days.</p>
-<p>We could have also gone for one week for the sake of simplicity. However there is an underlying idea behind our choice which was quite simply the pace of today’s life. Certifying someone can be a lengthy process as one needs to make sure they are correctly applying the Ğ1 licence and people nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea to allow one to certify at the end of every working week -five days- instead of a whole calendar one.</p>
-<h4 id="trust-me-now-trust-me-forever-sigvalidity-msvalidity">3.8.3. Trust me now, trust me forever ? (<code>sigValidity</code>, <code>msValidity</code>)</h4>
-<p>There would be two main drawbacks to a lifetime membership in the Ğ1’s Web of Trust:</p>
-<ul>
-<li>First of all, some members will pass and those accounts should no longer produce the Universal Dividend.</li>
-<li>Secondly it is of the utmost importance that ‘rogue’ accounts can be excluded from the web at some point.</li>
-</ul>
-<p>To achieve this, certifications have a limited lifespan. Members need to seek renewal from their peers after <code>sigValidity</code> time. On the other hand, this time can’t be too short that members would spend more time seeking renewal than they would exchanging in the currency. Furthermore, a certification with too short a lifespan would foster careless certifying behaviours. The act of certifying must have a high-enough ‘perceived’ cost to make it feel like an important act. Lastly, we also wanted this lifespan to be easy to remember. Historically speaking, we first settled on the values of <code>sigPeriod</code> and <code>sigStock</code>, meant one could issue all of their certifications in 495 days, one year was therefore not long enough. We deemed three years to be too much and that’s how we agreed on two years in the end.</p>
-<p>Thinking that a deceased member could continue producing the UD for two long years without anyone benefitting from it was also something we needed to address. We chose a value of one year for <strong>msValidity</strong>. The act of renewing every year is done through one of the clients interacting with the blockchain, through a simple click on a button. This parameter is less important than others and is mostly there to ‘prune’ the web of past or inactive members who don’t renew their membership.</p>
-<h4 id="keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow">3.8.4. Keeping the pools free of information glut (<code>idtyWindow</code>, <code>sigWindow</code>, <code>msWindow</code>)</h4>
-<p>The pools need to be cleaned up on a regular basis to avoid them clogging up with information and to ensure that machines with less calculating power can still run a Duniter node.</p>
-<p>To achieve this, identities with pending membership approval and the corresponding certifications have to remain the shortest time possible in the pool while still having a chance of making it into the blockchain.</p>
-<p>For the Ğ1, our opinion was that two months would be enough for all potential certifiers to agree on a specific identity to certify. We also wanted a time period that would be easy enough to remember by all. We settled on two months, and gave this value to all three parameters <code>idtyWindow</code>, <code>sigWindow</code> and <code>msWindow</code>.</p>
-<h4 id="avoiding-single-members-from-knowing-too-many-people-sigstock">3.8.5. Avoiding single members from ‘knowing too many people’ (<code>sigStock</code>)</h4>
-<p>We considered that on average, each person will certify 50 people. However, we know for a fact that some members will use more than 50 certifications. The maximum social network of one individual is around 150 people<a href="#fn11" class="footnote-ref" id="fnref11"><sup>11</sup></a>. Being conservative, we settled on a maximum certification number <code>sigstock</code> of 100. Since <code>sigStock</code>’s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.</p>
-<h4 id="avoiding-locking-minorities-xpercent">3.8.6. Avoiding locking minorities (<code>xpercent</code>)</h4>
-<p>It’s easy enough to become a referent member, one of the Sybil strategies could therefore be to create a region of referent members. Such a region would grow slower than otherwise but could confer a locking power to its members by using the distance rule. That’s why the distance rule cannot be calculated on 100% of the referent members. Hence the introduction of the <code>xpercent</code> parameter which defines the percentage of referent members needing to be less than five edges -steps- from each other.</p>
-<p>This percentage needs to be low enough to prevent the formation of a locking minority -referent Sybil members being too far from legitimate referent members-. On the other hand, it needs to be high enough so as to restrict the maximum size of the Sybil region through the distance rule. The <code>xpercent</code> parameter was one of the hardest to define, therefore we might decide to change its value during the Ğ1 experiment.</p>
-<p>We were inspired by the Pareto principle<a href="#fn12" class="footnote-ref" id="fnref12"><sup>12</sup></a>: if at least 20% of members give good density to the web, 80% of the referent members will be five or less steps from any other member -referent or not-. The maximum value for <code>xpercent</code> is therefore 80%, anything above that and the distance rule could be too restrictive for legitimate use cases. With security our top concern, we chose the maximum value of 80%.</p>
-<h4 id="spam-protection-with-msperiod">3.8.7. Spam protection with (<code>msPeriod</code>)</h4>
-<p>This parameter stands out a bit on its own, as it was added after the genesis block. It is there to protect the Duniter P2P infrastructure against ‘spam’ attacks. We had to think of a strategy against attacks such as high-frequency membership renewal requests -i.e: in every block, every five minutes- or worse still, hundreds of these requests per minute to flood the Duniter nodes. Without such limits, nodes are supposed to address all renewal requests, even in cases where they were last published five minutes ago! The <code>msPeriod</code> parameter was given the same value as <code>idtyWindow</code>, <code>sigWindow</code> and <code>msWindow</code>, i.e. two months.</p>
-<h2 id="proof-of-work-with-personalized-difficulty">4. Proof of Work with personal difficulty</h2>
-<p>As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.</p>
-<p>This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each “winning” member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.</p>
-<p>Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.</p>
-<p>One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an “ecological” PoW ?</p>
-<!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
-<h3 id="why-proof-of-work">4.1. Why do we need Proof of Work ?</h3>
-<p>Duniter nodes share a database as part of a p2p environment. The proof of work (PoW) allows machines to synchronize with each other. In Duniter’s case, the blockchain is our database, and acts as a ledger keeping a trace of all transactions, status of the WoT and more. How can we let several machines add data (ie: a transaction) at the same time? In addition, how do we settle on how much time has gone by since the blockchain was last updated? Agreement on time is of the utmost importance as we want to create Universal Dividends on a regular basis, and keep track of membership status, both in human time.</p>
-<p>Proof-of-work provides a clever solution to both problems:</p>
-<ol type="1">
-<li><p>Any machine can write into the blockchain (create a new block) but is only authorised to do so if it has previously solved a mathematical equation that require a certain amount of work. The challenge has to be hard enough to prevent two machines to solve it at the same time, ensuring the unicity of a block’s creator.</p></li>
-<li><p>Solving this challenge takes a certain amount of time, which depends on the calculating power of the whole network. This provides a common ground for defining the needed time reference. A block time is set (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to get an average duration corresponding to this block time.</p></li>
-</ol>
-<h3 id="only-members-can-mine">4.2. Only members can “mine”</h3>
-<p>One of Duniter’s major differences with other PoW-based cryptocurrencies is that only members are allowed to author blocks. Each block is signed with the member’s private key, allowing the algorithm to determine a personalised difficulty.</p>
-<p>This personalised difficulty eliminates the rat-race for the most sophisticated and powerful mining equipment. Another benefit is the fact that no “supercomputer” can take control of the blockchain. Lastly, Duniter implements a rotation in forging members thanks to this personalized difficulty.</p>
-<p>This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies. Members can mine with anything from a raspberry pi to a privacy-first internet cube.</p>
-<h3 id="how-does-duniter-pow-work">4.3. How does it work ?</h3>
-<h4 id="the-hash">4.3.1. The hash (aka digest)</h4>
-<p>Example of a valid hash:</p>
-<pre><code>00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653</code></pre>
-<p>As you can see this hash starts with five zeros which was very hard to achieve and took a lot of work for someone’s computer. Hence the term “proof of work”.</p>
-<h4 id="common-difficulty">4.3.2. The common difficulty</h4>
-<p>A common difficulty is needed to settle on a yardstick for our time reference. Its role is to make sure the blockchain moves forward at a steady pace - one block every <code>avgGenTime</code> seconds, <code>avgGenTime</code> being one of the 20 parameters behind the Duniter protocol-.</p>
-<p>This difficulty’s initial value can be set to any arbitrary value (<code>70</code> in Duniter <code>v1.5.x</code>) and then acts as a spring, regulating blocktime creation by increasing itself if the creation interval drops under <code>avgGenTime</code> and vice-versa.</p>
-<h5 id="how-is-difficulty-applied">4.3.2.1. How is difficulty applied ?</h5>
-<p>The numeric value of difficulty is taken from an array of possible hashes out of all possible hashes. In DUBPv13 the hash of a block is its sha256 hexadecimal hash.</p>
-<p>To understand the difficulty, we make a euclidiean division of the difficulty by 16.</p>
-<p>Here’s an example with a difficulty value of 70 :</p>
-<pre><code>70 // 16 = 4 with a remainder of 6. </code></pre>
-<p>The valid hashes are the ones starting with four zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation). The valid hashes are then written as starting with : <code>0000[0-9]</code>. This is a bit different from Bitcoin, where the difficulty is only ruled by the number of zeroes.</p>
-<h5 id="the-nonce">4.3.2.2. The Nonce</h5>
-<p>When a member is forging a new block, his computer freezes the block’s content and changes the Nonce until the hash reaches the required number of zeroes.</p>
-<p>The nonce allows us to mine a new block by finding a hash. The hash value allows us to determine the difficulty level of the proof-of-work performed. Examples of possible Nonce values:</p>
-<ul>
-<li>10100000112275</li>
-<li>10300000288743</li>
-<li>10400000008538</li>
-<li>10700000079653</li>
-<li>10300000070919</li>
-</ul>
-<p>In reality the <code>Nonce</code> value follows a pre-determined format akin to <code>XYY00000000000</code>. The Nonce’s value isn’t the number of attempts but rather a value within a set of possible ones. This is how the Nonce is built:</p>
-<ul>
-<li><p>X is a number assigned to a specific peer. Let’s assume that someone has several nodes each with the same private key, this would lead to possible collisions if this person were to mine the same block with different nodes. Each <del>block</del> <strong>node ?</strong> will therefore have its own unique X to prevent this from happening.</p></li>
-<li><p>Y is the number of cores of the processor. The Nonce starting with <code>107[…]</code> belongs to a seven cores processor, while <code>199[...]</code> could be the proof generated by a 99 cores processor.</p></li>
-</ul>
-<p>The rest of the Nonce, the part that follows after the XYY, is the numerical space for this individual node and is unique to each of the CPU’s core. This space is comprised of eleven digits (<code>00000000000</code>). For the sake of accuracy, we use the term CPU in the wider sense, it can be understood as a bi-CPU for example. We take into consideration the number of cores for the resulting PoW.</p>
-<h3 id="personalised-difficulty">4.4. Personalised difficulty</h3>
-<p>Earlier in this article, we explained that the personalised difficulty is the new and key concept that sets Duniter apart from other PoW-based cryptocurrencies.</p>
-<p>Here is how this personalised difficulty is calculated and assigned:</p>
-<p>It is determined by a combination of two different constraints with complimentary roles: the <strong>exclusion factor</strong> and the <strong>handicap</strong>.</p>
-<p>Let <code>powMin</code> be the common difficulty, <code>exFact</code> a member’s exclusion factor and <code>handicap</code> their handicap. This member’s personalised difficulty <code>diff</code> is:</p>
-<pre><code>diff = powMin*exFact + handicap</code></pre>
-<h4 id="the-exclusion-factor">4.4.1. Understanding <code>exFact</code>, the exclusion factor</h4>
-<p>Members who have never produced blocks or haven’t for quite some time are assigned an exclusion factor of <code>1</code>. Their personalised difficulty is therefore simply the sum of <code>powMin + handicap</code>.</p>
-<p>Before reading on, let’s precise the role of this exclusion factor. When a member adds a block to the chain, his <code>exFact</code> jumps up from one to a very high value, to prevent them from forging other blocks immediately after and taking control of the blockchain.</p>
-<p>The exclusion factor will then rapidly return to one. This delay is expressed as a number of blocks. It is calculated as a proportion of the number of members forging. In the Ğ1’s case, this proportion is 1/3, meaning that if there are fifteen members currently forging, the member’s exclusion factor will drop down to one after five blocks.</p>
-<h5 id="what-is-intended-by-the-number-of-members-forging">4.4.1.1. What is intended by “the number of members forging” ?</h5>
-<p>We mean the number of members trying to create the next block. In reality, there is no way to precisely know how many members are calculating at any given time, because it is impossible to view the entire network. But we need this information, whithout which assigning a personalised difficulty is impossible. To achieve this, Duniter looks back at the blockchain and assumes that there is as much members forging as those who have found at least one block in the last blocks in the current window, minus the very last one.</p>
-<h5 id="current-window">4.4.1.2. Current window</h5>
-<p>We use the concept of <strong>current window</strong>. The current window is the number of blocks we look back at to determine how many members are forging. Let’s see how it works:</p>
-<ul>
-<li><p><code>issuersFrame</code> is the size of the current window in blocks.</p></li>
-<li><p><code>issuersCount</code> the number of members who have calculated at least one block during the current window.</p></li>
-</ul>
-<p>Both <code>issuersFrame</code> and <code>issuersCount</code> are block fields. When first starting a blockchain, the very first block has an <code>issuersFrame=1</code> and an <code>issuersCount=0</code>. The genesis block is excluded as there are no members in the current window!</p>
-<p>From the second block onwards (block #1) we track the variation of <code>issuersCount</code>. The member having mined block #0 enters the current window and in block #1 we will therefore mention <code>issuersCount=1</code>.</p>
-<p><code>issuersFrame</code> then varies as follows:</p>
-<ul>
-<li>if <code>issuersCount</code> increases by N (with a maximum step of N = 1), then <code>issuersFrame</code> will increase by one unit over a period of 5N blocks.</li>
-<li>Conversely, if <code>issuersCount</code> decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then <code>issuersFrame</code> will decrease by one unit during 5Y blocks.</li>
-<li>When such events overlap, <code>issuersFrame</code> evolves as so :</li>
-</ul>
-<table>
-<thead>
-<tr class="header">
-<th>bloc</th>
-<th>event</th>
-<th>issuersFrame</th>
-</tr>
-</thead>
-<tbody>
-<tr class="odd">
-<td>T</td>
-<td>Babar writes a block and enters issuersCount</td>
-<td>160</td>
-</tr>
-<tr class="even">
-<td>T+1</td>
-<td>Celeste leaves issuersCount</td>
-<td>160 +1 = 161</td>
-</tr>
-<tr class="odd">
-<td>T+2</td>
-<td>N/a</td>
-<td>161 +1 -1 = 161</td>
-</tr>
-<tr class="even">
-<td>T+3/4/5</td>
-<td>N/a</td>
-<td>161 +1 -1 = 161</td>
-</tr>
-<tr class="odd">
-<td>T+6</td>
-<td>N/a</td>
-<td>161 -1 = 160</td>
-</tr>
-</tbody>
-</table>
-<p>The calculation can be found under rules <a href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe">BR_G05</a> and <a href="https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar">BR_G06</a> of the DUP protocol.</p>
-<h5 id="exfact-and-the-personalised-difficulty">4.4.1.3. exFact and the personalised difficulty</h5>
-<p>We explained that <code>exFact</code> spikes immediately after the member has found a block. It decreases then rapidly to <code>1</code> after a number of blocks equal to <code>1/3 * issuersCount</code>. Let’s see precisely how we calculate <code>exFact</code>:</p>
-<ul>
-<li><p><code>nbPreviousIssuers</code> is the value of issuersCount at the last block <code>N</code> found by the member.</p></li>
-<li><p><code>nbBlocksSince</code> is the number of blocks found by the rest of the network since block <code>N</code>.</p></li>
-<li><p><code>percentRot</code> is the number of <em>not excluded</em> peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.</p></li>
-</ul>
-<pre><code>a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]</code></pre>
-<p>The FLOOR is a simple truncate function. For <code>exFact</code> to exclude the member, we need :</p>
-<pre><code>(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) &gt;= 2</code></pre>
-<p>We can see that the member is not excluded if <code>nbBlocksSince</code> is greater than 1/3 of the calculating members. Take as an example <code>nbPreviousIssuers = 6</code> and <code>nbBlocksSince = 3</code>:</p>
-<pre><code>(0.67* 6 / )1 + 3)) = 1.005 -&gt; exFact = 1</code></pre>
-<p>However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:</p>
-<pre><code>(0.67 * 6 / (1 + 1)) = 2.01 -&gt; exFact = 2</code></pre>
-<p>Moreover if the last block was authored by the said member, then:</p>
-<pre><code>nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers</code></pre>
-<p>ExFact value increases according to the number of members calculating. Thus, if there is enough members calculating, even mining farms would be excluded. We have therefore succeeded in our intent to deter attempts to seize the blockchain and its currency.</p>
-<p>However, at any time <code>t</code>, the two-thirds of calculating members all have an exclusion factor of <code>1</code>, even though they might not all have the same computational power at hand. If the personalised difficulty only took into account the exclusion factor, then only the members with the highest computational power from the remaining third would be able to author new blocks and the other 2/3s would almost always be excluded. Lesser machines wouldn’t stand a chance…</p>
-<h4 id="the-handicap">4.4.2. The handicap</h4>
-<p>The handicap is the second parameter of the personalised difficulty. Its main role is to improve the rotation of forging peers. A higher handicap is assigned to members with higher calculating power, so lesser machines can also compute blocks. As a consequence, there is no incentive on forging with powerful computers. Security can be achieved with less computing power than with pure PoW.</p>
-<p>The aim is to handicap the half that has authored most blocks (the most powerful half) to favour the other one. So, the handicap formula will use the median number of blocks authored by peers within the current window.</p>
-<ul>
-<li><p><code>nbPersonalBlocksInFrame</code> is the number of blocks authored by a single member within the current window.</p></li>
-<li><p><code>medianOfBlocksInFrame</code> is the median number of blocks written by the calculating members during the same timeframe.</p></li>
-</ul>
-<pre><code>a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))</code></pre>
-<p>Let’s unwrap the formula:</p>
-<pre><code>(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)</code></pre>
-<p>is simply the ratio between the number of blocks authored by the peer and the median number of blocks. For example, if a peer has authored <code>9</code> blocks in the current window and the median is <code>5</code>, then the ratio will be <code>(9+1)/5 = 2</code>. The MAX function allows us to ensure that the handicap has a value at least equal to <code>1</code>.</p>
-<p>The Napierian Logarithm of this ratio prevents the handicap from becoming excluding. We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.</p>
-<p>If we wanted the handicap to be applied as soon as the median is reached, we would divide it by <code>LN(1)</code>. The problem is that we have already set a minimum value of <code>1</code> with the MAX function. If we were to divide the ratio by <code>LN(1)</code> all calculating peers would have a handicap <code>\&gt;= 1</code>. In addition, is it really fair to handicap a member who is right on the median?</p>
-<p>That’s why we went for <code>1.189</code> rather than <code>1</code>. A member has to be at least <code>18.9%</code> above the median to be assigned a handicap. 18.9% is actually 16^(1/16), the difficulty factor between two levels of the proof work (hexadecimal hash).</p>
-<p>To conclude, you have to remember that :</p>
-<ul>
-<li>The handicap is indexed on the logarithm of the ratio to the median,</li>
-<li>Handicap is only applied on members whose ratio to the median is greater than the ratio between two levels of the proof-of-work’s difficulty.</li>
-</ul>
-<h2 id="conclusion">Conclusion</h2>
-<!-- source : https://duniter.org/en/theoretical/ -->
-<p>Duniter’s Blockchain can be compared to Bitcoin’s : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.</p>
-<p>More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.</p>
-<p>The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :</p>
-<ul>
-<li>The freedom to choose your currency system: because money should not be imposed.</li>
-<li>The freedom to access resources: because we all should have access to economic &amp; monetary resources.</li>
-<li>The freedom to estimate and produce value: because value is a purely relative to each individual.</li>
-<li>The freedom to trade with the money: because we should not be limited by the avaible money supply.</li>
-</ul>
-<p>Those 4 economic freedoms should be understood together, not exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.</p>
-<h2 id="sources">Sources :</h2>
-<ul>
-<li>Relative Theory of Money, S.Laborde, 2010: <a href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a></li>
-<li>Bitcoin Whitepaper, S.Nakamoto, 2008: <a href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a></li>
-<li>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : <a href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a></li>
-<li>The GNU Privacy Handbook, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a></li>
-<li>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. <a href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.</li>
-<li>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : <a href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a></li>
-<li>Duniter Blockchain Protocol, v13, draft by Elois : <a href="https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md">git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md</a></li>
-<li>The Sibyl Attack, J.R.Douceur: <a href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a></li>
-<li>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992</li>
-</ul>
-</article>
-</main>
-</body>
-</html>
-<section class="footnotes">
-<hr />
-<ol>
-<li id="fn1"><p>Bitcoin Whitepaper, S.Nakamoto, 2008: <a href="https://bitcoin.org/bitcoin.pdf">bitcoin.org/bitcoin.pdf</a><a href="#fnref1" class="footnote-back">↩</a></p></li>
-<li id="fn2"><p>Relative Theory of Money, S.Laborde, 2010: <a href="http://en.trm.creationmonetaire.info/">en.trm.creationmonetaire.info/</a><a href="#fnref2" class="footnote-back">↩</a></p></li>
-<li id="fn3"><p>OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a><a href="#fnref3" class="footnote-back">↩</a></p></li>
-<li id="fn4"><p>High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. <a href="https://cr.yp.to/papers.html#ed25519">cr.yp.to/papers.html#ed25519</a>.<a href="#fnref4" class="footnote-back">↩</a></p></li>
-<li id="fn5"><p>PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &amp; S.Nadal, 2012 : <a href="https://archive.org/details/PPCoinPaper">archive.org/details/PPCoinPaper</a><a href="#fnref5" class="footnote-back">↩</a></p></li>
-<li id="fn6"><p>The Bitcoin Lightning Network, J.Poon &amp; T.Dryja, 2016 : <a href="http://lightning.network/lightning-network-paper.pdf">lightning.network/lightning-network-paper.pdf</a><a href="#fnref6" class="footnote-back">↩</a></p></li>
-<li id="fn7"><p>Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: <a href="http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf">snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf</a><a href="#fnref7" class="footnote-back">↩</a></p></li>
-<li id="fn8"><p>Public key validation on GnuPG manual, M.Ashley, 1999 : <a href="https://www.gnupg.org/gph/en/manual.html#AEN335">www.gnupg.org/gph/en/manual.html#AEN335</a><a href="#fnref8" class="footnote-back">↩</a></p></li>
-<li id="fn9"><p>The Sibyl Attack, J.R.Douceur: <a href="https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf">www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf</a><a href="#fnref9" class="footnote-back">↩</a></p></li>
-<li id="fn10"><p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992<a href="#fnref10" class="footnote-back">↩</a></p></li>
-<li id="fn11"><p>Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992<a href="#fnref11" class="footnote-back">↩</a></p></li>
-<li id="fn12"><p>Pareto principle : <a href="https://en.wikipedia.org/wiki/Pareto_principle">en.wikipedia.org/wiki/Pareto_principle</a><a href="#fnref12" class="footnote-back">↩</a></p></li>
-</ol>
-</section>
diff --git a/build/whitepaper_fr.md b/build/whitepaper_fr.md
deleted file mode 100644
index 6ab8bfa02502b162867261b90d3e11155ea90924..0000000000000000000000000000000000000000
--- a/build/whitepaper_fr.md
+++ /dev/null
@@ -1,1178 +0,0 @@
-Duniter: A libre currency blockchain generator.
-=======================================
-
-## Abstract {#abstract}
-
-Many currency principles involve non-equal rights to monetary creation between humans.
-We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human.
-This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution.
-Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process.
-We use a Web of Trust between living humans for identification.
-This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.
-
-
-
-## Introduction {#introduction}
-
-Duniter is a software to create and manage "libre currencies". Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :
-
-> How should a currency be created to match the principle of equality between all humans, now and between generations ?
-
-The results of this demonstration implies a monetary creation :
-
-* on a regular basis
-* for each human being
-* which amount has to be reassessed on fixed intervals according to a fixed formula.
-
-Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :
-
-```
-$$ UD(t+1) = UD(t) + c²*( {M(t) \over N(t) }) $$
-```
-Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.
-
-The first currency created through Duniter is Ğ1, pronounced "June". It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.
-
-
-## 1. State of the art : Bitcoin case {#state-of-the-art-bitcoin-case}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter uses the crypto-currency concept introduced by Bitcoin[^BTC_whitepaper], which is
-to use cryptographic tools such as signatures to create trustless digital
-currencies. Duniter fits this definition, but it has two completely
-different principles than Bitcoin : the Web of Trust and the Universal
-Dividend . These differences are on both monetary and technical aspects.
-
-[^BTC_whitepaper]: Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-
-### 1.1. Monetary creation of Bitcoin : a space-time asymmetry {#monetary-creation-a-space-time-asymmetry}
-
-Space-time asymmetry refers to the relative access of individuals to
-newly created money[^RTM]. Concretely, most existing currencies (c. 2020) are
-both spatially and temporally asymmetrical for their users. Let\'s take
-Bitcoin as an example to understand why.
-
-[^RTM]: Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-
-#### 1.1.1. Spatial asymmetry {#spatial-asymmetry}
-
-When new Bitcoins are created, only some Bitcoin users (the miners)
-are given new Bitcoins, while everyone else get nothing. We believe
-this is the first injustice. However, some might say:
-
-> \"Miners used their electricity and time to get it!\"
-
-\... we would answer that this work should not have been rewarded by
-newly created Bitcoins. New units should be distributed to the whole
-community. Miners should be rewared another way, but not by
-money issuance. Of course, Bitcoin cannot create money through Basic
-Income since Bitcoin users are not strongly identified, and one might
-benefit from money creation multiple times if they owned several wallets.
-Duniter gets rid of this problem by identifying its users and
-creating the same amount of Basic Income to everyone.
-
-#### 1.1.2. Temporal-asymmetry {#temporal-asymmetry}
-
-Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
-which means ever fewer bitcoins will be created over time until no new BTC are
-being generated. So, once the first adopters have mined every bitcoin,
-how will future joiners get Bitcoins? Just like most of us do for Euros or
-Dollars: to get money, they will have to work for the ones who already own it.
-
-We believe this is the second injustice. Every member of a
-monetary community should be equal concerning monetary creation, and get
-the same relative amount of money over time, even if they are a late
-adopter. Duniter aims to fix this by making the Universal Dividend
-(a.k.a. UD) grow by the time according to precise rules, thus making
-members equal toward money issuance on a half-lifespan.
-
-Most currencies present one of these two asymmetries, including metal currencies
-and mutual credit, as exposed in the RTM.
-
-#### 1.1.3. A solution {#a-solution}
-
-Bitcoin has taught us that it is possible to create a currency system
-allowing one to both create digital money and to exchange it without a
-central authority. What we need to change is the way money is issued
-so we finally have a symmetrical system. We need **Bitcoin + Universal
-Dividend**. But Universal Dividend implies that the community consists
-of only identified people. This is where the Web of Trust (WoT) comes
-into place.
-
-This concept, introduced by cryptography with the OpenPGP format[^OpenPGP],
-allows us to identify people in a decentralized manner. It works as
-follows: each person creates a personal identity that is linked to its
-cyptographic certificate. The identity must be confirmed by others
-members who use their own cryptographic key. It is that simple: people
-choose who is part of the community and who is not, not a central
-authority.
-
-[^OpenPGP]: OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-However, Duniter will not use OpenPGP for its cryptographic features:
-Elliptic Curves[^Elliptic] will be used instead for the conciseness of its
-generated keys and its pratical advantages. Duniter has its own Web 
-of Trust principles, that will be exposed later.
-
-[^Elliptic]: High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-
-### 1.2. Proof-of-Work mining : a power race {#proof-of-work-mining-a-power-race}
-
-In Bitcoin Model, the calculation and incentive principles cause a power race :
-new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers.
-This leads to a power race an places the control over the currency in the hands of the richest hardware owners.
-We want to make Duniter blockchain validation much less energy and hardware consuming while 
-keeping a strong level of security. This will be further explained later. A consequence of 
-this choice is the participation of low-end hardware in the Duniter network,
-leading to a better decentralization of blockchain validation.
-
-#### 1.2.1 What about Proof of Stake ? {#what-about-proof-of-stake}
-
-Proof of stake consensus algorythm was first introduced in 2012[^PPCoin]. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a "stake" they would lose in case of cheat.
-
-[^PPCoin]: PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-
-At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle.
-Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead 
-to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.
-
-## 2. Duniters Blockchain {#duniters-blockchain}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-
-Duniters Blockchain follows the basic principles of Bitcoins. 
-This is essential for synchronization between peers, as to prevent double-spend attacks. 
-However, Duniters Blockchain will store different informations than Bitcoins. 
-
-The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:
-
-* a former transaction (as in Bitcoin)
-* a Universal Dividend (specific to Duniter).
-
-Duniters Web of Trust is also written in the Blockchain. The identity of each
-member gets registered much like transactions are, with a strong link to the
-time reference. Thus, the Blockchain is a representation of a space-time frame
-of reference, where "space" are members of the WoT and "time" the basic blockchain
-units : the blocks. On each point of time, one can determine which account is
-legitimate to create the UD, only with a blockchain analysis.
-
-
-### 2.1. Spam countermeasures {#spam-countermeasures}
-
-
-An issue of most cryptocurrency projects is to prevent the common ledger from
-growing too much. This would require nodes to have a lot of storage and computing
-power to be usable. In particular, we don't want an attacker to be able to make the
-Blockchain grow too fast. Most projects implement transaction fees as a way to prevent
-this, making the attacker lose money. We don't want to introduce this mean since a
-currency with automatic fees on transactions is no more neutral. Several
-countermeasuers against such spam attacks are implemented.
-
-<!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
-
-#### 2.1.1. Minimum output amount {#minimum-output-amount}
-
-<!-- This has to be implemented in DUBPv13. -->
-
-Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.
-
-#### 2.1.2. Limited block size and chainability {#limited-block-size-and-chainability}
-
-The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.
-
-With the same goal to prevent too many transactions to get registered, while transactions can be "chained" (refer to another transaction in the same block), the chainability of transactions is limited to 5.
-
-
-### 2.2. Scaling {#scaling}
-
-Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :
-
-* Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don't want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.
-* Duniter's aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.
-
-However, Duniter has assets that will help if the number of users and transactions grow.
-
-#### 2.2.1 Dynamic block size {#dynamic-block-size}
-
-While Bitcoin has a fixed block size, Duniters blocks size can evolve. 
-On low use of the blockchain, the maximal block size is 500 bytes. 
-On high use of the blockchain, the maximal block size would be 110% of the
-average size of the current window blocks(see "personalised difficulty" part for more information).
-This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :
-
-```
-block_size < max(500 ; CEIL(1.10 * (average block size))
-```
-
-#### 2.2.2. Lightning Networks {#lightning-networks}
-
-The Lightning Networks[^Lightning] allow almost instant and off-chain transactions.
-They were first implemented on Lightcoin, and are now on Bitcoin.
-One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain.
-The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks.
-While not available yet, this payment channel might get implemented when needed.
-
-[^Lightning]: The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-
-#### 2.2.3. Unit base {#unit-base}
-
-As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the `unitbase` is updated each time the UD value reaches 100.00 : it goes from `99.99*10^(unitbase)` to `10.00*10^(unitbase+1)`. All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.
-
-With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.
-
-## 3. Duniter Web of Trust
-
-
-### 3.1. Basic Principles {#duniter-wot-basic-principles}
-
-In order to identify "members" accounts - which create monetary units -
-and other accounts, Duniter uses a Web of Trust. This can be summarized
-into few principles:
-
--   Each account becomes a member if it received a minimal number of
-    certifications - 5 for Ğ1 currency.
--   Only members accounts can send certifications. Certifications have a
-    limited lifespan.
--   A certification indicates that the sender accepts the receiver as a
-    legitimate identity.
-
-The aim of the WoT is to identify a blockchain account to a living
-human. According to Lauterbach et.al[^Couchsurf], the strengh of a relationship should be considered when building a vouch system.
-For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are.
-A certification represents a strong human relationship : one may certify a close relative, not an acquaintance.
-Each member has to accept this licence before being included in the WoT.
-Thus, if a member is part of an attack on the currency, they can be found by mutual relatives.
-Additional security rules occur to prevent cheat and attacks on a large scale.
-
-[^Couchsurf]: Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: [snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf](http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf)
-
-Note that non-members accounts can use the currency, but cannot create
-money. Non-members accounts can be used by individuals as secondary wallets, or by
-institutions.
-
-We were inspired by the OpenPGP Trust system[^OpenPGP_Trust]. However, the OpenPGP
-trust principles aim at defining trust from a particular point of view while Duniter needs to
-identify humans for the whole community. To achieve this goal, while OpenPGP allows each
-user to tweak its trust parameters individually, Duniter sets rules in the "genesis" block for the whole community.
-
-[^OpenPGP_Trust]: Public key validation on GnuPG manual, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-### 3.2. Why do we need a Web of Trust ? {#why-do-we-need-a-web-of-trust}
-
-There are two reasons we need it :
-
-1.  To make sure that only one Universal Dividend is produced per member
-    at each specified creation interval. In the Ğ1's case this interval
-    is set as daily `86 400` seconds, it is the *monetary parameter*
-    known as `dt`.
-2.  To identify the nodes hashing the blocks and assign each a
-    personalised difficulty. This custom difficulty proof of work is
-    there to avoid the blockchain's validation mechanism becoming too
-    centralised as is the case with many \'non-libre' cryptocurrencies.
-
-> **Monetary parameter** : Each currency that use Duniter has its own blockchain whose behaviour is
-> dictated by a set of 'parameters' defined in block zero - the so-called
-> genesis block - that can be tweaked to achieve the desired results. At
-> the time of writing the Whitepaper, the Duniter Blockchain Protocol
-> (DUBP) has a total of 21 parameters of which 10 are for the WoT alone.
-> We'll focus on these 10.
->
-> Suffice to say that in the Ğ1's case, the DU is created every 24 hours -
-> 86 400 seconds. This interval is set through the time derivative `dt`
-> parameter and can have a different value in other implementations of the
-> protocol.
-
-We want to make sure that each member can only have one account. As we
-all know, achieving zero-risk isn't possible[^Sybil_Attack].
-Our goal is therefore not to create a WoT within which fraud
-would be absolutely impossible, but instead to discourage it. Here is a
-rewording of our goal in 4 smaller ones :
-
-1.  Make the certification process lengthy enough that all members
-    exercise due diligence and are wary of risks.
-2.  Make fraudulent acts as hard as we can to the extent that they
-    become pointless.
-3.  Ensure that any Sybil attacks have a negligible impact on the
-    currency by ensuring that illegitimate double Universal Dividends
-    have no significant bearing on the legitimate monetary mass
-4.  Slow the growth of 'Sybil regions' to give enough time for the
-    community to react and isolate the threat.
-
-[^Sybil_Attack]: The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-
-> **Sybil attack** : A Sybil attack is an attack perpetrated on a
-> reputation system through the creation of fake identities. A Web of
-> Trust is a specific instance of a Reputation System.
-
-There are plenty of Sybil attack scenarios we can think of and just as
-many reasons why their perpetrators would want to carry them out. Our
-objective is that the configuration of the WoT protects both users and
-its IT backbone infrastructure against these attacks.
-
-This means that micro-attacks performed by small groups of individuals
-looking for personal enrichment are of no interest to us. The web's role
-isn't to deter these attacks, this being instead the role of the
-community. Just like the town you live in is responsible for providing
-your tap water and electricity but isn't responsible for any burglaries,
-etc. Much in the same way, Duniter's WoT guarantees us all a functional
-currency, but do not detect small fraud.
-
-### 3.3. The importance of having our own certification system {#own-certification-system}
-
-Centralized identification systems can achieve the goal we want. State
-Identification is an example. However, this has many drawbacks :
-
-* The authority may have arbitrary criteria for identification, for example
-preventing people without an official state-provided identity or
-homeless people to be included in the WoT.
-* Payment might be required
-to get identified, thus making the monetary creation not "free".
-* The authority is a point of failure for any attacker.
-
-It is of the utmost importance that we remain free from any state or
-corporation. The WoT is an answer to this criterium. To this day we
-depend only on the Internet and yet, were it to fail, there are already
-alternatives being tested around the world for a decentralised communication network.
-
-### 3.4. A few foundational concepts on graph theory : a bit of vocabulary {#graph-theory-vocabulary}
-
--   **Graph**: set of points -called 'vertices'- joined by edges -called
-    paths/walks-.
-
--   **Simple graph**: a graph with no loops and with no multiple edges.
-    That is, each edge connects two distinct endpoints and no two edges
-    have the same endpoints. A simple edge is an edge that is not part
-    of a multiple adjacency -of edges-. In many cases, graphs are
-    assumed to be simple unless specified otherwise.
-
--   **Directed graph**: a graph in which the edges have a distinguished
-    direction, from one vertex to another. A directed edge can also be
-    called a path or walk.
-    Arrow A --\> B is therefore different from arrow B --\> A.
-
--   **Endpoints**: the edge with vertex A --\> B has A and B as
-    endpoints, respectively as start and end of the path/walk.
-
--   **Isolated vertex**: a vertex whose degree is zero, that is, a
-    vertex with no incident edges.
-
--   **Degree of a vertex**: number of its incident edges -in and out-.
-
--   **Out-degree of vertex A**: number of outbound edges / tail ends
-    from A.
-
--   **In-degree of vertex A**: number of incoming edges / head ends
-    to A.
-
-![degrees of a vertex diagram](./images/degres.jpg)
-
--   **Path**: -aka "walk"- path to follow to get from vertex A to
-    vertex B.
-
-### 3.5. Definition of the Duniter Web of Trust {#definition-of-the-duniter-web-of-trust}
-
-The Duniter WoTs -one per currency- are simple directed graphs without
-isolated vertices. The vertices are the members and the edges are the
-certifications given and received.
-
-*Directed* means that the responsibility of issuing a certification is
-unique and personal to the certifier. The trust they place in the
-receiver cannot be imposed in the other direction although in most
-circumstances both parties equally trust each other.
-
-In addition, all vertices are either currently active members or
-past-members. Past-member vertices are in a specific 'deactivated state'
-and can no longer issue or receive certifications although the ones
-already issued or received to/from other members are still considered
-'pending' to avoid a collapse of the WoT. If these old members don't
-come back into the WoT, their pending certifications will eventually
-expire and they will switch from 'deactivated' to 'isolated' vertices.
-
-To wrap up with old members, after a certain period of time - set in the
-currency's parameters - their deactivated vertex is removed from the web
-and the associated identity is 'revoked'. The person who owned the
-account can no longer use this identity but is free to join the web with
-another one.
-
-> **Identity** : An identity is a set of three pieces of information: a public key, a
-> name and a blockstamp. A blockstamp points to a specific block in the
-> chain. Its main use is to freeze the point in time at which an identity
-> was created and to link this identity to a specific chain and a currency
-> - each currency having its own blockchain.
->
-> An identity can be in any one of 5 different status: pending, member,
-> old member, revoked or excluded.
-
-Let's take a simple example:
-
-```
-    A -> B -> C
-         |
-         \--> D
-```
-
-If, for whatever reason, A were to lose its member status, the web would
-crumble and all other members would be excluded as a consequence. To
-avoid this, the certification from A --\> B will remain valid until its
-expiry date, leaving enough time for B to receive certifications from C
-or D.
-
-Because our WoT doesn't have any isolated vertices, each new identity
-created needs to be pulled into the web with all of the certifications
-it has received, all in the same block. This calls for a temporary
-'buffer' storage space for **pending** identities and the certifications
-they have received. This storage space is called 'the pool' of Duniter
-nodes, which we could also have called the 'sandbox' as that's the name
-used in Duniter's code. Duniter nodes inclued other 'pools' for other
-documents and metadata not mentioned here.
-
-### 3.6. Exploring the rules behind a Duniter Web of Trust {#exploring-the-rules-behind-duniter-wot}
-
-The Duniter WoTs - one per currency - works with a set of eight
-fundamental rules enforced through eleven different parameters. Ten of
-these parameters are set within the genesis block, the eleventh one -
-`msPeriod`- having being hard-coded in the Ğ1's code subsequently.
-
-#### 3.6.1. Distance rule and referent members (`stepMax` and `xPercent`) {#distance-rule-and-referent-members-stepmax-and-xpercent}
-
-These two parameters are closely linked and together define the
-'distance rule'. The 'distance rule' can only be described after
-defining what a 'referent member' is:
-
-> **Referent member**: member A is said to be 'referent' if and only if
-> the total of their degrees are greater than or equal to
-> `CEIL-N^-1/stepMax` where N is the total number of members. As the
-> size of the web will grow this number will grow too, meaning it will
-> take more certification issuances to become a referent member. The
-> number of certifications needed to become a member shouldn't change.
-
-Let's now define the distance rule:
-
-> **Distance rule**: member A is said to observe this rule if and only
-> if for a subset xPercent % of referent members R there exists a path
-> of length less than or equal to `stepMax` between R and A.
-
-Referent members only exist so that the distance rule can take effect,
-they have no special privileges over non-referent members. In a perfect
-web, that is one in which each member has certified all members they
-legitimately can, all members would be referent members. However,
-because the web progressively grows in size and because members die and
-are replaced by new ones, there are always members at any given time `t`
-who haven't yet certified all members they legitimately could. These
-members would hinder the evolution of the web if they were taken into
-account in the calculation of the distance rule and the web would
-effectively stop growing.
-
-Because verifying the application of the distance rule is
-calculation-greedy, it is only performed when a new identity gets
-confirmed into the web or an existing member gets renewed. There is an
-exception to this rule: the distance rule is not observed in the genesis
-block -when the web is first implemented.
-
-#### 3.6.2. Rule of the minimum number of certifications needed (`sigQty`) {#rule-of-the-minimum-number-of-certifications-needed-sigqty}
-
-This is the simplest rule, it essentially says that each member must at
-any given time -meaning in any single block- have received at least
-`sigQty` active certifications. If, for whatever reason, member A were
-to have less than `sigQty` active certifications in a given block, they
-would cease to be a member and be required to publish a request for
-identity renewal.
-
-#### 3.6.3. The membership renewal rule (`msValidity`, `msPeriod` and `msWindow`) {#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow}
-
-Bear in mind that a membership doesn't last a lifetime but instead has a
-lifespan set to `msValidity` seconds.
-
-Every single member -or old member who hasn't revoked his identity or
-been excluded- can request a membership renewal so long as the last
-request was made more than `msPeriod` seconds ago. If a member has never
-requested a renewal, the date of last renewal is equal to the timestamp
-at which his membership was first created. A new request will be stored
-in the 'pool' for a maximum of `msWindow` seconds before it's included
-in the blockchain. Once again, this can only happen once/if the member
-meets both the `siqQty` rule and the distance rule -if these criterion
-are already matched it's just a case of waiting for a new block to be
-mined-.
-
-If a member hasn't requested a renewal for longer than `msValidity`
-seconds, they automatically cease to be a member. From this moment on,
-the ex-member has another `msValidity` window to renew their membership.
-When this period of `2 × msValidity` runs out, the membership will
-expire and this identity will never be available for use again in the
-web. If the person so desires, they will have to publish new identity
-and membership documents and find enough certifiers, as any newcomer.
-
-#### 3.6.4. Rule of certification lifespan (`sigValidity`) {#rule-of-certification-lifespan-sigvalidity}
-
-All certifications included in the blockchain expire **sigValidity**
-seconds after they were **issued**.
-
-> /!\\ The issuance and the inclusion of a certification in the
-> blockchain occur at different times. When member A issues a
-> certification at time t1, it gets stored in the pool starting at t1
-> and only finds its way into the blockchain at t2 when all of the web's
-> rules are observed. Several weeks can thus go by between t1 and t2!!!
-
-#### 3.6.5. Rule of limited supply of active certifications (`sigStock`) {#rule-of-limited-supply-of-active-certifications-sigstock}
-
-By 'active certifications' we refer to certifications included in the
-blockchain and that haven't yet expired.
-
-The total of active certifications issued by any member at any single
-time must be less than or equal to `sigStock`. When this threshold is
-reached the member will have to wait for one of his active
-certifications to expire before he/she can issue a new one.
-
-#### 3.6.6. Rule of the time period between two certification issuances. (`sigPeriod`) {#rule-of-the-time-period-between-two-certification-issuances-sigperiod}
-
-As soon as a certification issued by member A gets included in the
-blockchain, they will be unable to issue a new one before another
-`sigPeriod` seconds.
-
-#### 3.6.7. Expiry of a certification issuance (`sigWindow`) {#expiry-of-a-certification-issuance-sigwindow}
-
-When a certification is issued by member A, it will be stored in the
-'pool' for a maximum of `sigWindow` seconds. If the certification hasn't
-been included in the blockchain by then, it will be cancelled and the
-member's `sigStock` will be repleted by one.
-
-#### 3.6.8. Lifespan of a 'pending' identity (`idtyWindow`) {#lifespan-of-a-pending-identity-idtywindow}
-
-When a new identity is created, it is stored in the 'pool' for a maximum
-of `idtyWindow` seconds. If the person hasn't achieved member status by
-then, the certification will simply be cancelled.
-
-### 3.7. Details on some of the WoT's peculiarities at the genesis block {#details-on-some-of-the-wots-peculiarities-at-the-genesis-block}
-
-The aforementioned rules can only be enforced with an existing web. They
-cannot be observed when first creating the web, that is when defining
-the genesis block.
-
-Only rules 2 and 5 can be observed at the genesis block.
-
-The genesis block has to be manually created by the founding members. In
-practice this means that there must be a choice on which identities to
-include on the premise that all of them observe rules 2 and 5. In
-addition, the genesis block must be signed with the private key of one
-of these identities.
-
-As soon as the genesis block has been created, the other identities can
-start mining the blockchain and the member who created block \#0
-effectively looses the decision power he had at creation.
-
-### 3.8. Why these rules and application cases in the Ğ1 {#why-these-rules-and-application-cases-in-the-g1}
-
-#### 3.8.1. Distance and maximum size {#distance-and-maximum-size}
-
-The distance rule is there to curb the maximum size of a Sybil region as
-well as that of the monetary community as a whole. The `xpercent`
-parameter prevents the creation of a 'faction' that could take hold of
-the blockchain.
-
-![Sybil region](./images/wot-sybil.jpg)
-
-The Sybil regions are isolated from the rest of the graph in the sense
-that they can only receive certifications from other ill-intentioned
-Sybil members. As a consequence, the shortest edge/path between a
-legitimate member and a Sybil one has to have the attack's author as an
-endpoint. The maximum depth the Sybil region can attain is therefore
-contingent on the distance between the attacking edge-s- and the
-xpercent% closest referent members, this distance is known as
-`stepAttackers`. The maximum size of a Sybil region created by `sigQty`
-members depends on the L parameter, defined as `L = sigQty/sigStock`:
-
-```
-MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)
-```
-
-The maximum size of the Web of Trust is given by the following formula:
-
-```
-WoTmax = (sigStock)*L^(stepMax-1)
-```
-
-However we know for a fact that members will never use all of their
-available certifications.
-According to Dunbar[^Dunbar], on average, one is able to maintain relationships to around 150 people.
-Being conservative, we will consider that on average, each person will certify 50 accounts.
-We can calculate the size of the average web of trust `WoTavg` :
-
-```
-WoTavg= (50)*(sigQty/50)^(stepMax-1)
-```
-
-[^Dunbar]: Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
-
-
-Our goal with the Ğ1 is to create a community of about one million
-members to test the consequences of a libre monetary system. Let's see
-how we can tweak the pair of sigQty and stepMax- to reach this size:
-
-![Average WoT size graph as a function of sigQty and stepMax](./images/wot-moy.png)
-
-The maximum size of a Sybil region grows linearly with `sigQty` but
-exponentially with `stepMax`. Logic has it that we need to keep
-`stepMax` as low as possible to ensure sufficient strength to the web.
-The above graph shows that the lowest value of `stepMax` for a web of a
-million members is of 5. This is an order of magnitude and is likely to
-be much higher in reality, we cannot measure it for sure.
-
-For `sigQty` we can choose a value of **4** for a web of **1.5 million
-members** or **5** for **half a million members**. Bear in mind these
-are gross figures and could be significantly higher, we are talking
-anywhere between 1 and 10 million in reality. Calculating WOTavg gives
-us a pretty good idea of how the web would scale bearing in mind that it
-considers all members are referent members too -which isn't the case as
-explained previously-. Hence the maximum size of the web is likely
-larger, a ballpark figure of half a million is enough for now especially
-knowing that the smaller `sigQty` is, the easier it is to launch a Sybil
-attack -it's easier to find four accomplices than five-. For security
-reasons we have settled on five:
-
-```
-stepMax = 5
-sigQty = 5
-sigStock \>= 50
-```
-
-The maximum size of a Sybil region therefore is:
-
-```
-(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))
-```
-
-with sigStock = 50 we have a Sybil region of:
-
-```
-45*(1-10^(5-stepAttackers))/(-9)
-```
-
-A good practice for protecting the web is to maximise `stepAttackers`.
-That's why we decided that referent members in the genesis block had to
-be at least four steps away from each other.
-
-Another way to keep a Sybil attack at bay, were it slow enough for
-members to notice it, would be for referent members to 'stretch' the web
-intentionally to limit the growth of the region by ensuring that the
-attackers' legitimate certifications received in the first place aren't
-renewed. But what if bot accounts were created and certified each other
-super fast and following all rules, how would we counter that? By
-introducing a minimum length of time between two certifications!
-
-#### 3.8.2. Time is our friend {#time-is-our-friend}
-
-To help us deter a Sybil attack, we've decided to impose a minimum
-period of time between any two certifications issued from a single
-account. This parameter called `sigPeriod` affords us a greater chance
-to detect the formation of a 'hostile' faction.
-
-Here is a graph showing the evolution of a Sybil region with the
-variation of `sigPeriod`. The simulation considers that honest members
-and attackers both issue a certification each `sigPeriod` interval, in days:
-
-![size of the WoT according to sigPeriod and stepAttackers](./images/impact_sig_period.png)
-
-As we see, there is a strong link between the
-growth speed of the region and `sigPeriod`. As evidenced here, we need a
-`sigPeriod` high enough in order to ensure that the legitimate web can
-grow at least as fast as a Sybil region. In addition, the higher
-`sigPeriod` is, the more members will exercise their certification power
-gingerly, the action coming at a higher 'cost'.
-
-There are numerous advantages to giving `sigPeriod` a high value and no
-technical barriers to it, hence our choice of five days.
-
-We could have also gone for one week for the sake of simplicity. However
-there is an underlying idea behind our choice which was quite simply the
-pace of today's life. Certifying someone can be a lengthy process as one
-needs to make sure they are correctly applying the Ğ1 licence and people
-nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
-to allow one to certify at the end of every working week -five days-
-instead of a whole calendar one.
-
-#### 3.8.3. Trust me now, trust me forever ? (`sigValidity`, `msValidity`) {#trust-me-now-trust-me-forever-sigvalidity-msvalidity}
-
-There would be two main drawbacks to a lifetime membership in the Ğ1's
-Web of Trust:
-
--   First of all, some members will pass and those accounts should no
-    longer produce the Universal Dividend.
--   Secondly it is of the utmost importance that 'rogue' accounts can be
-    excluded from the web at some point.
-
-To achieve this, certifications have a limited lifespan. Members need to
-seek renewal from their peers after `sigValidity` time. On the other
-hand, this time can't be too short that members would spend more time
-seeking renewal than they would exchanging in the currency. Furthermore,
-a certification with too short a lifespan would foster careless
-certifying behaviours. The act of certifying must have a high-enough
-'perceived' cost to make it feel like an important act. Lastly, we also
-wanted this lifespan to be easy to remember. Historically speaking, we
-first settled on the values of `sigPeriod` and `sigStock`, meant one
-could issue all of their certifications in 495 days, one year was
-therefore not long enough. We deemed three years to be too much and
-that's how we agreed on two years in the end.
-
-Thinking that a deceased member could continue producing the UD for two
-long years without anyone benefitting from it was also something we
-needed to address. We chose a value of one year for **msValidity**. The
-act of renewing every year is done through one of the clients
-interacting with the blockchain, through a simple click on a button.
-This parameter is less important than others and is mostly there to
-'prune' the web of past or inactive members who don't renew their
-membership.
-
-#### 3.8.4. Keeping the pools free of information glut (`idtyWindow`, `sigWindow`, `msWindow`) {#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow}
-
-The pools need to be cleaned up on a regular basis to avoid them
-clogging up with information and to ensure that machines with less
-calculating power can still run a Duniter node.
-
-To achieve this, identities with pending membership approval and the
-corresponding certifications have to remain the shortest time possible
-in the pool while still having a chance of making it into the
-blockchain.
-
-For the Ğ1, our opinion was that two months would be enough for all
-potential certifiers to agree on a specific identity to certify. We also
-wanted a time period that would be easy enough to remember by all. We
-settled on two months, and gave this value to all three parameters
-`idtyWindow`, `sigWindow` and `msWindow`.
-
-#### 3.8.5. Avoiding single members from 'knowing too many people' (`sigStock`) {#avoiding-single-members-from-knowing-too-many-people-sigstock}
-
-We considered that on average, each person will certify 50 people.
-However, we know for a fact that some members will use more than 50 certifications.
-The maximum social network of one individual is around 150 people[^Dunbar].
-Being conservative, we settled on a maximum certification number `sigstock` of 100.
-Since `sigStock`'s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.
-
-#### 3.8.6. Avoiding locking minorities (`xpercent`) {#avoiding-locking-minorities-xpercent}
-
-It's easy enough to become a referent member, one of the Sybil
-strategies could therefore be to create a region of referent members.
-Such a region would grow slower than otherwise but could confer a
-locking power to its members by using the distance rule. That's why the
-distance rule cannot be calculated on 100% of the referent members.
-Hence the introduction of the `xpercent` parameter which defines the
-percentage of referent members needing to be less than five edges
--steps- from each other.
-
-This percentage needs to be low enough to prevent the formation of a
-locking minority -referent Sybil members being too far from legitimate
-referent members-. On the other hand, it needs to be high enough so as
-to restrict the maximum size of the Sybil region through the distance
-rule. The `xpercent` parameter was one of the hardest to define,
-therefore we might decide to change its value during the Ğ1 experiment.
-
-We were inspired by the Pareto
-principle[^Pareto]: if at least
-20% of members give good density to the web, 80% of the referent members
-will be five or less steps from any other member -referent or not-. The
-maximum value for `xpercent` is therefore 80%, anything above that and
-the distance rule could be too restrictive for legitimate use cases.
-With security our top concern, we chose the maximum value of 80%.
-
-[^Pareto]: Pareto principle : [en.wikipedia.org/wiki/Pareto_principle](https://en.wikipedia.org/wiki/Pareto_principle)
-
-#### 3.8.7. Spam protection with (`msPeriod`) {#spam-protection-with-msperiod}
-
-This parameter stands out a bit on its own, as it was added after the
-genesis block. It is there to protect the Duniter P2P infrastructure
-against 'spam' attacks. We had to think of a strategy against attacks
-such as high-frequency membership renewal requests -i.e: in every block,
-every five minutes- or worse still, hundreds of these requests per
-minute to flood the Duniter nodes. Without such limits, nodes are
-supposed to address all renewal requests, even in cases where they were
-last published five minutes ago! The `msPeriod` parameter was given the
-same value as `idtyWindow`, `sigWindow` and `msWindow`, i.e. two months.
-
-
-## 4. Proof of Work with personal difficulty {#proof-of-work-with-personalized-difficulty}
-
-As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.
-
-This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each "winning" member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.
-
-Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.
-
-One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an "ecological" PoW ?
-
-
-
-<!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
-
-### 4.1. Why do we need Proof of Work ? {#why-proof-of-work}
-
-Duniter nodes share a database as part of a p2p environment. The proof of
-work (PoW) allows machines to synchronize with each other. In Duniter's case, the blockchain is
-our database, and acts as a ledger keeping
-a trace of all transactions, status of the WoT and more. 
-How can we let several machines add data (ie: a transaction) at
-the same time? In addition, how do we settle on how much time has gone
-by since the blockchain was last updated? Agreement on time is of the utmost importance
-as we want to create Universal Dividends on a regular basis, and keep track
-of membership status, both in human time.
-
-
-Proof-of-work provides a clever solution to both problems:
-
-1. Any machine can write into the blockchain (create a new block) but is only
-authorised to do so if it has previously solved a mathematical equation
-that require a certain amount of work. The challenge has to
-be hard enough to prevent two machines to solve it at the same time,
-ensuring the unicity of a block's creator.
-
-2. Solving this challenge
-takes a certain amount of time, which depends on the calculating power
-of the whole network. This provides a common ground for defining
-the needed time reference. A block time is set (ie: 1 block = 5 min) and 
-Duniter adapts the challenge difficulty to get an average duration 
-corresponding to this block time.
-
-### 4.2. Only members can "mine" {#only-members-can-mine}
-
-One of Duniter's major differences with other PoW-based cryptocurrencies
-is that only members are allowed to author blocks. Each block is signed
-with the member's private key, allowing the algorithm to determine a
-personalised difficulty.
-
-This personalised difficulty eliminates the rat-race for the most
-sophisticated and powerful mining equipment. Another benefit is the fact
-that no "supercomputer" can take control of the blockchain. Lastly, Duniter 
-implements a rotation in forging members thanks to this personalized difficulty.
-
-This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies.
-Members can mine with anything from a raspberry pi to a privacy-first
-internet cube.
-
-### 4.3. How does it work ? {#how-does-duniter-pow-work}
-
-#### 4.3.1. The hash (aka digest) {#the-hash}
-
-Example of a valid hash:
-
-```
-00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653
-```
-
-As you can see this hash starts with five zeros which was very hard to
-achieve and took a lot of work for someone's computer. Hence the term
-"proof of work".
-
-#### 4.3.2. The common difficulty {#common-difficulty}
-
-A common difficulty is needed to settle on a yardstick for our time reference.
-Its role is to make sure the blockchain moves forward
-at a steady pace - one block every `avgGenTime` seconds, `avgGenTime`
-being one of the 20 parameters behind the Duniter protocol-. 
-
-This difficulty's initial value can be set to any arbitrary value (`70` in
-Duniter `v1.5.x`) and then acts as a spring, regulating blocktime
-creation by increasing itself if the creation interval drops under
-`avgGenTime` and vice-versa.
-
-##### 4.3.2.1. How is difficulty applied ? {#how-is-difficulty-applied}
-
-The numeric value of difficulty is taken from an array of possible
-hashes out of all possible hashes. In DUBPv13 the hash
-of a block is its sha256 hexadecimal hash.
-
-To understand the difficulty, we make a euclidiean division of the
-difficulty by 16.
-
-Here's an example with a difficulty value of 70 : 
-
-```
-70 // 16 = 4 with a remainder of 6. 
-```
-
-The valid hashes are the ones starting with four
-zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation).
-The valid hashes are then written as starting with : `0000[0-9]`. 
-This is a bit different from Bitcoin, 
-where the difficulty is only ruled by the number of zeroes.
-
-##### 4.3.2.2. The Nonce {#the-nonce}
-
-When a member is forging a new
-block, his computer freezes the block's content and changes the Nonce
-until the hash reaches the required number of zeroes. 
-
-The nonce allows us to mine a new block by finding a hash. The
-hash value allows us to determine the difficulty level of the
-proof-of-work performed. Examples of possible Nonce values:
-
--   10100000112275
--   10300000288743
--   10400000008538
--   10700000079653
--   10300000070919
-
-In reality the `Nonce` value follows a pre-determined format akin to
-`XYY00000000000`. The Nonce's value isn't the number of attempts but
-rather a value within a set of possible ones. This is how the Nonce is
-built:
-
--   X is a number assigned to a specific peer. Let's assume that someone
-    has several nodes each with the same private key, this would lead to
-    possible collisions if this person were to mine the same block with
-    different nodes. Each ~~block~~ **node ?** will therefore have its own unique X to
-    prevent this from happening.
-
--   Y is the number of cores of the processor. The Nonce starting with
-    `107[…]` belongs to a seven cores processor, while `199[...]` could
-    be the proof generated by a 99 cores processor.
-
-The rest of the Nonce, the part that follows after the XYY, is the
-numerical space for this individual node and is unique to each of the
-CPU's core. This space is comprised of eleven digits (`00000000000`).
-For the sake of accuracy, we use the term CPU in the wider sense, it can
-be understood as a bi-CPU for example. We take into consideration the
-number of cores for the resulting PoW.
-
-### 4.4. Personalised difficulty {#personalised-difficulty}
-
-Earlier in this article, we explained that the personalised difficulty
-is the new and key concept that sets Duniter apart from other
-PoW-based cryptocurrencies.
-
-Here is how this personalised difficulty is calculated and assigned:
-
-It is determined by a combination of two different constraints with
-complimentary roles: the **exclusion factor** and the **handicap**.
-
-Let `powMin` be the common difficulty, `exFact` a member's exclusion
-factor and `handicap` their handicap. This member's personalised
-difficulty `diff` is:
-
-```
-diff = powMin*exFact + handicap
-```
-
-#### 4.4.1. Understanding `exFact`, the exclusion factor {#the-exclusion-factor}
-
-Members who have never produced blocks or haven't for quite some time
-are assigned an exclusion factor of `1`. Their personalised difficulty
-is therefore simply the sum of `powMin + handicap`.
-
-Before reading on, let's precise the role of this exclusion factor.
-When a member adds a block to the chain, his `exFact` jumps up from one to
-a very high value, to prevent them from forging other blocks
-immediately after and taking control of the blockchain.
-
-The exclusion factor will then rapidly return to one. 
-This delay is expressed as a number of blocks. It is calculated as a
-proportion of the number of members forging. In the Ğ1's case, this
-proportion is 1/3, meaning that if there are fifteen members currently
-forging, the member's exclusion factor will drop down to one after five
-blocks.
-
-##### 4.4.1.1. What is intended by "the number of members forging" ?
-
-We mean the number of members trying to create the next block. 
-In reality, there is no way to precisely know how
-many members are calculating at any given time, because it is impossible
-to view the entire network. But we need this information, whithout which 
-assigning a personalised difficulty is impossible. 
-To achieve this, Duniter looks back at the blockchain and assumes that there is as much 
-members forging as those who have found at least one block
-in the last blocks in the current window, minus the very last one.
-
-##### 4.4.1.2. Current window
-
-We use the concept of **current window**. The current window is the number of blocks we look back at to determine how many members are forging.
-Let's see how it works: 
-
-* `issuersFrame` is the size of the
-current window in blocks.
-
-* `issuersCount` the number of members who
-have calculated at least one block during the current window. 
-
-Both `issuersFrame` and `issuersCount` are block fields. When first
-starting a blockchain, the very first block has an `issuersFrame=1` and
-an `issuersCount=0`. The genesis block is excluded as there are no members in the current
-window!
-
-From the second block onwards (block \#1) we track the variation of
-`issuersCount`. The member having mined block \#0 enters the current
-window and in block \#1 we will therefore mention `issuersCount=1`.
-
-
-`issuersFrame` then varies as follows: 
-
-* if `issuersCount` increases by N (with a maximum step of N = 1), then `issuersFrame` will increase by one unit over a period of 5N blocks. 
-* Conversely, if `issuersCount` decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then `issuersFrame` will decrease by one unit during 5Y blocks. 
-* When such events overlap, `issuersFrame` evolves as so :
-
-| bloc | event | issuersFrame|
-|---|---|---|
-| T | Babar writes a block and enters issuersCount | 160 |
-| T+1 | Celeste leaves issuersCount | 160 +1 = 161 |
-| T+2 | N/a | 161 +1 -1 = 161 |
-| T+3/4/5 | N/a | 161 +1 -1 = 161 |
-| T+6 | N/a | 161 -1 = 160 |
-
-
-The calculation can be found under rules
-[BR\_G05](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe)
-and
-[BR\_G06](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar)
-of the DUP protocol.
-
-##### 4.4.1.3. exFact and the personalised difficulty {#exfact-and-the-personalised-difficulty}
-
-We explained that `exFact` spikes immediately after the member has
-found a block. It decreases then rapidly to `1` after a number of 
-blocks equal to `1/3 * issuersCount`. Let's see precisely
-how we calculate `exFact`:
-
-* `nbPreviousIssuers` is the value of issuersCount at the
-last block `N` found by the member.
-
-* `nbBlocksSince` is the number of blocks
-found by the rest of the network since block `N`.
-
-* `percentRot` is the number of *not excluded* peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.
-
-```
-a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]
-```
-
-The FLOOR is a simple truncate function. For `exFact` to exclude the
-member, we need :
-
-```
-(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) >= 2
-```
-
-We can see that the member is not excluded if `nbBlocksSince` is greater than 1/3 of
-the calculating members. Take as an example `nbPreviousIssuers = 6` and `nbBlocksSince = 3`:
-
-```
-(0.67* 6 / )1 + 3)) = 1.005 -> exFact = 1
-```
-
-However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:
-
-```
-(0.67 * 6 / (1 + 1)) = 2.01 -> exFact = 2
-```
-
-Moreover if the last block was authored by the said member, then:
-```
-nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers
-```
-
-ExFact value increases according to the number of
-members calculating. Thus, if there is enough members calculating, even 
-mining farms would be excluded. We have therefore
-succeeded in our intent to deter attempts to seize the blockchain and
-its currency.
-
-
-However, at any time `t`, the two-thirds of
-calculating members all have an exclusion factor of `1`, even though
-they might not all have the same computational power at hand. If the
-personalised difficulty only took into account the exclusion factor, then
-only the members with the highest computational power from the remaining
-third would be able to author new blocks and the other 2/3s would almost
-always be excluded. Lesser machines wouldn't stand a
-chance...
-
-#### 4.4.2. The handicap {#the-handicap}
-
-The handicap is the second parameter of the personalised difficulty. Its
-main role is to improve the rotation of forging peers. 
-A higher handicap is assigned to members with higher calculating
-power, so lesser machines can also compute blocks. As a consequence, 
-there is no incentive on forging with powerful computers. 
-Security can be achieved with less computing power than with pure PoW.
-
-The aim is to handicap the half that has
-authored most blocks (the most powerful half) to favour the other one.
-So, the handicap formula will use the median number of blocks authored by peers within the current window.
-
-* `nbPersonalBlocksInFrame` is the number of blocks authored by a
-single member within the current window.
-
-* `medianOfBlocksInFrame` is the
-median number of blocks written by the calculating members during the
-same timeframe.
-
-```
-a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))
-```
-
-Let's unwrap the formula:
-
-```
-(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)
-``` 
-
-is simply the
-ratio between the number of blocks authored by the peer and the median
-number of blocks. For example, if a peer has authored `9`
-blocks in the current window and the median is `5`, then the ratio
-will be `(9+1)/5 = 2`. The MAX function allows us to ensure that
-the handicap has a value at least equal to `1`.
-
-The Napierian Logarithm of this ratio prevents the handicap from becoming excluding.
-We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.
-
-If we wanted the handicap to be applied as soon as the median is reached,
-we would divide it by `LN(1)`. The problem is that we have already set
-a minimum value of `1` with the MAX function. If we were to divide
-the ratio by `LN(1)` all calculating peers would have a handicap `\>=
-1`. In addition, is it really fair to handicap a member who is right on
-the median?
-
-That's why we went for `1.189` rather than `1`. A member has to
-be at least `18.9%` above the median to be assigned a handicap.
-18.9% is actually 16\^(1/16), the difficulty
-factor between two levels of the proof work (hexadecimal hash).
-
-To conclude, you have to remember that :
-
-* The handicap is indexed on the logarithm of the ratio to the median,
-* Handicap is only applied on members whose ratio to the median is greater than the ratio between two
-levels of the proof-of-work's difficulty.
-
-
-
-## Conclusion {#conclusion}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter's Blockchain can be compared to Bitcoin's : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.
-
-More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.
-
-The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :
-
-
-* The freedom to choose your currency system: because money should not be imposed.
-* The freedom to access resources: because we all should have access to economic & monetary resources.
-* The freedom to estimate and produce value: because value is a purely relative to each individual.
-* The freedom to trade with the money: because we should not be limited by the avaible money supply.
-
-
-Those 4 economic freedoms should be understood together, not exclusively. Plus, "freedom" has to be understood as "non-nuisance". So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.
-
-## Sources : {#sources}
-
-* Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-* Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-* The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-* The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-* High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-* PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-* Duniter Blockchain Protocol, v13, draft by Elois : [git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md](https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md)
-* The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-* Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
diff --git a/build/whitepaper_fr.mobi b/build/whitepaper_fr.mobi
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Binary files a/build/whitepaper_fr.mobi and /dev/null differ
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deleted file mode 100644
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+++ /dev/null
@@ -1,34 +0,0 @@
-Duniter: A libre currency blockchain generator.
-=======================================
-
-## Abstract {#abstract}
-
-Many currency principles involve non-equal rights to monetary creation between humans.
-We propose a monetary creation based on the Relative Theory of Money, which guarantee equal monetary creation for each willing human.
-This type of currency can be centralised, however, this could lead to censorship and arbitrary choices of the central institution.
-Thus, strongly inspired by Bitcoin example, we want the currency to be as decentralised as possible, in the transaction network as in the human identification process.
-We use a Web of Trust between living humans for identification.
-This web of trust allows us to impose personalised difficulty for transaction validation, keeping the calculation accessible to low-end hardware and allowing all competent members to secure the currency.
-
-
-
-## Introduction {#introduction}
-
-Duniter is a software to create and manage "libre currencies". Libre currency is a concept defined by S.Laborde in the Relative Theory of Money (RTM) that was published in 2010. This theory demonstrates the possibility of an invariant monetary unit : the Universal Dividend. Doing so, the RTM answers the question :
-
-> How should a currency be created to match the principle of equality between all humans, now and between generations ?
-
-The results of this demonstration implies a monetary creation :
-
-* on a regular basis
-* for each human being
-* which amount has to be reassessed on fixed intervals according to a fixed formula.
-
-Thus, Duniter project will associate a human to a digital identity. It will use a Web of Trust with specific rules. As the number of members may evolve, the Universal Dividend has to be created according to the formula :
-
-$$ UD(t+1) = UD(t) + c^2 *{M(t) \over N(t)} $$
-
-
-Duniter is based on a decentralized Blockchain. This technical choice allows irreversibility of transaction and uncensorability of trades and identities. While inspired by Bitcoin, Duniter uses a Web of Trust and the Proof of Work to secure the computation network, thus making obsolete the power race model used in Bitcoin.
-
-The first currency created through Duniter is Ğ1, pronounced "June". It was created on the 8th. March 2017. This whitepaper uses Ğ1 parameters as examples ; however, one can create another libre currency with custom parameters while still using Duniter software.
diff --git a/chapters/en/4_Web_Of_Trust.md.txt b/chapters/en/4_Web_Of_Trust.md.txt
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index a5e00e99fe6111cfb0d0004265594577b3b827b3..0000000000000000000000000000000000000000
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-## 3. Duniter Web of Trust
-
-
-### 3.1. Basic Principles {#duniter-wot-basic-principles}
-
-In order to identify "members" accounts - which create monetary units -
-and other accounts, Duniter uses a Web of Trust. This can be summarized
-into few principles:
-
--   Each account becomes a member if it received a minimal number of
-    certifications - 5 for Ğ1 currency.
--   Only members accounts can send certifications. Certifications have a
-    limited lifespan.
--   A certification indicates that the sender accepts the receiver as a
-    legitimate identity.
-
-The aim of the WoT is to identify a blockchain account to a living
-human. According to Lauterbach et.al[^Couchsurf], the strengh of a relationship should be considered when building a vouch system.
-For this reason, the Ğ1 Web of Trust rules are expressed in a licence stating what WoT certifications are.
-A certification represents a strong human relationship : one may certify a close relative, not an acquaintance.
-Each member has to accept this licence before being included in the WoT.
-Thus, if a member is part of an attack on the currency, they can be found by mutual relatives.
-Additional security rules occur to prevent cheat and attacks on a large scale.
-
-[^Couchsurf]: Surfing a Web of Trust, Reputation and Reciprocity on CouchSurfing.com, D.Lauterbach, H.Truong, T.Shah, L.Adamic: [snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf](http://snap.stanford.edu/class/cs224w-readings/lauterbach09trust.pdf)
-
-Note that non-members accounts can use the currency, but cannot create
-money. Non-members accounts can be used by individuals as secondary wallets, or by
-institutions.
-
-We were inspired by the OpenPGP Trust system[^OpenPGP_Trust]. However, the OpenPGP
-trust principles aim at defining trust from a particular point of view while Duniter needs to
-identify humans for the whole community. To achieve this goal, while OpenPGP allows each
-user to tweak its trust parameters individually, Duniter sets rules in the "genesis" block for the whole community. 
-
-[^OpenPGP_Trust]: Public key validation on GnuPG manual, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-### 3.2. Why do we need a Web of Trust ? {#why-do-we-need-a-web-of-trust}
-
-There are two reasons we need it :
-
-1.  To make sure that only one Universal Dividend is produced per member
-    at each specified creation interval. In the Ğ1's case this interval
-    is set as daily `86 400` seconds, it is the *monetary parameter*
-    known as `dt`.
-2.  To identify the nodes hashing the blocks and assign each a
-    personalised difficulty. This custom difficulty proof of work is
-    there to avoid the blockchain's validation mechanism becoming too
-    centralised as is the case with many \'non-libre' cryptocurrencies.
-
-> **Monetary parameter** : Each currency that use Duniter has its own blockchain whose behaviour is
-> dictated by a set of 'parameters' defined in block zero - the so-called
-> genesis block - that can be tweaked to achieve the desired results. At
-> the time of writing the Whitepaper, the Duniter Blockchain Protocol
-> (DUBP) has a total of 21 parameters of which 10 are for the WoT alone.
-> We'll focus on these 10.
-> 
-> Suffice to say that in the Ğ1's case, the DU is created every 24 hours -
-> 86 400 seconds. This interval is set through the time derivative `dt`
-> parameter and can have a different value in other implementations of the
-> protocol.
-
-We want to make sure that each member can only have one account. As we
-all know, achieving zero-risk isn't possible[^Sybil_Attack].
-Our goal is therefore not to create a WoT within which fraud
-would be absolutely impossible, but instead to discourage it. Here is a
-rewording of our goal in 4 smaller ones :
-
-1.  Make the certification process lengthy enough that all members
-    exercise due diligence and are wary of risks.
-2.  Make fraudulent acts as hard as we can to the extent that they
-    become pointless.
-3.  Ensure that any Sybil attacks have a negligible impact on the
-    currency by ensuring that illegitimate double Universal Dividends
-    have no significant bearing on the legitimate monetary mass
-4.  Slow the growth of 'Sybil regions' to give enough time for the
-    community to react and isolate the threat.
-    
-[^Sybil_Attack]: The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-
-> **Sybil attack** : A Sybil attack is an attack perpetrated on a
-> reputation system through the creation of fake identities. A Web of
-> Trust is a specific instance of a Reputation System. 
-
-There are plenty of Sybil attack scenarios we can think of and just as
-many reasons why their perpetrators would want to carry them out. Our
-objective is that the configuration of the WoT protects both users and
-its IT backbone infrastructure against these attacks.
-
-This means that micro-attacks performed by small groups of individuals
-looking for personal enrichment are of no interest to us. The web's role
-isn't to deter these attacks, this being instead the role of the
-community. Just like the town you live in is responsible for providing
-your tap water and electricity but isn't responsible for any burglaries,
-etc. Much in the same way, Duniter's WoT guarantees us all a functional
-currency, but do not detect small fraud.
-
-### 3.3. The importance of having our own certification system {#own-certification-system}
-
-Centralized identification systems can achieve the goal we want. State
-Identification is an example. However, this has many drawbacks :
-
-* The authority may have arbitrary criteria for identification, for example
-preventing people without an official state-provided identity or
-homeless people to be included in the WoT.
-* Payment might be required
-to get identified, thus making the monetary creation not "free".
-* The authority is a point of failure for any attacker.
-
-It is of the utmost importance that we remain free from any state or
-corporation. The WoT is an answer to this criterium. To this day we
-depend only on the Internet and yet, were it to fail, there are already
-alternatives being tested around the world for a decentralised communication network.
-
-### 3.4. A few foundational concepts on graph theory : a bit of vocabulary {#graph-theory-vocabulary}
-
--   **Graph**: set of points -called 'vertices'- joined by edges -called
-    paths/walks-.
-
--   **Simple graph**: a graph with no loops and with no multiple edges.
-    That is, each edge connects two distinct endpoints and no two edges
-    have the same endpoints. A simple edge is an edge that is not part
-    of a multiple adjacency -of edges-. In many cases, graphs are
-    assumed to be simple unless specified otherwise.
-    
--   **Directed graph**: a graph in which the edges have a distinguished
-    direction, from one vertex to another. A directed edge can also be
-    called a path or walk.
-    Arrow A --\> B is therefore different from arrow B --\> A.
-
--   **Endpoints**: the edge with vertex A --\> B has A and B as
-    endpoints, respectively as start and end of the path/walk.
-
--   **Isolated vertex**: a vertex whose degree is zero, that is, a
-    vertex with no incident edges.
-
--   **Degree of a vertex**: number of its incident edges -in and out-.
-
--   **Out-degree of vertex A**: number of outbound edges / tail ends
-    from A.
-
--   **In-degree of vertex A**: number of incoming edges / head ends
-    to A.
-
-![degrees of a vertex diagram](src/img/degrees_en.jpg)
-
--   **Path**: -aka "walk"- path to follow to get from vertex A to
-    vertex B.
-
-### 3.5. Definition of the Duniter Web of Trust {#definition-of-the-duniter-web-of-trust}
-
-The Duniter WoTs -one per currency- are simple directed graphs without
-isolated vertices. The vertices are the members and the edges are the
-certifications given and received.
-
-*Directed* means that the responsibility of issuing a certification is
-unique and personal to the certifier. The trust they place in the
-receiver cannot be imposed in the other direction although in most
-circumstances both parties equally trust each other.
-
-In addition, all vertices are either currently active members or
-past-members. Past-member vertices are in a specific 'deactivated state'
-and can no longer issue or receive certifications although the ones
-already issued or received to/from other members are still considered
-'pending' to avoid a collapse of the WoT. If these old members don't
-come back into the WoT, their pending certifications will eventually
-expire and they will switch from 'deactivated' to 'isolated' vertices.
-
-To wrap up with old members, after a certain period of time - set in the
-currency's parameters - their deactivated vertex is removed from the web
-and the associated identity is 'revoked'. The person who owned the
-account can no longer use this identity but is free to join the web with
-another one.
-
-> **Identity** : An identity is a set of three pieces of information: a public key, a
-> name and a blockstamp. A blockstamp points to a specific block in the
-> chain. Its main use is to freeze the point in time at which an identity
-> was created and to link this identity to a specific chain and a currency
-> - each currency having its own blockchain.
-> 
-> An identity can be in any one of 5 different status: pending, member,
-> old member, revoked or excluded.
-
-Let's take a simple example:
-
-```
-    A -> B -> C
-         |
-         \--> D
-```
-
-If, for whatever reason, A were to lose its member status, the web would
-crumble and all other members would be excluded as a consequence. To
-avoid this, the certification from A --\> B will remain valid until its
-expiry date, leaving enough time for B to receive certifications from C
-or D.
-
-Because our WoT doesn't have any isolated vertices, each new identity
-created needs to be pulled into the web with all of the certifications
-it has received, all in the same block. This calls for a temporary
-'buffer' storage space for **pending** identities and the certifications
-they have received. This storage space is called 'the pool' of Duniter
-nodes, which we could also have called the 'sandbox' as that's the name
-used in Duniter's code. Duniter nodes inclued other 'pools' for other
-documents and metadata not mentioned here.
-
-### 3.6. Exploring the rules behind a Duniter Web of Trust {#exploring-the-rules-behind-duniter-wot}
-
-The Duniter WoTs - one per currency - works with a set of eight
-fundamental rules enforced through eleven different parameters. Ten of
-these parameters are set within the genesis block, the eleventh one -
-`msPeriod`- having being hard-coded in the Ğ1's code subsequently.
-
-#### 3.6.1. Distance rule and referent members (`stepMax` and `xPercent`) {#distance-rule-and-referent-members-stepmax-and-xpercent}
-
-These two parameters are closely linked and together define the
-'distance rule'. The 'distance rule' can only be described after
-defining what a 'referent member' is:
-
-> **Referent member**: member A is said to be 'referent' if and only if
-> the total of their degrees are greater than or equal to
-> `CEIL-N^-1/stepMax` where N is the total number of members. As the
-> size of the web will grow this number will grow too, meaning it will
-> take more certification issuances to become a referent member. The
-> number of certifications needed to become a member shouldn't change.
-
-Let's now define the distance rule:
-
-> **Distance rule**: member A is said to observe this rule if and only
-> if for a subset xPercent % of referent members R there exists a path
-> of length less than or equal to `stepMax` between R and A.
-
-Referent members only exist so that the distance rule can take effect,
-they have no special privileges over non-referent members. In a perfect
-web, that is one in which each member has certified all members they
-legitimately can, all members would be referent members. However,
-because the web progressively grows in size and because members die and
-are replaced by new ones, there are always members at any given time `t`
-who haven't yet certified all members they legitimately could. These
-members would hinder the evolution of the web if they were taken into
-account in the calculation of the distance rule and the web would
-effectively stop growing.
-
-Because verifying the application of the distance rule is
-calculation-greedy, it is only performed when a new identity gets
-confirmed into the web or an existing member gets renewed. There is an
-exception to this rule: the distance rule is not observed in the genesis
-block -when the web is first implemented.
-
-#### 3.6.2. Rule of the minimum number of certifications needed (`sigQty`) {#rule-of-the-minimum-number-of-certifications-needed-sigqty}
-
-This is the simplest rule, it essentially says that each member must at
-any given time -meaning in any single block- have received at least
-`sigQty` active certifications. If, for whatever reason, member A were
-to have less than `sigQty` active certifications in a given block, they
-would cease to be a member and be required to publish a request for
-identity renewal.
-
-#### 3.6.3. The membership renewal rule (`msValidity`, `msPeriod` and `msWindow`) {#the-membership-renewal-rule-msvalidity-msperiod-and-mswindow}
-
-Bear in mind that a membership doesn't last a lifetime but instead has a
-lifespan set to `msValidity` seconds.
-
-Every single member -or old member who hasn't revoked his identity or
-been excluded- can request a membership renewal so long as the last
-request was made more than `msPeriod` seconds ago. If a member has never
-requested a renewal, the date of last renewal is equal to the timestamp
-at which his membership was first created. A new request will be stored
-in the 'pool' for a maximum of `msWindow` seconds before it's included
-in the blockchain. Once again, this can only happen once/if the member
-meets both the `siqQty` rule and the distance rule -if these criterion
-are already matched it's just a case of waiting for a new block to be
-mined-.
-
-If a member hasn't requested a renewal for longer than `msValidity`
-seconds, they automatically cease to be a member. From this moment on,
-the ex-member has another `msValidity` window to renew their membership.
-When this period of `2 × msValidity` runs out, the membership will
-expire and this identity will never be available for use again in the
-web. If the person so desires, they will have to publish new identity
-and membership documents and find enough certifiers, as any newcomer.
-
-#### 3.6.4. Rule of certification lifespan (`sigValidity`) {#rule-of-certification-lifespan-sigvalidity}
-
-All certifications included in the blockchain expire **sigValidity**
-seconds after they were **issued**.
-
-> /!\\ The issuance and the inclusion of a certification in the
-> blockchain occur at different times. When member A issues a
-> certification at time t1, it gets stored in the pool starting at t1
-> and only finds its way into the blockchain at t2 when all of the web's
-> rules are observed. Several weeks can thus go by between t1 and t2!!!
-
-#### 3.6.5. Rule of limited supply of active certifications (`sigStock`) {#rule-of-limited-supply-of-active-certifications-sigstock}
-
-By 'active certifications' we refer to certifications included in the
-blockchain and that haven't yet expired.
-
-The total of active certifications issued by any member at any single
-time must be less than or equal to `sigStock`. When this threshold is
-reached the member will have to wait for one of his active
-certifications to expire before he/she can issue a new one.
-
-#### 3.6.6. Rule of the time period between two certification issuances. (`sigPeriod`) {#rule-of-the-time-period-between-two-certification-issuances-sigperiod}
-
-As soon as a certification issued by member A gets included in the
-blockchain, they will be unable to issue a new one before another
-`sigPeriod` seconds.
-
-#### 3.6.7. Expiry of a certification issuance (`sigWindow`) {#expiry-of-a-certification-issuance-sigwindow}
-
-When a certification is issued by member A, it will be stored in the
-'pool' for a maximum of `sigWindow` seconds. If the certification hasn't
-been included in the blockchain by then, it will be cancelled and the
-member's `sigStock` will be repleted by one.
-
-#### 3.6.8. Lifespan of a 'pending' identity (`idtyWindow`) {#lifespan-of-a-pending-identity-idtywindow}
-
-When a new identity is created, it is stored in the 'pool' for a maximum
-of `idtyWindow` seconds. If the person hasn't achieved member status by
-then, the certification will simply be cancelled.
-
-### 3.7. Details on some of the WoT's peculiarities at the genesis block {#details-on-some-of-the-wots-peculiarities-at-the-genesis-block}
-
-The aforementioned rules can only be enforced with an existing web. They
-cannot be observed when first creating the web, that is when defining
-the genesis block.
-
-Only rules 2 and 5 can be observed at the genesis block.
-
-The genesis block has to be manually created by the founding members. In
-practice this means that there must be a choice on which identities to
-include on the premise that all of them observe rules 2 and 5. In
-addition, the genesis block must be signed with the private key of one
-of these identities.
-
-As soon as the genesis block has been created, the other identities can
-start mining the blockchain and the member who created block \#0
-effectively looses the decision power he had at creation.
-
-### 3.8. Why these rules and application cases in the Ğ1 {#why-these-rules-and-application-cases-in-the-g1}
-
-#### 3.8.1. Distance and maximum size {#distance-and-maximum-size}
-
-The distance rule is there to curb the maximum size of a Sybil region as
-well as that of the monetary community as a whole. The `xpercent`
-parameter prevents the creation of a 'faction' that could take hold of
-the blockchain.
-
-![Sybil region](src/img/wot-sybil.jpg)
-
-The Sybil regions are isolated from the rest of the graph in the sense
-that they can only receive certifications from other ill-intentioned
-Sybil members. As a consequence, the shortest edge/path between a
-legitimate member and a Sybil one has to have the attack's author as an
-endpoint. The maximum depth the Sybil region can attain is therefore
-contingent on the distance between the attacking edge-s- and the
-xpercent% closest referent members, this distance is known as
-`stepAttackers`. The maximum size of a Sybil region created by `sigQty`
-members depends on the L parameter, defined as `L = sigQty/sigStock`:
-
-```
-MaxSybilSize= (sigStock-sigQty)*(1-L^(stepMax-stepAttackers))/(1-L)
-```
-
-The maximum size of the Web of Trust is given by the following formula:
-
-```
-WoTmax = (sigStock)*L^(stepMax-1)
-```
-
-However we know for a fact that members will never use all of their
-available certifications. 
-According to Dunbar[^Dunbar], on average, one is able to maintain relationships to around 150 people.
-Being conservative, we will consider that on average, each person will certify 50 accounts. 
-We can calculate the size of the average web of trust `WoTavg` :
-
-```
-WoTavg= (50)*(sigQty/50)^(stepMax-1)
-```
-
-[^Dunbar]: Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
-
-
-Our goal with the Ğ1 is to create a community of about one million
-members to test the consequences of a libre monetary system. Let's see
-how we can tweak the pair of sigQty and stepMax- to reach this size:
-
-![Average WoT size graph as a function of sigQty and stepMax](src/img/wot-moy.png)
-
-The maximum size of a Sybil region grows linearly with `sigQty` but
-exponentially with `stepMax`. Logic has it that we need to keep
-`stepMax` as low as possible to ensure sufficient strength to the web.
-The above graph shows that the lowest value of `stepMax` for a web of a
-million members is of 5. This is an order of magnitude and is likely to
-be much higher in reality, we cannot measure it for sure.
-
-For `sigQty` we can choose a value of **4** for a web of **1.5 million
-members** or **5** for **half a million members**. Bear in mind these
-are gross figures and could be significantly higher, we are talking
-anywhere between 1 and 10 million in reality. Calculating WOTavg gives
-us a pretty good idea of how the web would scale bearing in mind that it
-considers all members are referent members too -which isn't the case as
-explained previously-. Hence the maximum size of the web is likely
-larger, a ballpark figure of half a million is enough for now especially
-knowing that the smaller `sigQty` is, the easier it is to launch a Sybil
-attack -it's easier to find four accomplices than five-. For security
-reasons we have settled on five:
-
-```
-stepMax = 5
-sigQty = 5
-sigStock \>= 50
-```
-
-The maximum size of a Sybil region therefore is:
-
-```
-(sigStock-sigQty)*(1-(sigStock/5)^(5-stepAttackers))/(1-(sigStock/5))
-```
-
-with sigStock = 50 we have a Sybil region of:
-
-```
-45*(1-10^(5-stepAttackers))/(-9)
-```
-
-A good practice for protecting the web is to maximise `stepAttackers`.
-That's why we decided that referent members in the genesis block had to
-be at least four steps away from each other.
-
-Another way to keep a Sybil attack at bay, were it slow enough for
-members to notice it, would be for referent members to 'stretch' the web
-intentionally to limit the growth of the region by ensuring that the
-attackers' legitimate certifications received in the first place aren't
-renewed. But what if bot accounts were created and certified each other
-super fast and following all rules, how would we counter that? By
-introducing a minimum length of time between two certifications!
-
-#### 3.8.2. Time is our friend {#time-is-our-friend}
-
-To help us deter a Sybil attack, we've decided to impose a minimum
-period of time between any two certifications issued from a single
-account. This parameter called `sigPeriod` affords us a greater chance
-to detect the formation of a 'hostile' faction.
-
-Here is a graph showing the evolution of a Sybil region with the
-variation of `sigPeriod`. The simulation considers that honest members 
-and attackers both issue a certification each `sigPeriod` interval, in days:
-
-![size of the WoT according to sigPeriod and stepAttackers](src/img/impact_sig_period.png)
-
-As we see, there is a strong link between the
-growth speed of the region and `sigPeriod`. As evidenced here, we need a
-`sigPeriod` high enough in order to ensure that the legitimate web can
-grow at least as fast as a Sybil region. In addition, the higher
-`sigPeriod` is, the more members will exercise their certification power
-gingerly, the action coming at a higher 'cost'.
-
-There are numerous advantages to giving `sigPeriod` a high value and no
-technical barriers to it, hence our choice of five days.
-
-We could have also gone for one week for the sake of simplicity. However
-there is an underlying idea behind our choice which was quite simply the
-pace of today's life. Certifying someone can be a lengthy process as one
-needs to make sure they are correctly applying the Ğ1 licence and people
-nowadays wait for the weekend to enjoy a bit of free-time. Thus the idea
-to allow one to certify at the end of every working week -five days-
-instead of a whole calendar one.
-
-#### 3.8.3. Trust me now, trust me forever ? (`sigValidity`, `msValidity`) {#trust-me-now-trust-me-forever-sigvalidity-msvalidity}
-
-There would be two main drawbacks to a lifetime membership in the Ğ1's
-Web of Trust:
-
--   First of all, some members will pass and those accounts should no
-    longer produce the Universal Dividend.
--   Secondly it is of the utmost importance that 'rogue' accounts can be
-    excluded from the web at some point.
-
-To achieve this, certifications have a limited lifespan. Members need to
-seek renewal from their peers after `sigValidity` time. On the other
-hand, this time can't be too short that members would spend more time
-seeking renewal than they would exchanging in the currency. Furthermore,
-a certification with too short a lifespan would foster careless
-certifying behaviours. The act of certifying must have a high-enough
-'perceived' cost to make it feel like an important act. Lastly, we also
-wanted this lifespan to be easy to remember. Historically speaking, we
-first settled on the values of `sigPeriod` and `sigStock`, meant one
-could issue all of their certifications in 495 days, one year was
-therefore not long enough. We deemed three years to be too much and
-that's how we agreed on two years in the end.
-
-Thinking that a deceased member could continue producing the UD for two
-long years without anyone benefitting from it was also something we
-needed to address. We chose a value of one year for **msValidity**. The
-act of renewing every year is done through one of the clients
-interacting with the blockchain, through a simple click on a button.
-This parameter is less important than others and is mostly there to
-'prune' the web of past or inactive members who don't renew their
-membership.
-
-#### 3.8.4. Keeping the pools free of information glut (`idtyWindow`, `sigWindow`, `msWindow`) {#keeping-the-pools-free-of-information-glut-idtywindow-sigwindow-mswindow}
-
-The pools need to be cleaned up on a regular basis to avoid them
-clogging up with information and to ensure that machines with less
-calculating power can still run a Duniter node.
-
-To achieve this, identities with pending membership approval and the
-corresponding certifications have to remain the shortest time possible
-in the pool while still having a chance of making it into the
-blockchain.
-
-For the Ğ1, our opinion was that two months would be enough for all
-potential certifiers to agree on a specific identity to certify. We also
-wanted a time period that would be easy enough to remember by all. We
-settled on two months, and gave this value to all three parameters
-`idtyWindow`, `sigWindow` and `msWindow`.
-
-#### 3.8.5. Avoiding single members from 'knowing too many people' (`sigStock`) {#avoiding-single-members-from-knowing-too-many-people-sigstock}
-
-We considered that on average, each person will certify 50 people. 
-However, we know for a fact that some members will use more than 50 certifications.
-The maximum social network of one individual is around 150 people[^Dunbar].
-Being conservative, we settled on a maximum certification number `sigstock` of 100.  
-Since `sigStock`'s impact on the size of a Sybil region is fairly limited, we did not investigate further this parameter.
-
-#### 3.8.6. Avoiding locking minorities (`xpercent`) {#avoiding-locking-minorities-xpercent}
-
-It's easy enough to become a referent member, one of the Sybil
-strategies could therefore be to create a region of referent members.
-Such a region would grow slower than otherwise but could confer a
-locking power to its members by using the distance rule. That's why the
-distance rule cannot be calculated on 100% of the referent members.
-Hence the introduction of the `xpercent` parameter which defines the
-percentage of referent members needing to be less than five edges
--steps- from each other.
-
-This percentage needs to be low enough to prevent the formation of a
-locking minority -referent Sybil members being too far from legitimate
-referent members-. On the other hand, it needs to be high enough so as
-to restrict the maximum size of the Sybil region through the distance
-rule. The `xpercent` parameter was one of the hardest to define,
-therefore we might decide to change its value during the Ğ1 experiment.
-
-We were inspired by the Pareto
-principle[^Pareto]: if at least
-20% of members give good density to the web, 80% of the referent members
-will be five or less steps from any other member -referent or not-. The
-maximum value for `xpercent` is therefore 80%, anything above that and
-the distance rule could be too restrictive for legitimate use cases.
-With security our top concern, we chose the maximum value of 80%.
-
-[^Pareto]: Pareto principle : [en.wikipedia.org/wiki/Pareto_principle](https://en.wikipedia.org/wiki/Pareto_principle)
-
-#### 3.8.7. Spam protection with (`msPeriod`) {#spam-protection-with-msperiod}
-
-This parameter stands out a bit on its own, as it was added after the
-genesis block. It is there to protect the Duniter P2P infrastructure
-against 'spam' attacks. We had to think of a strategy against attacks
-such as high-frequency membership renewal requests -i.e: in every block,
-every five minutes- or worse still, hundreds of these requests per
-minute to flood the Duniter nodes. Without such limits, nodes are
-supposed to address all renewal requests, even in cases where they were
-last published five minutes ago! The `msPeriod` parameter was given the
-same value as `idtyWindow`, `sigWindow` and `msWindow`, i.e. two months.
diff --git a/chapters/fr/2_looking_at_Bitcoin.md.txt b/chapters/fr/2_looking_at_Bitcoin.md.txt
deleted file mode 100644
index 48518a67f1e976432868d8bd226188af5161e6d8..0000000000000000000000000000000000000000
--- a/chapters/fr/2_looking_at_Bitcoin.md.txt
+++ /dev/null
@@ -1,104 +0,0 @@
-
-
-## 1. State of the art : Bitcoin case {#state-of-the-art-bitcoin-case}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter uses the crypto-currency concept introduced by Bitcoin[^BTC_whitepaper], which is
-to use cryptographic tools such as signatures to create trustless digital
-currencies. Duniter fits this definition, but it has two completely
-different principles than Bitcoin : the Web of Trust and the Universal
-Dividend . These differences are on both monetary and technical aspects.
-
-[^BTC_whitepaper]: Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-
-### 1.1. Monetary creation of Bitcoin : a space-time asymmetry {#monetary-creation-a-space-time-asymmetry}
-
-Space-time asymmetry refers to the relative access of individuals to
-newly created money[^RTM]. Concretely, most existing currencies (c. 2020) are
-both spatially and temporally asymmetrical for their users. Let\'s take
-Bitcoin as an example to understand why.
-
-[^RTM]: Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-
-#### 1.1.1. Spatial asymmetry {#spatial-asymmetry}
-
-When new Bitcoins are created, only some Bitcoin users (the miners)
-are given new Bitcoins, while everyone else get nothing. We believe
-this is the first injustice. However, some might say:
-
-> \"Miners used their electricity and time to get it!\"
-
-\... we would answer that this work should not have been rewarded by
-newly created Bitcoins. New units should be distributed to the whole
-community. Miners should be rewared another way, but not by
-money issuance. Of course, Bitcoin cannot create money through Basic
-Income since Bitcoin users are not strongly identified, and one might
-benefit from money creation multiple times if they owned several wallets.
-Duniter gets rid of this problem by identifying its users and
-creating the same amount of Basic Income to everyone.
-
-#### 1.1.2. Temporal-asymmetry {#temporal-asymmetry}
-
-Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
-which means ever fewer bitcoins will be created over time until no new BTC are
-being generated. So, once the first adopters have mined every bitcoin,
-how will future joiners get Bitcoins? Just like most of us do for Euros or
-Dollars: to get money, they will have to work for the ones who already own it.
-
-We believe this is the second injustice. Every member of a
-monetary community should be equal concerning monetary creation, and get
-the same relative amount of money over time, even if they are a late
-adopter. Duniter aims to fix this by making the Universal Dividend
-(a.k.a. UD) grow by the time according to precise rules, thus making
-members equal toward money issuance on a half-lifespan.
-
-Most currencies present one of these two asymmetries, including metal currencies
-and mutual credit, as exposed in the RTM.
-
-#### 1.1.3. A solution {#a-solution}
-
-Bitcoin has taught us that it is possible to create a currency system
-allowing one to both create digital money and to exchange it without a
-central authority. What we need to change is the way money is issued
-so we finally have a symmetrical system. We need **Bitcoin + Universal
-Dividend**. But Universal Dividend implies that the community consists
-of only identified people. This is where the Web of Trust (WoT) comes
-into place.
-
-This concept, introduced by cryptography with the OpenPGP format[^OpenPGP],
-allows us to identify people in a decentralized manner. It works as
-follows: each person creates a personal identity that is linked to its
-cyptographic certificate. The identity must be confirmed by others
-members who use their own cryptographic key. It is that simple: people
-choose who is part of the community and who is not, not a central
-authority.
-
-[^OpenPGP]: OpenPGP protocol defines standard formats for encrypted messages, signatures, private keys, and certificates for exchanging public keys. The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-
-However, Duniter will not use OpenPGP for its cryptographic features:
-Elliptic Curves[^Elliptic] will be used instead for the conciseness of its
-generated keys and its pratical advantages. Duniter has its own Web 
-of Trust principles, that will be exposed later.
-
-[^Elliptic]: High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-
-### 1.2. Proof-of-Work mining : a power race {#proof-of-work-mining-a-power-race}
-
-In Bitcoin Model, the calculation and incentive principles cause a power race :
-new Bitcoins are created for the owners of the most numerous, powerful (and energy-consuming) computers.
-This leads to a power race an places the control over the currency in the hands of the richest hardware owners.
-We want to make Duniter blockchain validation much less energy and hardware consuming while 
-keeping a strong level of security. This will be further explained later. A consequence of 
-this choice is the participation of low-end hardware in the Duniter network,
-leading to a better decentralization of blockchain validation.
-
-#### 1.2.1 What about Proof of Stake ? {#what-about-proof-of-stake}
-
-Proof of stake consensus algorythm was first introduced in 2012[^PPCoin]. The basic principle is to allow the richest wallets to issue blocks, putting their coin balance as a "stake" they would lose in case of cheat.
-
-[^PPCoin]: PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-
-At the time of conceiving Duniter, the PoS algorythms had not been tested enough to be used as a fundamental base. We did not chose this consensus principle.
-Moreover, the principle of allowing owners of large amounts of money to validate transaction can only lead 
-to placing power over the currency in the richests hands : this is contrary to the symmetical principles of a libre currency.
diff --git a/chapters/fr/3_blockchain.md.txt b/chapters/fr/3_blockchain.md.txt
deleted file mode 100644
index 641e5407c9037a004b5f2aa12886125e366df4e6..0000000000000000000000000000000000000000
--- a/chapters/fr/3_blockchain.md.txt
+++ /dev/null
@@ -1,86 +0,0 @@
-
-## 2. Duniters Blockchain {#duniters-blockchain}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-
-Duniters Blockchain follows the basic principles of Bitcoins. 
-This is essential for synchronization between peers, as to prevent double-spend attacks. 
-However, Duniters Blockchain will store different informations than Bitcoins. 
-
-The basic use of Blockchain will be registering transactions. For this part, we use the same principles as Bitcoin : transactions have inputs (spending accounts) and outputs (receiving accounts). But contrary to Bitcoin, no generation transaction exists : monetary creation happens only through UD. So, in Duniters Blockchain, Inputs can be either:
-
-* a former transaction (as in Bitcoin)
-* a Universal Dividend (specific to Duniter).
-
-Duniters Web of Trust is also written in the Blockchain. The identity of each
-member gets registered much like transactions are, with a strong link to the
-time reference. Thus, the Blockchain is a representation of a space-time frame
-of reference, where "space" are members of the WoT and "time" the basic blockchain
-units : the blocks. On each point of time, one can determine which account is
-legitimate to create the UD, only with a blockchain analysis.
-
-
-### 2.1. Spam countermeasures {#spam-countermeasures}
-
-
-An issue of most cryptocurrency projects is to prevent the common ledger from
-growing too much. This would require nodes to have a lot of storage and computing
-power to be usable. In particular, we don't want an attacker to be able to make the
-Blockchain grow too fast. Most projects implement transaction fees as a way to prevent
-this, making the attacker lose money. We don't want to introduce this mean since a
-currency with automatic fees on transactions is no more neutral. Several
-countermeasuers against such spam attacks are implemented.
-
-<!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
-
-#### 2.1.1. Minimum output amount {#minimum-output-amount}
-
-<!-- This has to be implemented in DUBPv13. -->
-
-Fixing a minimal output amount reduces the power of an attack. Duniter deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could create thousand accounts with only 1 UD. To prevent this, a valid transaction must have output amounts of minimum 1Ğ1. This reduces the power an attack by 100.
-
-#### 2.1.2. Limited block size and chainability {#limited-block-size-and-chainability}
-
-The block size is always limited. While the protocol allows this limit to evolve to address scaling issues, an attacker cannot register as many transaction as they wish.
-
-With the same goal to prevent too many transactions to get registered, while transactions can be "chained" (refer to another transaction in the same block), the chainability of transactions is limited to 5.
-
-
-### 2.2. Scaling {#scaling}
-
-Most of the time, the scaling issue rises for distributed systems that should work on a very large scale. This is not the case of Duniter, for multiple reasons :
-
-* Ğ1 is the first libre currency, and is still experimental on the monetary creation principle. We don't want it to reach the whole world, we only want it to work, to validate or invalidate the RTM. Moreover, the rules chosen for the Ğ1 WoT should limit its size to around 16 million members.
-* Duniter's aim is to be used to create multiple libre currencies, that would fit local or regional economies. As a consequence, it would deal with less transactions than if it was a world-scale system. The RTM proposes a formula to calculate the exchange rate between two currencies, that could be used to create automatic exchanges for a member travelling away from their community.
-
-However, Duniter has assets that will help if the number of users and transactions grow.
-
-#### 2.2.1 Dynamic block size {#dynamic-block-size}
-
-While Bitcoin has a fixed block size, Duniters blocks size can evolve. 
-On low use of the blockchain, the maximal block size is 500 bytes. 
-On high use of the blockchain, the maximal block size would be 110% of the
-average size of the current window blocks(see "personalised difficulty" part for more information).
-This way, the blocks are bounded in size, but can slowly grow if a massive and legitimate use of the blockchain needs it. The block size (in bytes) is limited as so :
-
-```
-block_size < max(500 ; CEIL(1.10 * (average block size))
-```
-
-#### 2.2.2. Lightning Networks {#lightning-networks}
-
-The Lightning Networks[^Lightning] allow almost instant and off-chain transactions.
-They were first implemented on Lightcoin, and are now on Bitcoin.
-One of their benefits is to make the blockchain store a lot of transactions at once, thus reducing the groth of the blockchain.
-The Duniter protocol allows XHX() and CSV() unlock conditions that are necessary to implement Lightning Networks.
-While not available yet, this payment channel might get implemented when needed.
-
-[^Lightning]: The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-
-#### 2.2.3. Unit base {#unit-base}
-
-As the Universal Dividend grows exponentially, with time Duniter nodes would have had to deal with always largest amounts, eventually reaching the BIGINT limit. To avoid this, the amounts are expressed with a unit base in base 10. We want the UD amount to always fit in 4 digits. To manage it, the `unitbase` is updated each time the UD value reaches 100.00 : it goes from `99.99*10^(unitbase)` to `10.00*10^(unitbase+1)`. All the unit amounts are thus divided by 10. While this might seem strange, this process has already hapened in state currencies. Moreover, the amounts expressed in UD will not change.
-
-With a monetary growth of 10% each year and a stable population, such a change of unit base would happen each 25 years.
-
diff --git a/chapters/fr/5_individualized_difficulty.md.txt b/chapters/fr/5_individualized_difficulty.md.txt
deleted file mode 100644
index 5019ea3d0c80c5825b7440866c5a6fa532201ef1..0000000000000000000000000000000000000000
--- a/chapters/fr/5_individualized_difficulty.md.txt
+++ /dev/null
@@ -1,356 +0,0 @@
-
-
-## 4. Proof of Work with personal difficulty {#proof-of-work-with-personalized-difficulty}
-
-As each P2P cryptocurrency, Duniter has a way to synchronize its peers. It uses a proof of Work (PoW) to write the Blockchain on a regular basis, much like BitCoin. However, Duniter has a unique asset : the WoT, where each member represents a unique living human.
-
-This difference might seem minimal, but it has an enormous consequence : while Bitcoin uses a race based on computing power only, Duniter creates a validation frame that is no race. It is more like a lottery where each "winning" member is excluded for a certain amount of time. Moreover, those who have more computing power get a handicap, as a way to let other peers win. All this is possible through the WoT, that allows personalised difficulty while PoW is used for synchronization. All the rules of this PoW/WoT mechanism can be verified by reading the blockchain. As a consequence, a peer only needs to have an up-to-date copy of the blockchain to apply the rules. A view of the whole network is not needed.
-
-Another strong difference is that forging peers are not rewarded by the protocol. There is no economical incentive on forging lots of blocs, neither on having a lot of computing power.
-
-One could say that Duniter uses a PoW that needs very low energy consumption compared to BitCoin : an "ecological" PoW ?
-
-
-
-<!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
-
-### 4.1. Why do we need Proof of Work ? {#why-proof-of-work}
-
-Duniter nodes share a database as part of a p2p environment. The proof of
-work (PoW) allows machines to synchronize with each other. In Duniter's case, the blockchain is
-our database, and acts as a ledger keeping
-a trace of all transactions, status of the WoT and more. 
-How can we let several machines add data (ie: a transaction) at
-the same time? In addition, how do we settle on how much time has gone
-by since the blockchain was last updated? Agreement on time is of the utmost importance
-as we want to create Universal Dividends on a regular basis, and keep track
-of membership status, both in human time.
-
-
-Proof-of-work provides a clever solution to both problems:
-
-1. Any machine can write into the blockchain (create a new block) but is only
-authorised to do so if it has previously solved a mathematical equation
-that require a certain amount of work. The challenge has to
-be hard enough to prevent two machines to solve it at the same time,
-ensuring the unicity of a block's creator.
-
-2. Solving this challenge
-takes a certain amount of time, which depends on the calculating power
-of the whole network. This provides a common ground for defining
-the needed time reference. A block time is set (ie: 1 block = 5 min) and 
-Duniter adapts the challenge difficulty to get an average duration 
-corresponding to this block time.
-
-### 4.2. Only members can "mine" {#only-members-can-mine}
-
-One of Duniter's major differences with other PoW-based cryptocurrencies
-is that only members are allowed to author blocks. Each block is signed
-with the member's private key, allowing the algorithm to determine a
-personalised difficulty.
-
-This personalised difficulty eliminates the rat-race for the most
-sophisticated and powerful mining equipment. Another benefit is the fact
-that no "supercomputer" can take control of the blockchain. Lastly, Duniter 
-implements a rotation in forging members thanks to this personalized difficulty.
-
-This lightweight PoW is much less energy-consuming than other PoW cryptocurrencies.
-Members can mine with anything from a raspberry pi to a privacy-first
-internet cube.
-
-### 4.3. How does it work ? {#how-does-duniter-pow-work}
-
-#### 4.3.1. The hash (aka digest) {#the-hash}
-
-Example of a valid hash:
-
-```
-00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653
-```
-
-As you can see this hash starts with five zeros which was very hard to
-achieve and took a lot of work for someone's computer. Hence the term
-"proof of work".
-
-#### 4.3.2. The common difficulty {#common-difficulty}
-
-A common difficulty is needed to settle on a yardstick for our time reference.
-Its role is to make sure the blockchain moves forward
-at a steady pace - one block every `avgGenTime` seconds, `avgGenTime`
-being one of the 20 parameters behind the Duniter protocol-. 
-
-This difficulty's initial value can be set to any arbitrary value (`70` in
-Duniter `v1.5.x`) and then acts as a spring, regulating blocktime
-creation by increasing itself if the creation interval drops under
-`avgGenTime` and vice-versa.
-
-##### 4.3.2.1. How is difficulty applied ? {#how-is-difficulty-applied}
-
-The numeric value of difficulty is taken from an array of possible
-hashes out of all possible hashes. In DUBPv13 the hash
-of a block is its sha256 hexadecimal hash.
-
-To understand the difficulty, we make a euclidiean division of the
-difficulty by 16.
-
-Here's an example with a difficulty value of 70 : 
-
-```
-70 // 16 = 4 with a remainder of 6. 
-```
-
-The valid hashes are the ones starting with four
-zeros and with the fifth character less than or equal to 9 (6 in hexadecimal notation).
-The valid hashes are then written as starting with : `0000[0-9]`. 
-This is a bit different from Bitcoin, 
-where the difficulty is only ruled by the number of zeroes.
-
-##### 4.3.2.2. The Nonce {#the-nonce}
-
-When a member is forging a new
-block, his computer freezes the block's content and changes the Nonce
-until the hash reaches the required number of zeroes. 
-
-The nonce allows us to mine a new block by finding a hash. The
-hash value allows us to determine the difficulty level of the
-proof-of-work performed. Examples of possible Nonce values:
-
--   10100000112275
--   10300000288743
--   10400000008538
--   10700000079653
--   10300000070919
-
-In reality the `Nonce` value follows a pre-determined format akin to
-`XYY00000000000`. The Nonce's value isn't the number of attempts but
-rather a value within a set of possible ones. This is how the Nonce is
-built:
-
--   X is a number assigned to a specific peer. Let's assume that someone
-    has several nodes each with the same private key, this would lead to
-    possible collisions if this person were to mine the same block with
-    different nodes. Each ~~block~~ **node ?** will therefore have its own unique X to
-    prevent this from happening.
-
--   Y is the number of cores of the processor. The Nonce starting with
-    `107[…]` belongs to a seven cores processor, while `199[...]` could
-    be the proof generated by a 99 cores processor.
-
-The rest of the Nonce, the part that follows after the XYY, is the
-numerical space for this individual node and is unique to each of the
-CPU's core. This space is comprised of eleven digits (`00000000000`).
-For the sake of accuracy, we use the term CPU in the wider sense, it can
-be understood as a bi-CPU for example. We take into consideration the
-number of cores for the resulting PoW.
-
-### 4.4. Personalised difficulty {#personalised-difficulty}
-
-Earlier in this article, we explained that the personalised difficulty
-is the new and key concept that sets Duniter apart from other
-PoW-based cryptocurrencies.
-
-Here is how this personalised difficulty is calculated and assigned:
-
-It is determined by a combination of two different constraints with
-complimentary roles: the **exclusion factor** and the **handicap**.
-
-Let `powMin` be the common difficulty, `exFact` a member's exclusion
-factor and `handicap` their handicap. This member's personalised
-difficulty `diff` is:
-
-```
-diff = powMin*exFact + handicap
-```
-
-#### 4.4.1. Understanding `exFact`, the exclusion factor {#the-exclusion-factor}
-
-Members who have never produced blocks or haven't for quite some time
-are assigned an exclusion factor of `1`. Their personalised difficulty
-is therefore simply the sum of `powMin + handicap`.
-
-Before reading on, let's precise the role of this exclusion factor.
-When a member adds a block to the chain, his `exFact` jumps up from one to
-a very high value, to prevent them from forging other blocks
-immediately after and taking control of the blockchain.
-
-The exclusion factor will then rapidly return to one. 
-This delay is expressed as a number of blocks. It is calculated as a
-proportion of the number of members forging. In the Ğ1's case, this
-proportion is 1/3, meaning that if there are fifteen members currently
-forging, the member's exclusion factor will drop down to one after five
-blocks.
-
-##### 4.4.1.1. What is intended by "the number of members forging" ?
-
-We mean the number of members trying to create the next block. 
-In reality, there is no way to precisely know how
-many members are calculating at any given time, because it is impossible
-to view the entire network. But we need this information, whithout which 
-assigning a personalised difficulty is impossible. 
-To achieve this, Duniter looks back at the blockchain and assumes that there is as much 
-members forging as those who have found at least one block
-in the last blocks in the current window, minus the very last one.
-
-##### 4.4.1.2. Current window
-
-We use the concept of **current window**. The current window is the number of blocks we look back at to determine how many members are forging.
-Let's see how it works: 
-
-* `issuersFrame` is the size of the
-current window in blocks.
-
-* `issuersCount` the number of members who
-have calculated at least one block during the current window. 
-
-Both `issuersFrame` and `issuersCount` are block fields. When first
-starting a blockchain, the very first block has an `issuersFrame=1` and
-an `issuersCount=0`. The genesis block is excluded as there are no members in the current
-window!
-
-From the second block onwards (block \#1) we track the variation of
-`issuersCount`. The member having mined block \#0 enters the current
-window and in block \#1 we will therefore mention `issuersCount=1`.
-
-
-`issuersFrame` then varies as follows: 
-
-* if `issuersCount` increases by N (with a maximum step of N = 1), then `issuersFrame` will increase by one unit over a period of 5N blocks. 
-* Conversely, if `issuersCount` decreases by Y (with a maximum step of Y = 2 = current window inching forward + loss of one calculating member), then `issuersFrame` will decrease by one unit during 5Y blocks. 
-* When such events overlap, `issuersFrame` evolves as so :
-
-| bloc | event | issuersFrame|
-|---|---|---|
-| T | Babar writes a block and enters issuersCount | 160 |
-| T+1 | Celeste leaves issuersCount | 160 +1 = 161 |
-| T+2 | N/a | 161 +1 -1 = 161 |
-| T+3/4/5 | N/a | 161 +1 -1 = 161 |
-| T+6 | N/a | 161 -1 = 160 |
-
-
-The calculation can be found under rules
-[BR\_G05](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe)
-and
-[BR\_G06](https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar)
-of the DUP protocol.
-
-##### 4.4.1.3. exFact and the personalised difficulty {#exfact-and-the-personalised-difficulty}
-
-We explained that `exFact` spikes immediately after the member has
-found a block. It decreases then rapidly to `1` after a number of 
-blocks equal to `1/3 * issuersCount`. Let's see precisely
-how we calculate `exFact`:
-
-* `nbPreviousIssuers` is the value of issuersCount at the
-last block `N` found by the member.
-
-* `nbBlocksSince` is the number of blocks
-found by the rest of the network since block `N`.
-
-* `percentRot` is the number of *not excluded* peers we want. It is a monetary parameter, its value is 0.67 for Ğ1 currency.
-
-```
-a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
-exFact = MAX [ 1 ; a ]
-```
-
-The FLOOR is a simple truncate function. For `exFact` to exclude the
-member, we need :
-
-```
-(percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) >= 2
-```
-
-We can see that the member is not excluded if `nbBlocksSince` is greater than 1/3 of
-the calculating members. Take as an example `nbPreviousIssuers = 6` and `nbBlocksSince = 3`:
-
-```
-(0.67* 6 / )1 + 3)) = 1.005 -> exFact = 1
-```
-
-However, if the member computed a block one block ago (nbBlocksSince = 1), exFact = 2 and the forging peer is excluded:
-
-```
-(0.67 * 6 / (1 + 1)) = 2.01 -> exFact = 2
-```
-
-Moreover if the last block was authored by the said member, then:
-```
-nbBlocksSince=0   and 
-exFact = 0.67 * nbPreviousIssuers
-```
-
-ExFact value increases according to the number of
-members calculating. Thus, if there is enough members calculating, even 
-mining farms would be excluded. We have therefore
-succeeded in our intent to deter attempts to seize the blockchain and
-its currency.
-
-
-However, at any time `t`, the two-thirds of
-calculating members all have an exclusion factor of `1`, even though
-they might not all have the same computational power at hand. If the
-personalised difficulty only took into account the exclusion factor, then
-only the members with the highest computational power from the remaining
-third would be able to author new blocks and the other 2/3s would almost
-always be excluded. Lesser machines wouldn't stand a
-chance...
-
-#### 4.4.2. The handicap {#the-handicap}
-
-The handicap is the second parameter of the personalised difficulty. Its
-main role is to improve the rotation of forging peers. 
-A higher handicap is assigned to members with higher calculating
-power, so lesser machines can also compute blocks. As a consequence, 
-there is no incentive on forging with powerful computers. 
-Security can be achieved with less computing power than with pure PoW.
-
-The aim is to handicap the half that has
-authored most blocks (the most powerful half) to favour the other one.
-So, the handicap formula will use the median number of blocks authored by peers within the current window.
-
-* `nbPersonalBlocksInFrame` is the number of blocks authored by a
-single member within the current window.
-
-* `medianOfBlocksInFrame` is the
-median number of blocks written by the calculating members during the
-same timeframe.
-
-```
-a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
-handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))
-```
-
-Let's unwrap the formula:
-
-```
-(nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)
-``` 
-
-is simply the
-ratio between the number of blocks authored by the peer and the median
-number of blocks. For example, if a peer has authored `9`
-blocks in the current window and the median is `5`, then the ratio
-will be `(9+1)/5 = 2`. The MAX function allows us to ensure that
-the handicap has a value at least equal to `1`.
-
-The Napierian Logarithm of this ratio prevents the handicap from becoming excluding.
-We want the handicap to level the calculating field so that all peers stand a chance, not to exclude peers.
-
-If we wanted the handicap to be applied as soon as the median is reached,
-we would divide it by `LN(1)`. The problem is that we have already set
-a minimum value of `1` with the MAX function. If we were to divide
-the ratio by `LN(1)` all calculating peers would have a handicap `\>=
-1`. In addition, is it really fair to handicap a member who is right on
-the median?
-
-That's why we went for `1.189` rather than `1`. A member has to
-be at least `18.9%` above the median to be assigned a handicap.
-18.9% is actually 16\^(1/16), the difficulty
-factor between two levels of the proof work (hexadecimal hash).
-
-To conclude, you have to remember that :
-
-* The handicap is indexed on the logarithm of the ratio to the median,
-* Handicap is only applied on members whose ratio to the median is greater than the ratio between two
-levels of the proof-of-work's difficulty.
-
diff --git a/chapters/fr/6_conclusion.md.txt b/chapters/fr/6_conclusion.md.txt
deleted file mode 100644
index eb4c02b2dbfa1cb1753c26eb33a5847abf01dced..0000000000000000000000000000000000000000
--- a/chapters/fr/6_conclusion.md.txt
+++ /dev/null
@@ -1,20 +0,0 @@
-
-
-## Conclusion {#conclusion}
-
-<!-- source : https://duniter.org/en/theoretical/ -->
-
-Duniter's Blockchain can be compared to Bitcoin's : a common document retracing the history of the currency. However, Duniter registers not only trades, but also the history of relationships in the community as a mean to identify a human to a digital account. This way, Duniter has information about the fondamental reference of RTM : living humans. A libre Currency can be issued thanks to the Universal Dividend.
-
-More than that, Duniter proposes a new model for securing a Blockchain in an efficient and decentralized way. Basing the security on a Web of Trust with an individualised security makes the calculation rules more fair. A side-effect of this choice is a network consisting mostly of low-end computers, maintaining a good security and helping decentralization of calculation.
-
-The ultimate goal of Duniter project is to allow people to participate in a libre economy, thanks to a libre currency. What is a libre economy ? The Relative Theory of Money defines it through four economic liberties :
-
-
-* The freedom to choose your currency system: because money should not be imposed.
-* The freedom to access resources: because we all should have access to economic & monetary resources.
-* The freedom to estimate and produce value: because value is a purely relative to each individual.
-* The freedom to trade with the money: because we should not be limited by the avaible money supply.
-
-
-Those 4 economic freedoms should be understood together, not exclusively. Plus, "freedom" has to be understood as "non-nuisance". So here, freedom does not mean the right to take all of a resource (like water source in a desert) so no more is available to the others. Now you get it, this is the goal: free economy through free currency.
diff --git a/chapters/fr/9_sources.md.txt b/chapters/fr/9_sources.md.txt
deleted file mode 100644
index 1cf07c80f7834d351c890c57112ccdc6e96c5cc8..0000000000000000000000000000000000000000
--- a/chapters/fr/9_sources.md.txt
+++ /dev/null
@@ -1,12 +0,0 @@
-
-## Sources : {#sources}
-
-* Relative Theory of Money, S.Laborde, 2010: [en.trm.creationmonetaire.info/](http://en.trm.creationmonetaire.info/)
-* Bitcoin Whitepaper, S.Nakamoto, 2008: [bitcoin.org/bitcoin.pdf](https://bitcoin.org/bitcoin.pdf)
-* The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 : [lightning.network/lightning-network-paper.pdf](http://lightning.network/lightning-network-paper.pdf)
-* The GNU Privacy Handbook, M.Ashley, 1999 : [www.gnupg.org/gph/en/manual.html#AEN335](https://www.gnupg.org/gph/en/manual.html#AEN335)
-* High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange, P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012), 77–89. [cr.yp.to/papers.html#ed25519](https://cr.yp.to/papers.html#ed25519).
-* PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King & S.Nadal, 2012 : [archive.org/details/PPCoinPaper](https://archive.org/details/PPCoinPaper)
-* Duniter Blockchain Protocol, v13, draft by Elois : [git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md](https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md)
-* The Sibyl Attack, J.R.Douceur: [www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf](https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf)
-* Neocortex size as a constraint on group size in primates, R.I.M.Dunbar, Journal of Human Evolution, 1992
diff --git a/make.bat b/make.bat
new file mode 100644
index 0000000000000000000000000000000000000000..6247f7e231716482115f34084ac61030743e0715
--- /dev/null
+++ b/make.bat
@@ -0,0 +1,35 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.http://sphinx-doc.org/
+	exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd
diff --git a/publication.sh b/publication.sh
index 556bb09e46a84bb5890ca8fa2eb0d75fa0b1bbbf..49b9cacfbe1f30c4bacdd0ee4382b6d45139f51d 100644
--- a/publication.sh
+++ b/publication.sh
@@ -6,27 +6,37 @@
 # ce script doit être lancé dans le dossier contenant les chapitres.
 
 # dépendances : pandoc
-hash pandoc 2>/dev/null || { echo >&2 "Ce générateur a besoin de la commande pandoc pour fonctionner. Mais cette commande n'est pas installée. Fin de l'exécution."; exit 1; }
+hash sphinx-build 2>/dev/null || { echo >&2 "Ce générateur a besoin de la commande sphinx-build pour fonctionner. Mais cette commande n'est pas installée. Fin de l'exécution."; exit 1; }
 ## Clean des dossiers de build et copie des assets
-[ -f whitepaper.html ] && rm whitepaper.html
-rm -rf build temp_whitepaper_html_en temp_whitepaper_html_fr temp_whitepaper_en.rst temp_whitepaper_fr.rst
-mkdir -p build/src/img/
-cp src/img/* build/src/img/
-mkdir -p build/src/js/
-cp src/js/* build/src/js/
-cp src/*.css build/
+#[ -f whitepaper.html ] && rm whitepaper.html
+#rm -rf build temp_whitepaper_html_en temp_whitepaper_html_fr temp_whitepaper_en.rst temp_whitepaper_fr.rst
+#mkdir -p build/src/img/
+#cp src/img/* build/src/img/
+#mkdir -p build/src/js/
+#cp src/js/* build/src/js/
+#cp src/*.css build/
+
+rm -rf build/*
 
 ## Compilation des différents chapitres
 ### (ceci devrait être refactorisé pour le support de davantage de langues)
 ### version anglaise
-touch temp_whitepaper_en.rst
-for i in chapters/en/*.rst ; do
-    cat $i >> temp_whitepaper_en.rst
+cp source/base_index.rst source/index.rst
+for i in source/parts/en/*.rst ; do
+    cat $i >> source/index.rst
 done
-pandoc -t html -f rst temp_whitepaper_en.rst -o temp_whitepaper_html_en
-cat src/head.html >> whitepaper_en.html
-cat temp_whitepaper_html_en >> whitepaper_en.html
-cat src/foot.html >> whitepaper_en.html
+
+sphinx-build -b html source build
+
+if [ -e build/index.html ] ; then
+    echo "===== HTML OK ====="
+fi
+
+
+#pandoc -t html -f rst temp_whitepaper_en.rst -o temp_whitepaper_html_en
+#cat src/head.html >> whitepaper_en.html
+#cat temp_whitepaper_html_en >> whitepaper_en.html
+#cat src/foot.html >> whitepaper_en.html
 
 
 ### version française
@@ -45,9 +55,9 @@ cat src/foot.html >> whitepaper_en.html
 #pandoc -o whitepaper_en.html temp_whitepaper_html_en
 
 #mv whitepaper_fr.html build/whitepaper_fr.html
-mv whitepaper_en.html build/whitepaper_en.html
+#mv whitepaper_en.html build/whitepaper_en.html
 
-firefox "$PWD/build/whitepaper_en.html"
+#firefox "$PWD/build/whitepaper_en.html"
 ## add ebook conversion
 #hash pandoc 2>/dev/null || { echo >&2 "Ce générateur peut utiliser ebook-convert fourni avec Calibre, disponible dans les dépots apt. Mais cette commande n'est pas installée. Fin de l'exécution."; exit 1; }
 #ebook-convert build/whitepaper_fr.html build/whitepaper_fr.mobi
@@ -62,14 +72,10 @@ firefox "$PWD/build/whitepaper_en.html"
 ## Création du fichier lateX et pdf
 ## Attention, certains caractères (U+2028) ne sont pas acceptés par LaTeX.
 #pandoc -o whitepaper_fr.pdf temp_whitepaper_fr.md
-pandoc -o whitepaper_en.pdf temp_whitepaper_en.rst
 
 ## déplacer les md, html et pdf dans le dossier de build
 #mv temp_whitepaper_fr.md build/whitepaper_fr.md
-mv temp_whitepaper_en.rst build/whitepaper_en.rst
 
-mv whitepaper_fr.pdf build/whitepaper_fr.pdf
-mv whitepaper_en.pdf build/whitepaper_en.pdf
+# clean fichiers temporaires
+rm index.rst
 
-# clean de fichiers temporaires
-rm temp_whitepaper_fr.md temp_whitepaper_en.md temp_whitepaper_html_fr temp_whitepaper_html_en missfont.log
diff --git a/source/_static/js/tex-mml-chtml.js b/source/_static/js/tex-mml-chtml.js
new file mode 100644
index 0000000000000000000000000000000000000000..f2f97033da58372a837ab169351c6b8f34a109ad
--- /dev/null
+++ b/source/_static/js/tex-mml-chtml.js
@@ -0,0 +1 @@
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ht,pt=(ht=d.BaseItem,i(ft,ht),Object.defineProperty(ft.prototype,"kind",{get:function(){return"dots"},enumerable:!0,configurable:!0}),ft.prototype.checkItem=function(t){if(t.isKind("open")||t.isKind("left"))return d.BaseItem.success;var e=this.getProperty("ldots"),r=t.First;if(t.isKind("mml")&&f.default.isEmbellished(r)){var n=f.default.getTexClass(f.default.getCoreMO(r));n!==u.TEXCLASS.BIN&&n!==u.TEXCLASS.REL||(e=this.getProperty("cdots"))}return[[e,t],!0]},ft);function ft(){return null!==ht&&ht.apply(this,arguments)||this}e.DotsItem=pt;var dt,mt=(dt=d.BaseItem,i(yt,dt),Object.defineProperty(yt.prototype,"kind",{get:function(){return"array"},enumerable:!0,configurable:!0}),Object.defineProperty(yt.prototype,"isOpen",{get:function(){return!0},enumerable:!0,configurable:!0}),Object.defineProperty(yt.prototype,"copyEnv",{get:function(){return!1},enumerable:!0,configurable:!0}),yt.prototype.checkItem=function(t){if(!t.isClose||t.isKind("over"))return dt.prototype.checkItem.call(this,t);if(t.getProperty("isEntry"))return this.EndEntry(),this.clearEnv(),d.BaseItem.fail;if(t.getProperty("isCR"))return this.EndEntry(),this.EndRow(),this.clearEnv(),d.BaseItem.fail;this.EndTable(),this.clearEnv();var e=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var r=this.create("node","mtable",this.table,this.arraydef);4===this.frame.length?f.default.setAttribute(r,"frame",this.dashed?"dashed":"solid"):this.frame.length&&(this.arraydef.rowlines&&(this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")),r=this.create("node","menclose",[r],{notation:this.frame.join(" "),isFrame:!0}),"none"===(this.arraydef.columnlines||"none")&&"none"===(this.arraydef.rowlines||"none")||f.default.setAttribute(r,"padding",0)),e&&(r=this.create("node","mstyle",[r],{scriptlevel:e})),(this.getProperty("open")||this.getProperty("close"))&&(r=p.default.fenced(this.factory.configuration,this.getProperty("open"),r,this.getProperty("close")));var n=this.factory.create("mml",r);if(this.getProperty("requireClose")){if(t.isKind("close"))return[[n],!0];throw new h.default("MissingCloseBrace","Missing close brace")}return[[n,t],!0]},yt.prototype.EndEntry=function(){var t=this.create("node","mtd",this.nodes);this.hfill.length&&(0===this.hfill[0]&&f.default.setAttribute(t,"columnalign","right"),this.hfill[this.hfill.length-1]===this.Size()&&f.default.setAttribute(t,"columnalign",f.default.getAttribute(t,"columnalign")?"center":"left")),this.row.push(t),this.Clear(),this.hfill=[]},yt.prototype.EndRow=function(){var t;t=this.getProperty("isNumbered")&&3===this.row.length?(this.row.unshift(this.row.pop()),this.create("node","mlabeledtr",this.row)):this.create("node","mtr",this.row),this.table.push(t),this.row=[]},yt.prototype.EndTable=function(){(this.Size()||this.row.length)&&(this.EndEntry(),this.EndRow()),this.checkLines()},yt.prototype.checkLines=function(){if(this.arraydef.rowlines){var t=this.arraydef.rowlines.split(/ /);t.length===this.table.length?(this.frame.push("bottom"),t.pop(),this.arraydef.rowlines=t.join(" ")):t.length<this.table.length-1&&(this.arraydef.rowlines+=" none")}if(this.getProperty("rowspacing")){for(var e=this.arraydef.rowspacing.split(/ /);e.length<this.table.length;)e.push(this.getProperty("rowspacing")+"em");this.arraydef.rowspacing=e.join(" ")}},yt);function yt(){var t=null!==dt&&dt.apply(this,arguments)||this;return t.table=[],t.row=[],t.frame=[],t.hfill=[],t.arraydef={},t.dashed=!1,t}e.ArrayItem=mt;var vt,bt=(i(gt,vt=mt),Object.defineProperty(gt.prototype,"kind",{get:function(){return"eqnarray"},enumerable:!0,configurable:!0}),gt.prototype.EndEntry=function(){this.row.length&&p.default.fixInitialMO(this.factory.configuration,this.nodes);var t=this.create("node","mtd",this.nodes);this.row.push(t),this.Clear()},gt.prototype.EndRow=function(){var t="mtr",e=this.factory.configuration.tags.getTag();e&&(this.row=[e].concat(this.row),t="mlabeledtr"),this.factory.configuration.tags.clearTag();var r=this.create("node",t,this.row);this.table.push(r),this.row=[]},gt.prototype.EndTable=function(){vt.prototype.EndTable.call(this),this.factory.configuration.tags.end()},gt);function gt(t){for(var e=[],r=1;r<arguments.length;r++)e[r-1]=arguments[r];var n=vt.call(this,t)||this;return n.factory.configuration.tags.start(e[0],e[2],e[1]),n}e.EqnArrayItem=bt;var Mt,Ot=(Mt=d.BaseItem,i(xt,Mt),Object.defineProperty(xt.prototype,"kind",{get:function(){return"equation"},enumerable:!0,configurable:!0}),Object.defineProperty(xt.prototype,"isOpen",{get:function(){return!0},enumerable:!0,configurable:!0}),xt.prototype.checkItem=function(t){if(t.isKind("end")){var e=this.toMml(),r=this.factory.configuration.tags.getTag();return this.factory.configuration.tags.end(),[[r?this.factory.configuration.tags.enTag(e,r):e,t],!0]}if(t.isKind("stop"))throw new h.default("EnvMissingEnd","Missing \\end{%1}",this.getName());return Mt.prototype.checkItem.call(this,t)},xt);function xt(t){for(var e=[],r=1;r<arguments.length;r++)e[r-1]=arguments[r];var n=Mt.call(this,t)||this;return n.factory.configuration.tags.start("equation",!0,e[0]),n}e.EquationItem=Ot},function(t,e,r){"use strict";var f=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 0===e||0<e--)&&!(n=o.next()).done;)a.push(n.value)}catch(t){i={error:t}}finally{try{n&&!n.done&&(r=o.return)&&r.call(o)}finally{if(i)throw i.error}}return a};Object.defineProperty(e,"__esModule",{value:!0});var d=r(35),h=r(7),m=r(5),c=r(21),y=r(16),v=r(9),p=r(0),s=r(27),o=r(14);r(222),r(232),r(233);var i={},u={fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,class:1,href:1,style:1};function a(t,e){var r=t.stack.env,n=r.inRoot;r.inRoot=!0;var i=new c.default(e,r,t.configuration),o=i.mml(),a=i.stack.global;if(a.leftRoot||a.upRoot){var s={};a.leftRoot&&(s.width=a.leftRoot),a.upRoot&&(s.voffset=a.upRoot,s.height=a.upRoot),o=t.create("node","mpadded",[o],s)}return r.inRoot=n,o}i.Open=function(t,e){t.Push(t.itemFactory.create("open"))},i.Close=function(t,e){t.Push(t.itemFactory.create("close"))},i.Tilde=function(t,e){t.Push(t.create("token","mtext",{},o.entities.nbsp))},i.Space=function(t,e){},i.Superscript=function(t,e){var r,n,i;t.GetNext().match(/\d/)&&(t.string=t.string.substr(0,t.i+1)+" "+t.string.substr(t.i+1));var o=t.stack.Top();o.isKind("prime")?(i=(r=f(o.Peek(2),2))[0],n=r[1],t.stack.Pop()):i=(i=t.stack.Prev())||t.create("token","mi",{},"");var a=h.default.getProperty(i,"movesupsub"),s=h.default.isType(i,"msubsup")?i.sup:i.over;if(h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")&&h.default.getChildAt(i,i.sup)||h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&h.default.getChildAt(i,i.over)&&!h.default.getProperty(i,"subsupOK"))throw new m.default("DoubleExponent","Double exponent: use braces to clarify");h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")||(s=a?(h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&!h.default.getChildAt(i,i.over)||(i=t.create("node","munderover",[i],{movesupsub:!0})),i.over):(i=t.create("node","msubsup",[i])).sup),t.Push(t.itemFactory.create("subsup",i).setProperties({position:s,primes:n,movesupsub:a}))},i.Subscript=function(t,e){var r,n,i;t.GetNext().match(/\d/)&&(t.string=t.string.substr(0,t.i+1)+" "+t.string.substr(t.i+1));var o=t.stack.Top();o.isKind("prime")?(i=(r=f(o.Peek(2),2))[0],n=r[1],t.stack.Pop()):i=(i=t.stack.Prev())||t.create("token","mi",{},"");var a=h.default.getProperty(i,"movesupsub"),s=h.default.isType(i,"msubsup")?i.sub:i.under;if(h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")&&h.default.getChildAt(i,i.sub)||h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&h.default.getChildAt(i,i.under)&&!h.default.getProperty(i,"subsupOK"))throw new m.default("DoubleSubscripts","Double subscripts: use braces to clarify");h.default.isType(i,"msubsup")&&!h.default.isType(i,"msup")||(s=a?(h.default.isType(i,"munderover")&&!h.default.isType(i,"mover")&&!h.default.getChildAt(i,i.under)||(i=t.create("node","munderover",[i],{movesupsub:!0})),i.under):(i=t.create("node","msubsup",[i])).sub),t.Push(t.itemFactory.create("subsup",i).setProperties({position:s,primes:n,movesupsub:a}))},i.Prime=function(t,e){var r=t.stack.Prev();if(r=r||t.create("node","mi"),h.default.isType(r,"msubsup")&&!h.default.isType(r,"msup")&&h.default.getChildAt(r,r.sup))throw new m.default("DoubleExponentPrime","Prime causes double exponent: use braces to clarify");var n="";for(t.i--;n+=o.entities.prime,t.i++,"'"===(e=t.GetNext())||e===o.entities.rquote;);n=["","\u2032","\u2033","\u2034","\u2057"][n.length]||n;var i=t.create("token","mo",{},n);t.Push(t.itemFactory.create("prime",r,i))},i.Comment=function(t,e){for(;t.i<t.string.length&&"\n"!==t.string.charAt(t.i);)t.i++},i.Hash=function(t,e){throw new m.default("CantUseHash1","You can't use 'macro parameter character #' in math mode")},i.SetFont=function(t,e,r){t.stack.env.font=r},i.SetStyle=function(t,e,r,n,i){t.stack.env.style=r,t.stack.env.level=i,t.Push(t.itemFactory.create("style").setProperty("styles",{displaystyle:n,scriptlevel:i}))},i.SetSize=function(t,e,r){t.stack.env.size=r,t.Push(t.itemFactory.create("style").setProperty("styles",{mathsize:r+"em"}))},i.Spacer=function(t,e,r){var n=t.create("node","mspace",[],{width:r}),i=t.create("node","mstyle",[n],{scriptlevel:0});t.Push(i)},i.LeftRight=function(t,e){var r=e.substr(1);t.Push(t.itemFactory.create(r).setProperty("delim",t.GetDelimiter(e)))},i.Middle=function(t,e){var r=t.GetDelimiter(e),n=t.create("node","TeXAtom",[],{texClass:p.TEXCLASS.CLOSE});if(t.Push(n),!t.stack.Top().isKind("left"))throw new m.default("MisplacedMiddle","%1 must be within \\left and \\right",t.currentCS);n=t.create("token","mo",{stretchy:!0},r),t.Push(n),n=t.create("node","TeXAtom",[],{texClass:p.TEXCLASS.OPEN}),t.Push(n)},i.NamedFn=function(t,e,r){r=r||e.substr(1);var n=t.create("token","mi",{texClass:p.TEXCLASS.OP},r);t.Push(t.itemFactory.create("fn",n))},i.NamedOp=function(t,e,r){r=(r=r||e.substr(1)).replace(/&thinsp;/,"\u2006");var n=t.create("token","mo",{movablelimits:!0,movesupsub:!0,form:y.TexConstant.Form.PREFIX,texClass:p.TEXCLASS.OP},r);t.Push(n)},i.Limits=function(t,e,r){var n=t.stack.Prev(!0);if(!n||h.default.getTexClass(h.default.getCoreMO(n))!==p.TEXCLASS.OP&&null==h.default.getProperty(n,"movesupsub"))throw new m.default("MisplacedLimits","%1 is allowed only on operators",t.currentCS);var i,o=t.stack.Top();h.default.isType(n,"munderover")&&!r?(i=t.create("node","msubsup"),h.default.copyChildren(n,i),n=o.Last=i):h.default.isType(n,"msubsup")&&r&&(i=t.create("node","munderover"),h.default.copyChildren(n,i),n=o.Last=i),h.default.setProperty(n,"movesupsub",!!r),h.default.setProperties(h.default.getCoreMO(n),{movablelimits:!1}),(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1})},i.Over=function(t,e,r,n){var i=t.itemFactory.create("over").setProperty("name",t.currentCS);r||n?(i.setProperty("open",r),i.setProperty("close",n)):e.match(/withdelims$/)&&(i.setProperty("open",t.GetDelimiter(e)),i.setProperty("close",t.GetDelimiter(e))),e.match(/^\\above/)?i.setProperty("thickness",t.GetDimen(e)):(e.match(/^\\atop/)||r||n)&&i.setProperty("thickness",0),t.Push(i)},i.Frac=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e),i=t.create("node","mfrac",[r,n]);t.Push(i)},i.Sqrt=function(t,e){var r=t.GetBrackets(e),n=t.GetArgument(e);"\\frac"===n&&(n+="{"+t.GetArgument(n)+"}{"+t.GetArgument(n)+"}");var i=new c.default(n,t.stack.env,t.configuration).mml();i=r?t.create("node","mroot",[i,a(t,r)]):t.create("node","msqrt",[i]),t.Push(i)},i.Root=function(t,e){var r=t.GetUpTo(e,"\\of"),n=t.ParseArg(e),i=t.create("node","mroot",[n,a(t,r)]);t.Push(i)},i.MoveRoot=function(t,e,r){if(!t.stack.env.inRoot)throw new m.default("MisplacedMoveRoot","%1 can appear only within a root",t.currentCS);if(t.stack.global[r])throw new m.default("MultipleMoveRoot","Multiple use of %1",t.currentCS);var n=t.GetArgument(e);if(!n.match(/-?[0-9]+/))throw new m.default("IntegerArg","The argument to %1 must be an integer",t.currentCS);"-"!==(n=parseInt(n,10)/15+"em").substr(0,1)&&(n="+"+n),t.stack.global[r]=n},i.Accent=function(t,e,r,n){var i=t.ParseArg(e),o=v.default.getFontDef(t);o.accent=!0;var a=h.default.createEntity(r),s=t.create("token","mo",o,a);h.default.setAttribute(s,"stretchy",!!n);var l=h.default.isEmbellished(i)?h.default.getCoreMO(i):i;h.default.isType(l,"mo")&&h.default.setProperties(l,{movablelimits:!1});var c=t.create("node","munderover");h.default.setChild(c,0,i),h.default.setChild(c,1,null),h.default.setChild(c,2,s);var u=t.create("node","TeXAtom",[c]);t.Push(u)},i.UnderOver=function(t,e,r,n,i){var o,a=t.ParseArg(e),s=h.default.getForm(a);(s&&s[3]&&s[3].movablelimits||h.default.getProperty(a,"movablelimits"))&&h.default.setProperties(a,{movablelimits:!1}),h.default.isType(a,"munderover")&&h.default.isEmbellished(a)&&(h.default.setProperties(h.default.getCoreMO(a),{lspace:0,rspace:0}),o=t.create("node","mo",[],{rspace:0}),a=t.create("node","mrow",[o,a]));var l=t.create("node","munderover",[a]),c=h.default.createEntity(r);o=t.create("token","mo",{stretchy:!0,accent:!i},c),h.default.setChild(l,"o"===e.charAt(1)?l.over:l.under,o);var u=l;n&&(u=t.create("node","TeXAtom",[l],{texClass:p.TEXCLASS.OP,movesupsub:!0})),h.default.setProperty(u,"subsupOK",!0),t.Push(u)},i.Overset=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e);(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1});var i=t.create("node","mover",[n,r]);t.Push(i)},i.Underset=function(t,e){var r=t.ParseArg(e),n=t.ParseArg(e);(h.default.getAttribute(n,"movablelimits")||h.default.getProperty(n,"movablelimits"))&&h.default.setProperties(n,{movablelimits:!1});var i=t.create("node","munder",[n,r]);t.Push(i)},i.TeXAtom=function(t,e,r){var n,i,o,a={texClass:r};if(r===p.TEXCLASS.OP){a.movesupsub=a.movablelimits=!0;var s=t.GetArgument(e),l=s.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);i=l?(a.mathvariant=y.TexConstant.Variant.NORMAL,t.create("token","mi",a,l[1])):(o=new c.default(s,t.stack.env,t.configuration).mml(),t.create("node","TeXAtom",[o],a)),n=t.itemFactory.create("fn",i)}else o=t.ParseArg(e),n=t.create("node","TeXAtom",[o],a);t.Push(n)},i.MmlToken=function(t,e){var r,n=t.GetArgument(e),i=t.GetBrackets(e,"").replace(/^\s+/,""),o=t.GetArgument(e),a={};try{r=t.create("node",n)}catch(t){r=null}if(!r||!r.isToken)throw new m.default("NotMathMLToken","%1 is not a token element",n);for(;""!==i;){var s=i.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!s)throw new m.default("InvalidMathMLAttr","Invalid MathML attribute: %1",i);if(!r.attributes.hasDefault(s[1])&&!u[s[1]])throw new m.default("UnknownAttrForElement","%1 is not a recognized attribute for %2",s[1],n);var l=v.default.MmlFilterAttribute(t,s[1],s[2].replace(/^(['"])(.*)\1$/,"$2"));l&&("true"===l.toLowerCase()?l=!0:"false"===l.toLowerCase()&&(l=!1),a[s[1]]=l),i=i.substr(s[0].length)}var c=t.create("text",o);r.appendChild(c),h.default.setProperties(r,a),t.Push(r)},i.Strut=function(t,e){var r=t.create("node","mrow"),n=t.create("node","mpadded",[r],{height:"8.6pt",depth:"3pt",width:0});t.Push(n)},i.Phantom=function(t,e,r,n){var i=t.create("node","mphantom",[t.ParseArg(e)]);(r||n)&&(i=t.create("node","mpadded",[i]),n&&(h.default.setAttribute(i,"height",0),h.default.setAttribute(i,"depth",0)),r&&h.default.setAttribute(i,"width",0));var o=t.create("node","TeXAtom",[i]);t.Push(o)},i.Smash=function(t,e){var r=v.default.trimSpaces(t.GetBrackets(e,"")),n=t.create("node","mpadded",[t.ParseArg(e)]);switch(r){case"b":h.default.setAttribute(n,"depth",0);break;case"t":h.default.setAttribute(n,"height",0);break;default:h.default.setAttribute(n,"height",0),h.default.setAttribute(n,"depth",0)}var i=t.create("node","TeXAtom",[n]);t.Push(i)},i.Lap=function(t,e){var r=t.create("node","mpadded",[t.ParseArg(e)],{width:0});"\\llap"===e&&h.default.setAttribute(r,"lspace","-1width");var n=t.create("node","TeXAtom",[r]);t.Push(n)},i.RaiseLower=function(t,e){var 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e=this.standardCHTMLnode(t),r=this.getScriptData(),n=this.combinePrePost(r.sub,r.psub),i=this.combinePrePost(r.sup,r.psup),o=l(this.getUVQ(r.base,n,i),3),a=o[0],s=o[1];o[2],r.numPrescripts&&this.addScripts(a,-s,!0,r.psub,r.psup,this.firstPrescript,r.numPrescripts),this.childNodes[0].toCHTML(e),r.numScripts&&this.addScripts(a,-s,!1,r.sub,r.sup,1,r.numScripts)},h.prototype.addScripts=function(t,e,r,n,i,o,a){var s=this.adaptor,l=t-i.d+(e-n.h),c=t<0&&0===e?n.h+t:t,u=0<l?{style:{height:this.em(l)}}:{},h=c?{style:{"vertical-align":this.em(c)}}:{},p=this.html("mjx-row"),f=this.html("mjx-row",u),d=this.html("mjx-row"),m="mjx-"+(r?"pre":"")+"scripts";s.append(this.chtml,this.html(m,h,[p,f,d]));for(var y=o+2*a;o<y;)this.childNodes[o++].toCHTML(s.append(d,this.html("mjx-cell"))),this.childNodes[o++].toCHTML(s.append(p,this.html("mjx-cell")))},h.kind=c.MmlMmultiscripts.prototype.kind,h.styles={"mjx-prescripts":{display:"inline-table","padding-left":".05em"},"mjx-scripts":{display:"inline-table","padding-right":".05em"},"mjx-prescripts > mjx-row > mjx-cell":{"text-align":"right"}},h);function h(){return null!==o&&o.apply(this,arguments)||this}e.CHTMLmmultiscripts=u},function(t,s,e){"use strict";var n,r=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])})(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),d=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 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r=this.font.params.scriptspace,n=this.getScriptData(),i=this.combinePrePost(n.sub,n.psub),o=this.combinePrePost(n.sup,n.psup),a=d(this.getUVQ(n.base,i,o),2),s=a[0],l=a[1];if(t.empty(),n.numPrescripts&&(t.combine(n.psup,r,s),t.combine(n.psub,r,l)),t.append(n.base),n.numScripts){var c=t.w;t.combine(n.sup,c,s),t.combine(n.sub,c,l),t.w+=r}t.clean(),this.setChildPWidths(e)},e.prototype.getScriptData=function(){if(this.scriptData)return this.scriptData;var t=this.scriptData={base:null,sub:i.BBox.empty(),sup:i.BBox.empty(),psub:i.BBox.empty(),psup:i.BBox.empty(),numPrescripts:0,numScripts:0},e=this.getScriptBBoxLists();return this.combineBBoxLists(t.sub,t.sup,e.subList,e.supList),this.combineBBoxLists(t.psub,t.psup,e.psubList,e.psupList),this.scriptData.base=e.base[0],this.scriptData.numPrescripts=e.psubList.length,this.scriptData.numScripts=e.subList.length,this.scriptData},e.prototype.getScriptBBoxLists=function(){var 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i=d([0,0,0],3),o=i[0],a=i[1],s=i[2];0===e.h&&0===e.d?o=this.getU(t,r):0===r.h&&0===r.d?o=-this.getV(t,e):(o=(n=d(l.prototype.getUVQ.call(this,t,e,r),3))[0],a=n[1],s=n[2]),this.UVQ=[o,a,s]}return this.UVQ},e;function e(){var t=null!==l&&l.apply(this,arguments)||this;return t.scriptData=null,t.firstPrescript=0,t}var l}},function(t,e,r){"use strict";var n,i=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)e.hasOwnProperty(r)&&(t[r]=e[r])})(t,e)},function(t,e){function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),y=this&&this.__values||function(t){var e="function"==typeof Symbol&&Symbol.iterator,r=e&&t[e],n=0;if(r)return r.call(t);if(t&&"number"==typeof t.length)return{next:function(){return t&&n>=t.length&&(t=void 0),{value:t&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,i,o=r.call(t),a=[];try{for(;(void 0===e||0<e--)&&!(n=o.next()).done;)a.push(n.value)}catch(t){i={error:t}}finally{try{n&&!n.done&&(r=o.return)&&r.call(o)}finally{if(i)throw i.error}}return a};Object.defineProperty(e,"__esModule",{value:!0});var o,a=r(3),s=r(163),l=r(63),h=r(8),c=(o=s.CommonMtableMixin(a.CHTMLWrapper),i(p,o),p.prototype.getAlignShift=function(){var t=o.prototype.getAlignShift.call(this);return this.isTop||(t[1]=0),t},p.prototype.toCHTML=function(t){var e,r,n=this.standardCHTMLnode(t);this.adaptor.append(n,this.html("mjx-table",{},[this.itable]));try{for(var i=y(this.childNodes),o=i.next();!o.done;o=i.next())o.value.toCHTML(this.itable)}catch(t){e={error:t}}finally{try{o&&!o.done&&(r=i.return)&&r.call(i)}finally{if(e)throw 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l=s.value,c=0;try{for(var u=(r=void 0,y(l.tableCells)),h=u.next();!h.done;h=u.next()){var p=h.value,f=i[c++],d=i[c],m=p?p.chtml:this.adaptor.childNodes(l.chtml)[c];(1<c&&"0.4em"!==f||o&&1===c)&&this.adaptor.setStyle(m,"paddingLeft",f),(c<this.numCols&&"0.4em"!==d||o&&c===this.numCols)&&this.adaptor.setStyle(m,"paddingRight",d)}}catch(t){r={error:t}}finally{try{h&&!h.done&&(n=u.return)&&n.call(u)}finally{if(r)throw r.error}}}}catch(t){e={error:t}}finally{try{s&&!s.done&&(t=a.return)&&t.call(a)}finally{if(e)throw e.error}}},p.prototype.handleColumnLines=function(){var e,t,r,n;if("none"!==this.node.attributes.get("columnlines")){var i=this.getColumnAttributes("columnlines");try{for(var o=y(this.childNodes),a=o.next();!a.done;a=o.next()){var s=a.value,l=0;try{for(var c=(r=void 0,y(this.adaptor.childNodes(s.chtml).slice(1))),u=c.next();!u.done;u=c.next()){var h=u.value,p=i[l++];"none"!==p&&this.adaptor.setStyle(h,"borderLeft",".07em 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s=y(this.childNodes),l=s.next();!l.done;l=s.next()){var c=l.value,u=i[a++],h=i[a];try{for(var p=(r=void 0,y(c.childNodes)),f=p.next();!f.done;f=p.next()){var d=f.value;(1<a&&"0.215em"!==u||o&&1===a)&&this.adaptor.setStyle(d.chtml,"paddingTop",u),(a<this.numRows&&"0.215em"!==h||o&&a===this.numRows)&&this.adaptor.setStyle(d.chtml,"paddingBottom",h)}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=p.return)&&n.call(p)}finally{if(r)throw r.error}}}}catch(t){e={error:t}}finally{try{l&&!l.done&&(t=s.return)&&t.call(s)}finally{if(e)throw e.error}}},p.prototype.handleRowLines=function(){var e,t,r,n;if("none"!==this.node.attributes.get("rowlines")){var i=this.getRowAttributes("rowlines"),o=0;try{for(var a=y(this.childNodes.slice(1)),s=a.next();!s.done;s=a.next()){var l=s.value,c=i[o++];if("none"!==c)try{for(var u=(r=void 0,y(this.adaptor.childNodes(l.chtml))),h=u.next();!h.done;h=u.next()){var p=h.value;this.adaptor.setStyle(p,"borderTop",".07em 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i=t.node.attributes.get("rowalign");if("baseline"===i||"axis"===i){var o=this.adaptor,a=o.lastChild(t.chtml);o.setStyle(a,"height",this.em(r)),o.setStyle(a,"verticalAlign",this.em(-n));var s=t.parent;if(!(s.node.isKind("mlabeledtr")&&t===s.childNodes[0]||"baseline"!==e&&"axis"!==e))return!0}return!1},p.prototype.handleFrame=function(){this.frame&&this.adaptor.setStyle(this.itable,"border",".07em "+this.node.attributes.get("frame"))},p.prototype.handleWidth=function(){var t=this.adaptor,e=this.getBBox(),r=e.w,n=e.L,i=e.R;t.setStyle(this.chtml,"minWidth",this.em(n+r+i));var o=this.node.attributes.get("width");if(h.isPercent(o))t.setStyle(this.chtml,"width",""),t.setAttribute(this.chtml,"width","full");else if(!this.hasLabels){if("auto"===o)return;o=this.em(this.length2em(o)+2*this.fLine)}var a=t.firstChild(this.chtml);t.setStyle(a,"width",o),t.setStyle(a,"minWidth",this.em(r)),(n||i)&&(t.setStyle(this.chtml,"margin",""),n===i?t.setStyle(a,"margin","0 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e=u(this.getPadAlignShift(t),3),r=(e[0],e[1]),n=e[2],i={};if("right"===t){var o=this.node.attributes.get("width"),a=this.getBBox(),s=a.w,l=a.L,c=a.R;i.style={width:h.isPercent(o)?"calc("+o+" + "+this.em(l+c)+")":this.em(l+s+c)}}return this.adaptor.append(this.chtml,this.html("mjx-labels",i,[this.labels])),[r,n]},p.prototype.updateRowHeights=function(){if(!this.node.attributes.get("equalrows"))for(var t=this.getTableData(),e=t.H,r=t.D,n=t.NH,i=t.ND,o=this.getRowHalfSpacing(),a=0;a<this.numRows;a++){var s=this.childNodes[a];e[a]!==n[a]||r[a]!==i[a]?this.setRowHeight(s,e[a]+r[a],r[a],o[a]+o[a+1]):s.node.isKind("mlabeledtr")&&this.setCellBaseline(s.childNodes[0],"",e[a]+r[a],r[a])}},p.prototype.addLabelSpacing=function(){for(var t=this.adaptor,e=this.node.attributes.get("equalrows"),r=this.getTableData(),n=r.H,i=r.D,o=e?this.getEqualRowHeight():0,a=this.getRowHalfSpacing(),s=this.fLine,l=t.firstChild(this.labels),c=0;c<this.numRows;c++)this.childNodes[c].node.isKind("mlabeledtr")?(s&&t.insert(this.html("mjx-mtr",{style:{height:this.em(s)}}),l),t.setStyle(l,"height",this.em((e?o:n[c]+i[c])+a[c]+a[c+1])),l=t.next(l),s=this.rLines[c]):s+=a[c]+(e?o:n[c]+i[c])+a[c+1]+this.rLines[c]},p.kind=l.MmlMtable.prototype.kind,p.styles={"mjx-mtable":{"vertical-align":".25em","text-align":"center",position:"relative","box-sizing":"border-box"},"mjx-labels":{position:"absolute",left:0,top:0},"mjx-table":{display:"inline-block","vertical-align":"-.5ex"},"mjx-table > mjx-itable":{"vertical-align":"middle","text-align":"left","box-sizing":"border-box"},"mjx-labels > mjx-itable":{position:"absolute",top:0},'mjx-mtable[justify="left"]':{"text-align":"left"},'mjx-mtable[justify="right"]':{"text-align":"right"},'mjx-mtable[justify="left"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="left"][side="right"]':{"padding-left":"0 ! important"},'mjx-mtable[justify="right"][side="left"]':{"padding-right":"0 ! important"},'mjx-mtable[justify="right"][side="right"]':{"padding-left":"0 ! important"},"mjx-mtable[align]":{"vertical-align":"baseline"},'mjx-mtable[align="top"] > mjx-table':{"vertical-align":"top"},'mjx-mtable[align="bottom"] > mjx-table':{"vertical-align":"bottom"},'mjx-mtable[side="right"] mjx-labels':{"min-width":"100%"}},p);function p(t,e,r){void 0===r&&(r=null);var n=o.call(this,t,e,r)||this;return n.itable=n.html("mjx-itable"),n.labels=n.html("mjx-itable"),n}e.CHTMLmtable=c},function(t,e,r){"use strict";var n,o=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof 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e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return"number"==typeof e.cWidths[t]?e.cWidths[t]:r[t]});return this.node.attributes.get("equalcolumns")&&(t=Array(t.length).fill(b.max(t))),t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):v.isPercent(t)?this.getColumnWidthsPercent(e,t):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);if("auto"===t){var n=this.getTableData().W;e=b.max(n)}else if(v.isPercent(t))e=this.percent(1/r);else{var i=b.sum([].concat(this.cLines,this.cSpace))+2*this.fSpace[0];e=Math.max(0,this.length2em(t)-i)/r}return Array(this.numCols).fill(e)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return 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r=this.node.attributes.get("equalrows"),n=this.getTableData(),i=n.H,o=n.D,a=r?this.getEqualRowHeight():0,s=this.getRowHalfSpacing(),l=this.fLine,c=0;c<t;c++)l+=s[c]+(r?a:i[c]+o[c])+s[c+1]+this.rLines[c];var u=y(r?[(a+i[t]-o[t])/2,(a-i[t]+o[t])/2]:[i[t],o[t]],2),h=u[0],p=u[1];return l+={top:0,center:s[t]+(h+p)/2,bottom:s[t]+h+p+s[t+1],baseline:s[t]+h,axis:s[t]+h-.25}[e]||0},e.prototype.getEmHalfSpacing=function(t,e){var r=this.em(t),n=this.addEm(e,2);return n.unshift(r),n.push(r),n},e.prototype.getRowHalfSpacing=function(){var t=this.rSpace.map(function(t){return t/2});return t.unshift(this.fSpace[1]),t.push(this.fSpace[1]),t},e.prototype.getColumnHalfSpacing=function(){var t=this.cSpace.map(function(t){return t/2});return t.unshift(this.fSpace[0]),t.push(this.fSpace[0]),t},e.prototype.getAlignmentRow=function(){var t=y(v.split(this.node.attributes.get("align")),2),e=t[0],r=t[1];if(null==r)return[e,null];var n=parseInt(r);return 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n=u(Object.keys(this.settings)),i=n.next();!i.done;i=n.next()){var o=i.value;this.settings[o]!==this.defaultSettings[o]&&(r[o]=this.settings[o])}}catch(t){e={error:t}}finally{try{i&&!i.done&&(t=n.return)&&t.call(n)}finally{if(e)throw e.error}}try{Object.keys(r).length?localStorage.setItem(d.MENU_STORAGE,JSON.stringify(r)):localStorage.removeItem(d.MENU_STORAGE)}catch(t){console.log("MathJax localStorage error: "+t.message)}},d.prototype.setA11y=function(t){h._.a11y&&h._.a11y.explorer&&h._.a11y.explorer_ts.setA11yOptions(this.document,t)},d.prototype.getA11y=function(t){if(h._.a11y&&h._.a11y.explorer)return this.document.options.a11y[t]},d.prototype.setScale=function(t){this.document.outputJax.options.scale=parseFloat(t),this.document.rerender()},d.prototype.setRenderer=function(e){var r=this;if(this.jax[e])this.setOutputJax(e);else{var n=e.toLowerCase();this.loadComponent("output/"+n,function(){var t=h.startup;n in t.constructors&&(t.useOutput(n,!0),t.output=t.getOutputJax(),r.jax[e]=t.output,r.setOutputJax(e))})}},d.prototype.setOutputJax=function(t){this.jax[t].setAdaptor(this.document.adaptor),this.document.outputJax=this.jax[t],this.rerender()},d.prototype.setTabOrder=function(t){this.menu.getStore().inTaborder(t)},d.prototype.setAssistiveMml=function(t){!t||h._.a11y&&h._.a11y["assistive-mml"]?this.rerender():this.loadA11y("assistive-mml")},d.prototype.setExplorer=function(t){this.enableExplorerItems(t),!t||h._.a11y&&h._.a11y.explorer?this.rerender(this.settings.collapsible?c.STATE.RERENDER:c.STATE.COMPILED):this.loadA11y("explorer")},d.prototype.setCollapsible=function(t){!t||h._.a11y&&h._.a11y.complexity?this.rerender(c.STATE.COMPILED):this.loadA11y("complexity")},d.prototype.scaleAllMath=function(){var t=(100*parseFloat(this.settings.scale)).toFixed(1).replace(/.0$/,""),e=prompt("Scale all mathematics (compared to surrounding text) 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n=r.load(t).then(function(){d.loading--,d.loadingPromises.delete(t),e(),0===d.loading&&d._loadingPromise&&(d._loadingPromise=null,d._loadingOK())}).catch(function(t){d._loadingPromise?(d._loadingPromise=null,d._loadingFailed(t)):console.log(t)});d.loadingPromises.set(t,n)}}},d.prototype.loadA11y=function(r){var n=this,i=!c.STATE.ENRICHED;this.loadComponent("a11y/"+r,function(){var t=h.startup;o.mathjax.handlers.unregister(t.handler),t.handler=t.getHandler(),o.mathjax.handlers.register(t.handler);var e=n.document;n.document=t.document=t.getDocument(),(n.document.menu=n).transferMathList(e),n.document.processed=e.processed,d._loadingPromise||n.rerender("complexity"===r||i?c.STATE.COMPILED:c.STATE.TYPESET)})},d.prototype.transferMathList=function(t){var e,r,n=this.document.options.MathItem;try{for(var i=u(t.math),o=i.next();!o.done;o=i.next()){var a=o.value,s=new 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qt(t,e){var r=mt.call(this)||this;return r.title="",r.window=null,r.localSettings={left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},r.windowList=[],r.mobileFlag=!1,r.active=null,r.title=t,r.content=e||function(){return""},r}r=vt=vt||{},gt.prototype.getName=function(){return this.name},gt.prototype.getValue=function(t){try{return this.getter(t)}catch(t){r.MenuUtil.error(t,"Command of variable "+this.name+" failed.")}},gt.prototype.setValue=function(t,e){try{this.setter(t,e)}catch(t){r.MenuUtil.error(t,"Command of variable "+this.name+" failed.")}this.update()},gt.prototype.register=function(t){-1===this.items.indexOf(t)&&this.items.push(t)},gt.prototype.unregister=function(t){var e=this.items.indexOf(t);-1!==e&&this.items.splice(e,1)},gt.prototype.update=function(){this.items.forEach(function(t){return t.update()})},gt.prototype.registerCallback=function(e){this.items.forEach(function(t){return 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e in t)this.html.setAttribute(e,t[e])},Ct.prototype.getHtml=function(){return this.html||this.generateHtml(),this.html},Ct.prototype.setHtml=function(t){this.html=t,this.addEvents(t)},Ct.prototype.generateHtml=function(){var t=document.createElement("div");t.classList.add(this.className),t.setAttribute("role",this.role),this.setHtml(t)},Ct.prototype.focus=function(){var t=this.getHtml();t.setAttribute("tabindex","0"),t.focus()},Ct.prototype.unfocus=function(){var t=this.getHtml();t.hasAttribute("tabindex")&&t.setAttribute("tabindex","-1");try{t.blur()}catch(t){}},m=Ct,f.MenuElement=m,y=vt=vt||{},v=y.MenuElement,bt(_t,v),_t.prototype.getMenu=function(){return this.menu},_t.prototype.setMenu=function(t){this.menu=t},_t.prototype.getType=function(){return this.type},_t.prototype.hide=function(){this.hidden=!0,this.menu.generateMenu()},_t.prototype.show=function(){this.hidden=!1,this.menu.generateMenu()},_t.prototype.isHidden=function(){return this.hidden},b=_t,y.AbstractEntry=b,g=vt=vt||{},M=g.MenuElement,bt(wt,M),wt.prototype.isPosted=function(){return this.posted},wt.prototype.post=function(t,e){this.posted||(void 0!==t&&void 0!==e&&this.getHtml().setAttribute("style","left: "+t+"px; top: "+e+"px;"),this.display(),this.posted=!0)},wt.prototype.unpost=function(){if(this.posted){var t=this.getHtml();t.parentNode&&t.parentNode.removeChild(t),this.posted=!1}},O=wt,g.AbstractPostable=O,x=vt=vt||{},S=x.AbstractPostable,bt(At,S),At.prototype.getItems=function(){return this.items},At.prototype.getPool=function(){return this.variablePool},At.prototype.getFocused=function(){return this.focused},At.prototype.setFocused=function(t){if(this.focused!==t){this.focused||this.unfocus();var e=this.focused;this.focused=t,e&&e.unfocus()}},At.prototype.up=function(t){var e=this.getItems().filter(function(t){return t instanceof x.AbstractItem&&!t.isHidden()});if(0!==e.length)if(this.focused){var r=e.indexOf(this.focused);-1!==r&&e[r=r?--r:e.length-1].focus()}else e[e.length-1].focus()},At.prototype.down=function(t){var e=this.getItems().filter(function(t){return t instanceof x.AbstractItem&&!t.isHidden()});if(0!==e.length)if(this.focused){var r=e.indexOf(this.focused);-1!==r&&e[r=++r===e.length?0:r].focus()}else e[0].focus()},At.prototype.generateHtml=function(){S.prototype.generateHtml.call(this),this.generateMenu()},At.prototype.generateMenu=function(){var t=this.getHtml();t.classList.add(x.HtmlClasses.MENU);for(var e=0,r=this.items;e<r.length;e++){var n=r[e];if(n.isHidden()){var i=n.getHtml();i.parentNode&&i.parentNode.removeChild(i)}else t.appendChild(n.getHtml())}},At.prototype.post=function(t,e){this.variablePool.update(),S.prototype.post.call(this,t,e)},At.prototype.unpostSubmenus=function(){for(var t=0,e=this.items.filter(function(t){return t instanceof x.Submenu});t<e.length;t++){var r=e[t];r.getSubmenu().unpost(),r!==this.getFocused()&&r.unfocus()}},At.prototype.unpost=function(){S.prototype.unpost.call(this),this.unpostSubmenus(),this.setFocused(null)},At.prototype.find=function(t){for(var e=0,r=this.getItems();e<r.length;e++){var n=r[e];if("rule"!==n.getType()){if(n.getId()===t)return n;if("submenu"===n.getType()){var i=n.getSubmenu().find(t);if(i)return i}}}return null},At.prototype.parseItems=function(t){var e=this;t.map(function(t){return[e.parseItem.bind(e)(t),t.hidden]}).forEach(function(t){return t[1]&&t[0].hide()})},At.prototype.parseItem=function(t){var e={checkbox:x.Checkbox.parse,combo:x.Combo.parse,command:x.Command.parse,label:x.Label.parse,radio:x.Radio.parse,rule:x.Rule.parse,submenu:x.Submenu.parse}[t.type];if(e){var r=e(t,this);return this.getItems().push(r),t.disabled&&r.disable(),r}},E=At,x.AbstractMenu=E,C=vt=vt||{},Tt.prototype.setActive=function(t){do{if(-1!==this.store.indexOf(t)){this.active=t;break}t=t.parentNode}while(t)},Tt.prototype.getActive=function(){return this.active},Tt.prototype.next=function(){var t=this.store.length;if(0===t)return this.active=null;var e=this.store.indexOf(this.active);return e=-1!==e&&e<t-1?e+1:0,this.active=this.store[e],this.active},Tt.prototype.previous=function(){var t=this.store.length;if(0===t)return this.active=null;var e=t-1,r=this.store.indexOf(this.active);return r=-1===r||0===r?e:r-1,this.active=this.store[r],this.active},Tt.prototype.clear=function(){this.remove(this.store)},Tt.prototype.insert=function(t){for(var e=0,r=t instanceof HTMLElement?[t]:t;e<r.length;e++){var n=r[e];this.insertElement(n)}this.sort()},Tt.prototype.remove=function(t){for(var e=0,r=t instanceof HTMLElement?[t]:t;e<r.length;e++){var n=r[e];this.removeElement(n)}this.sort()},Tt.prototype.inTaborder=function(t){this.taborder&&!t&&this.removeTaborder(),!this.taborder&&t&&this.insertTaborder(),this.taborder=t},Tt.prototype.insertTaborder=function(){this.taborder&&this.insertTaborder_()},Tt.prototype.removeTaborder=function(){this.taborder&&this.removeTaborder_()},Tt.prototype.insertElement=function(t){t.classList.contains(this.attachedClass)||(t.classList.add(this.attachedClass),this.taborder&&this.addTabindex(t),this.addEvents(t))},Tt.prototype.removeElement=function(t){t.classList.contains(this.attachedClass)&&(t.classList.remove(this.attachedClass),this.taborder&&this.removeTabindex(t),this.removeEvents(t))},Tt.prototype.sort=function(){var t=document.getElementsByClassName(this.attachedClass);this.store=[].slice.call(t)},Tt.prototype.insertTaborder_=function(){this.store.forEach(function(t){return t.setAttribute("tabindex","0")})},Tt.prototype.removeTaborder_=function(){this.store.forEach(function(t){return t.setAttribute("tabindex","-1")})},Tt.prototype.addTabindex=function(t){t.hasAttribute("tabindex")&&t.setAttribute(C.HtmlAttrs.OLDTAB,t.getAttribute("tabindex")),t.setAttribute("tabindex","0")},Tt.prototype.removeTabindex=function(t){t.hasAttribute(C.HtmlAttrs.OLDTAB)?(t.setAttribute("tabindex",t.getAttribute(C.HtmlAttrs.OLDTAB)),t.removeAttribute(C.HtmlAttrs.OLDTAB)):t.removeAttribute("tabindex")},Tt.prototype.addEvents=function(t){t.hasAttribute(C.HtmlAttrs.COUNTER)||(this.addEvent(t,"contextmenu",this.menu.post.bind(this.menu)),this.addEvent(t,"keydown",this.keydown.bind(this)),t.setAttribute(C.HtmlAttrs.COUNTER,this.counter.toString()),this.counter++)},Tt.prototype.addEvent=function(t,e,r){var n=C.HtmlAttrs[e.toUpperCase()+"FUNC"];this.attrMap[n+this.counter]=r,t.addEventListener(e,r)},Tt.prototype.removeEvents=function(t){if(t.hasAttribute(C.HtmlAttrs.COUNTER)){var e=t.getAttribute(C.HtmlAttrs.COUNTER);this.removeEvent(t,"contextmenu",e),this.removeEvent(t,"keydown",e),t.removeAttribute(C.HtmlAttrs.COUNTER)}},Tt.prototype.removeEvent=function(t,e,r){var n=C.HtmlAttrs[e.toUpperCase()+"FUNC"],i=this.attrMap[n+r];t.removeEventListener(e,i)},Tt.prototype.keydown=function(t){t.keyCode===C.KEY.SPACE&&(this.menu.post(t),t.preventDefault(),t.stopImmediatePropagation())},_=Tt,C.MenuStore=_,w=vt=vt||{},A=w.AbstractMenu,bt(Lt,A),Lt.parse=function(t){var e=t.menu;if(e){var r=e.pool,n=e.items,i=(e.id,new this);return r.forEach(i.parseVariable.bind(i)),i.parseItems(n),i}w.MenuUtil.error(null,"Wrong JSON format for menu.")},Lt.prototype.generateHtml=function(){this.isPosted()&&this.unpost(),A.prototype.generateHtml.call(this),this.frame=document.createElement("div"),this.frame.classList.add(w.HtmlClasses.MENUFRAME);var t="left: 0px; top: 0px; z-index: 200; width: 100%; height: 100%; border: 0px; padding: 0px; margin: 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this.moving||this.getStore().removeTaborder(),void A.prototype.post.call(this,t,e);var r,n,i,o=t;if(o instanceof Event?(r=o.target,this.stop(o)):r=o,o instanceof MouseEvent&&(n=o.pageX,i=o.pageY,n||i||!o.clientX||(n=o.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,i=o.clientY+document.body.scrollTop+document.documentElement.scrollTop)),!n&&!i&&r){var a=window.pageXOffset||document.documentElement.scrollLeft,s=window.pageYOffset||document.documentElement.scrollTop,l=r.getBoundingClientRect();n=(l.right+l.left)/2+a,i=(l.bottom+l.top)/2+s}this.getStore().setActive(r),this.anchor=this.getStore().getActive();var c=this.getHtml();n+c.offsetWidth>document.body.offsetWidth-5&&(n=document.body.offsetWidth-c.offsetWidth-5),this.post(n,i)},Lt.prototype.registerWidget=function(t){this.widgets.push(t)},Lt.prototype.unregisterWidget=function(t){var e=this.widgets.indexOf(t);-1<e&&this.widgets.splice(e,1),0===this.widgets.length&&this.unpost()},Lt.prototype.unpostWidgets=function(){this.widgets.forEach(function(t){return t.unpost()})},Lt.prototype.move_=function(t){this.anchor&&t!==this.anchor&&(this.moving=!0,this.unpost(),this.post(t),this.moving=!1)},Lt.prototype.parseVariable=function(t){var e=t.name,r=t.getter,n=t.setter;this.getPool().insert(new w.Variable(e,r,n))},T=Lt,w.ContextMenu=T,"undefined"!=typeof window&&(window.ContextMenu=vt),L=vt=vt||{},N=L.AbstractMenu,bt(Nt,N),Nt.parse=function(t,e){var r=t.items,n=(t.id,new Nt(e));return n.parseItems(r),n},Nt.prototype.getAnchor=function(){return this.anchor},Nt.prototype.post=function(){if(this.anchor.getMenu().isPosted()){for(var t=this.anchor.getHtml(),e=this.getHtml(),r=this.baseMenu.getFrame(),n=t.offsetWidth,i=n-2,o=0;t&&t!==r;)i+=t.offsetLeft,o+=t.offsetTop,t=t.parentNode;i+e.offsetWidth>document.body.offsetWidth-5&&(i=Math.max(5,i-n-e.offsetWidth+6)),N.prototype.post.call(this,i,o)}},Nt.prototype.display=function(){this.baseMenu.getFrame().appendChild(this.getHtml())},Nt.prototype.setBaseMenu=function(){for(var t=this;(t=t.anchor.getMenu())instanceof Nt;);this.baseMenu=t},I=Nt,L.SubMenu=I,function(t){t.close=function(t){var e=t.getMenu();e instanceof P.SubMenu?e.baseMenu.unpost():e.unpost()},t.getActiveElement=function(t){var e=t.getMenu();return(e instanceof P.SubMenu?e.baseMenu:e).getStore().getActive()},t.error=function(t,e){console.log("ContextMenu Error: "+e)},t.counter=function(){return e++};var e=0}((P=vt=vt||{}).MenuUtil||(P.MenuUtil={})),k=vt=vt||{},R=k.AbstractEntry,bt(It,R),Object.defineProperty(It.prototype,"content",{get:function(){return 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t=this.getHtml();t.setAttribute("aria-disabled","false"),t.textContent=this.content},It.prototype.activate=function(){this.disabled||this.getHtml().classList.add(k.HtmlClasses.MENUACTIVE)},It.prototype.deactivate=function(){this.getHtml().classList.remove(k.HtmlClasses.MENUACTIVE)},It.prototype.focus=function(){this.getMenu().setFocused(this),R.prototype.focus.call(this),this.activate()},It.prototype.unfocus=function(){this.deactivate(),R.prototype.unfocus.call(this)},It.prototype.escape=function(t){k.MenuUtil.close(this)},It.prototype.up=function(t){this.getMenu().up(t)},It.prototype.down=function(t){this.getMenu().down(t)},It.prototype.left=function(t){if(this.getMenu()instanceof k.ContextMenu)this.getMenu().left(t);else{var e=this.getMenu();e.setFocused(null),e.getAnchor().focus()}},It.prototype.right=function(t){this.getMenu().right(t)},It.prototype.space=function(t){this.press()},It.prototype.disable=function(){this.disabled=!0;var t=this.getHtml();t.classList.add(k.HtmlClasses.MENUDISABLED),t.setAttribute("aria-disabled","true")},It.prototype.enable=function(){this.disabled=!1;var t=this.getHtml();t.classList.remove(k.HtmlClasses.MENUDISABLED),t.removeAttribute("aria-disabled")},It.prototype.executeCallbacks_=function(){k.MenuUtil.getActiveElement(this);for(var t=0,e=this.callbacks;t<e.length;t++){var r=e[t];try{r(this)}catch(t){k.MenuUtil.error(t,"Callback for menu entry "+this.getId()+" failed.")}}},j=It,k.AbstractItem=j,B=vt=vt||{},D=B.AbstractItem,bt(Pt,D),Pt.prototype.generateHtml=function(){D.prototype.generateHtml.call(this);var t=this.getHtml();this.span||this.generateSpan(),t.appendChild(this.span),this.update()},Pt.prototype.register=function(){this.variable.register(this)},Pt.prototype.unregister=function(){this.variable.unregister(this)},Pt.prototype.update=function(){this.updateAria(),this.span&&this.updateSpan()},H=Pt,B.AbstractVariableItem=H,function(t){function 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diff --git a/source/base_index.rst b/source/base_index.rst
new file mode 100644
index 0000000000000000000000000000000000000000..56311dc37ccdf6c5c2d047c8b2c87c422fa4bd71
--- /dev/null
+++ b/source/base_index.rst
@@ -0,0 +1,12 @@
+.. Duniter technical description documentation master file, created by
+   sphinx-quickstart on Sat Jun 20 12:05:38 2020.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Duniter technical description
+=============================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
diff --git a/source/conf.py b/source/conf.py
new file mode 100644
index 0000000000000000000000000000000000000000..82206c2cce71c2b7106bc9975fc561b404180f84
--- /dev/null
+++ b/source/conf.py
@@ -0,0 +1,61 @@
+# Configuration file for the Sphinx documentation builder.
+#
+# This file only contains a selection of the most common options. For a full
+# list see the documentation:
+# https://www.sphinx-doc.org/en/master/usage/configuration.html
+
+# -- Path setup --------------------------------------------------------------
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#
+# import os
+# import sys
+# sys.path.insert(0, os.path.abspath('.'))
+
+
+# -- Project information -----------------------------------------------------
+
+project = 'Duniter technical description'
+copyright = '2020, Matograine'
+author = 'Matograine'
+
+# The full version, including alpha/beta/rc tags
+release = '0.0.2'
+
+
+# -- General configuration ---------------------------------------------------
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = [
+'sphinx.ext.mathjax',
+]
+
+mathjax_path = './js/tex-mml-chtml.js'
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This pattern also affects html_static_path and html_extra_path.
+exclude_patterns = []
+
+
+# -- Options for HTML output -------------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+
+html_theme = 'pyramid'
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+
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diff --git a/chapters/en/1_intro.rst b/source/parts/en/1_intro.rst
similarity index 95%
rename from chapters/en/1_intro.rst
rename to source/parts/en/1_intro.rst
index d2184f15c770f5f7d98c6a4e02b534b9e2fbbc6d..5c4247f7f024e99c6fcf2faa76bd18f443d83e52 100644
--- a/chapters/en/1_intro.rst
+++ b/source/parts/en/1_intro.rst
@@ -1,5 +1,6 @@
-Duniter: A libre currency blockchain generator.
-===============================================
+.. Duniter: A libre currency blockchain generator.
+
+.. ===============================================
 
 Abstract
 --------
diff --git a/source/parts/en/2_looking_at_Bitcoin.rst b/source/parts/en/2_looking_at_Bitcoin.rst
new file mode 100644
index 0000000000000000000000000000000000000000..5cffb6aa45f17b2fc854d08702c37269f8933e6a
--- /dev/null
+++ b/source/parts/en/2_looking_at_Bitcoin.rst
@@ -0,0 +1,139 @@
+
+1. State of the art : Bitcoin case
+----------------------------------
+
+.. raw:: html
+
+   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniter uses the crypto-currency concept introduced by Bitcoin [1]_,
+which is to use cryptographic tools such as signatures to create
+trustless digital currencies. Duniter fits this definition, but it has
+two completely different principles than Bitcoin : the Web of Trust and
+the Universal Dividend . These differences are on both monetary and
+technical aspects.
+
+.. _monetary-creation-a-space-time-asymmetry:
+
+1.1. Monetary creation of Bitcoin : a space-time asymmetry
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Space-time asymmetry refers to the relative access of individuals to
+newly created money [2]_. Concretely, most existing currencies (c. 2020)
+are both spatially and temporally asymmetrical for their users. Let's
+take Bitcoin as an example to understand why.
+
+1.1.1. Spatial asymmetry
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+When new Bitcoins are created, only some Bitcoin users (the miners) are
+given new Bitcoins, while everyone else get nothing. We believe this is
+the first injustice. However, some might say:
+
+   "Miners used their electricity and time to get it!"
+
+... we would answer that this work should not have been rewarded by
+newly created Bitcoins. New units should be distributed to the whole
+community. Miners should be rewared another way, but not by money
+issuance. Of course, Bitcoin cannot create money through Basic Income
+since Bitcoin users are not strongly identified, and one might benefit
+from money creation multiple times if they owned several wallets.
+Duniter gets rid of this problem by identifying its users and creating
+the same amount of Basic Income to everyone.
+
+1.1.2. Temporal-asymmetry
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Bitcoin has an absolute limit of 21 million BTC (its unit of currency),
+which means ever fewer bitcoins will be created over time until no new
+BTC are being generated. So, once the first adopters have mined every
+bitcoin, how will future joiners get Bitcoins? Just like most of us do
+for Euros or Dollars: to get money, they will have to work for the ones
+who already own it.
+
+We believe this is the second injustice. Every member of a monetary
+community should be equal concerning monetary creation, and get the same
+relative amount of money over time, even if they are a late adopter.
+Duniter aims to fix this by making the Universal Dividend (a.k.a. UD)
+grow by the time according to precise rules, thus making members equal
+toward money issuance on a half-lifespan.
+
+Most currencies present one of these two asymmetries, including metal
+currencies and mutual credit, as exposed in the RTM.
+
+1.1.3. A solution
+^^^^^^^^^^^^^^^^^
+
+Bitcoin has taught us that it is possible to create a currency system
+allowing one to both create digital money and to exchange it without a
+central authority. What we need to change is the way money is issued so
+we finally have a symmetrical system. We need **Bitcoin + Universal
+Dividend**. But Universal Dividend implies that the community consists
+of only identified people. This is where the Web of Trust (WoT) comes
+into place.
+
+This concept, introduced by cryptography with the OpenPGP format [3]_,
+allows us to identify people in a decentralized manner. It works as
+follows: each person creates a personal identity that is linked to its
+cyptographic certificate. The identity must be confirmed by others
+members who use their own cryptographic key. It is that simple: people
+choose who is part of the community and who is not, not a central
+authority.
+
+However, Duniter will not use OpenPGP for its cryptographic features:
+Elliptic Curves [4]_ will be used instead for the conciseness of its
+generated keys and its pratical advantages. Duniter has its own Web of
+Trust principles, that will be exposed later.
+
+1.2. Proof-of-Work mining : a power race
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+In Bitcoin Model, the calculation and incentive principles cause a power
+race : new Bitcoins are created for the owners of the most numerous,
+powerful (and energy-consuming) computers. This leads to a power race an
+places the control over the currency in the hands of the richest
+hardware owners. We want to make Duniter blockchain validation much less
+energy and hardware consuming while keeping a strong level of security.
+This will be further explained later. A consequence of this choice is
+the participation of low-end hardware in the Duniter network, leading to
+a better decentralization of blockchain validation.
+
+1.2.1 What about Proof of Stake ?
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Proof of stake consensus algorythm was first introduced in 2012 [5]_.
+The basic principle is to allow the richest wallets to issue blocks,
+putting their coin balance as a “stake” they would lose in case of
+cheat.
+
+At the time of conceiving Duniter, the PoS algorythms had not been
+tested enough to be used as a fundamental base. We did not chose this
+consensus principle. Moreover, the principle of allowing owners of large
+amounts of money to validate transaction can only lead to placing power
+over the currency in the richests hands : this is contrary to the
+symmetical principles of a libre currency.
+
+.. [1]
+   Bitcoin Whitepaper, S.Nakamoto, 2008:
+   `bitcoin.org/bitcoin.pdf <https://bitcoin.org/bitcoin.pdf>`__
+
+.. [2]
+   Relative Theory of Money, S.Laborde, 2010:
+   `en.trm.creationmonetaire.info/ <http://en.trm.creationmonetaire.info/>`__
+
+.. [3]
+   OpenPGP protocol defines standard formats for encrypted messages,
+   signatures, private keys, and certificates for exchanging public
+   keys. The GNU Privacy Handbook, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+
+.. [4]
+   High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+   P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+   77–89.
+   `cr.yp.to/papers.html#ed25519 <https://cr.yp.to/papers.html#ed25519>`__.
+
+.. [5]
+   PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &
+   S.Nadal, 2012 :
+   `archive.org/details/PPCoinPaper <https://archive.org/details/PPCoinPaper>`__
diff --git a/source/parts/en/3_blockchain.rst b/source/parts/en/3_blockchain.rst
new file mode 100644
index 0000000000000000000000000000000000000000..9d187381a36b95cd51e3582d1d20bcbec778fed7
--- /dev/null
+++ b/source/parts/en/3_blockchain.rst
@@ -0,0 +1,130 @@
+2. Duniters Blockchain
+----------------------
+
+..   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniters Blockchain follows the basic principles of Bitcoins. This is
+essential for synchronization between peers, as to prevent double-spend
+attacks. However, Duniters Blockchain will store different informations
+than Bitcoins.
+
+The basic use of Blockchain will be registering transactions. For this
+part, we use the same principles as Bitcoin : transactions have inputs
+(spending accounts) and outputs (receiving accounts). But contrary to
+Bitcoin, no generation transaction exists : monetary creation happens
+only through UD. So, in Duniters Blockchain, Inputs can be either:
+
+-  a former transaction (as in Bitcoin)
+-  a Universal Dividend (specific to Duniter).
+
+Duniters Web of Trust is also written in the Blockchain. The identity of
+each member gets registered much like transactions are, with a strong
+link to the time reference. Thus, the Blockchain is a representation of
+a space-time frame of reference, where “space” are members of the WoT
+and “time” the basic blockchain units : the blocks. On each point of
+time, one can determine which account is legitimate to create the UD,
+only with a blockchain analysis.
+
+2.1. Spam countermeasures
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+An issue of most cryptocurrency projects is to prevent the common ledger
+from growing too much. This would require nodes to have a lot of storage
+and computing power to be usable. In particular, we don’t want an
+attacker to be able to make the Blockchain grow too fast. Most projects
+implement transaction fees as a way to prevent this, making the attacker
+lose money. We don’t want to introduce this mean since a currency with
+automatic fees on transactions is no more neutral. Several
+countermeasuers against such spam attacks are implemented.
+
+..   <!-- see : https://forum.duniter.org/t/sans-frais-de-transaction-comment-resister-aux-attaques/3846/25 (implemented ?)-->
+
+2.1.1. Minimum output amount
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. raw:: html
+
+   <!-- This has to be implemented in DUBPv13. -->
+
+Fixing a minimal output amount reduces the power of an attack. Duniter
+deals with cents of Ğ1 or 1/1000 of the first UD. An attacker could
+create thousand accounts with only 1 UD. To prevent this, a valid
+transaction must have output amounts of minimum 1Ğ1. This reduces the
+power an attack by 100.
+
+2.1.2. Limited block size and chainability
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The block size is always limited. While the protocol allows this limit
+to evolve to address scaling issues, an attacker cannot register as many
+transaction as they wish.
+
+With the same goal to prevent too many transactions to get registered,
+while transactions can be “chained” (refer to another transaction in the
+same block), the chainability of transactions is limited to 5.
+
+2.2. Scaling
+~~~~~~~~~~~~
+
+Most of the time, the scaling issue rises for distributed systems that
+should work on a very large scale. This is not the case of Duniter, for
+multiple reasons :
+
+-  Ğ1 is the first libre currency, and is still experimental on the
+   monetary creation principle. We don’t want it to reach the whole
+   world, we only want it to work, to validate or invalidate the RTM.
+   Moreover, the rules chosen for the Ğ1 WoT should limit its size to
+   around 16 million members.
+-  Duniter’s aim is to be used to create multiple libre currencies, that
+   would fit local or regional economies. As a consequence, it would
+   deal with less transactions than if it was a world-scale system. The
+   RTM proposes a formula to calculate the exchange rate between two
+   currencies, that could be used to create automatic exchanges for a
+   member travelling away from their community.
+
+However, Duniter has assets that will help if the number of users and
+transactions grow.
+
+2.2.1 Dynamic block size
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+While Bitcoin has a fixed block size, Duniters blocks size can evolve.
+On low use of the blockchain, the maximal block size is 500 bytes. On
+high use of the blockchain, the maximal block size would be 110% of the
+average size of the current window blocks(see “personalised difficulty”
+part for more information). This way, the blocks are bounded in size,
+but can slowly grow if a massive and legitimate use of the blockchain
+needs it. The block size (in bytes) is limited as so :
+
+.. math::  \textrm{blockSize} < \max \left({500 ; \textrm{CEIL}(1.10 \times (\textrm{average block size}))}\right) 
+
+2.2.2. Lightning Networks
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The Lightning Networks [1]_ allow almost instant and off-chain
+transactions. They were first implemented on Lightcoin, and are now on
+Bitcoin. One of their benefits is to make the blockchain store a lot of
+transactions at once, thus reducing the groth of the blockchain. The
+Duniter protocol allows XHX() and CSV() unlock conditions that are
+necessary to implement Lightning Networks. While not available yet, this
+payment channel might get implemented when needed.
+
+2.2.3. Unit base
+^^^^^^^^^^^^^^^^
+
+As the Universal Dividend grows exponentially, with time Duniter nodes
+would have had to deal with always largest amounts, eventually reaching
+the BIGINT limit. To avoid this, the amounts are expressed with a unit
+base in base 10. We want the UD amount to always fit in 4 digits. To
+manage it, the ``unitbase`` is updated each time the UD value reaches
+100.00 : it goes from ``99.99*10^(unitbase)`` to
+``10.00*10^(unitbase+1)``. All the unit amounts are thus divided by 10.
+While this might seem strange, this process has already hapened in state
+currencies. Moreover, the amounts expressed in UD will not change.
+
+With a monetary growth of 10% each year and a stable population, such a
+change of unit base would happen each 25 years.
+
+.. [1]
+   The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 :
+   `lightning.network/lightning-network-paper.pdf <http://lightning.network/lightning-network-paper.pdf>`__
diff --git a/chapters/en/4_Web_Of_Trust.rst b/source/parts/en/4_Web_Of_Trust.rst
similarity index 99%
rename from chapters/en/4_Web_Of_Trust.rst
rename to source/parts/en/4_Web_Of_Trust.rst
index a56e7d31ca3dd8ebeaf8fdb16ba25d96a3df5881..5fc1f51b2dbedb588d5724b4c20fb388de503dcf 100644
--- a/chapters/en/4_Web_Of_Trust.rst
+++ b/source/parts/en/4_Web_Of_Trust.rst
@@ -154,7 +154,7 @@ communication network.
 
 -  **In-degree of vertex A**: number of incoming edges / head ends to A.
 
-.. figure:: src/img/degrees_en.jpg
+.. figure:: img/degrees_en.jpg
    :alt: degrees of a vertex diagram
    :width: 40%
 
@@ -388,7 +388,7 @@ well as that of the monetary community as a whole. The ``xpercent``
 parameter prevents the creation of a ‘faction’ that could take hold of
 the blockchain.
 
-.. figure:: src/img/wot-sybil.jpg
+.. figure:: img/wot-sybil.jpg
    :alt: Sybil region
    :width: 90%
 
@@ -425,7 +425,7 @@ Our goal with the Ğ1 is to create a community of about one million
 members to test the consequences of a libre monetary system. Let’s see
 how we can tweak the pair of sigQty and stepMax- to reach this size:
 
-.. figure:: src/img/wot-moy.png
+.. figure:: img/wot-moy.png
    :alt: Average WoT size graph as a function of sigQty and stepMax
    :width: 90%
 
@@ -496,7 +496,7 @@ variation of ``sigPeriod``. The simulation considers that honest members
 and attackers both issue a certification each ``sigPeriod`` interval, in
 days:
 
-.. figure:: src/img/impact_sig_period.png
+.. figure:: img/impact_sig_period.png
    :alt: size of the WoT according to sigPeriod and stepAttackers
    :width: 100%
 
diff --git a/source/parts/en/5_individualized_difficulty.rst b/source/parts/en/5_individualized_difficulty.rst
new file mode 100644
index 0000000000000000000000000000000000000000..a7d1e47936300c578936476915ce9b412bc7c985
--- /dev/null
+++ b/source/parts/en/5_individualized_difficulty.rst
@@ -0,0 +1,408 @@
+.. _proof-of-work-with-personalized-difficulty:
+
+4. Proof of Work with personal difficulty
+-----------------------------------------
+
+As each P2P cryptocurrency, Duniter has a way to synchronize its peers.
+It uses a proof of Work (PoW) to write the Blockchain on a regular
+basis, much like BitCoin. However, Duniter has a unique asset : the WoT,
+where each member represents a unique living human.
+
+This difference might seem minimal, but it has an enormous consequence :
+while Bitcoin uses a race based on computing power only, Duniter creates
+a validation frame that is no race. It is more like a lottery where each
+“winning” member is excluded for a certain amount of time. Moreover,
+those who have more computing power get a handicap, as a way to let
+other peers win. All this is possible through the WoT, that allows
+personalised difficulty while PoW is used for synchronization. All the
+rules of this PoW/WoT mechanism can be verified by reading the
+blockchain. As a consequence, a peer only needs to have an up-to-date
+copy of the blockchain to apply the rules. A view of the whole network
+is not needed.
+
+Another strong difference is that forging peers are not rewarded by the
+protocol. There is no economical incentive on forging lots of blocs,
+neither on having a lot of computing power.
+
+One could say that Duniter uses a PoW that needs very low energy
+consumption compared to BitCoin : an “ecological” PoW ?
+
+.. <!-- source : https://duniter.org/en/wiki/duniter/2018-11-27-duniter-proof-of-work/ -->
+
+.. _why-proof-of-work:
+
+4.1. Why do we need Proof of Work ?
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Duniter nodes share a database as part of a p2p environment. The proof
+of work (PoW) allows machines to synchronize with each other. In
+Duniter’s case, the blockchain is our database, and acts as a ledger
+keeping a trace of all transactions, status of the WoT and more. How can
+we let several machines add data (ie: a transaction) at the same time?
+In addition, how do we settle on how much time has gone by since the
+blockchain was last updated? Agreement on time is of the utmost
+importance as we want to create Universal Dividends on a regular basis,
+and keep track of membership status, both in human time.
+
+Proof-of-work provides a clever solution to both problems:
+
+1. Any machine can write into the blockchain (create a new block) but is
+   only authorised to do so if it has previously solved a mathematical
+   equation that require a certain amount of work. The challenge has to
+   be hard enough to prevent two machines to solve it at the same time,
+   ensuring the unicity of a block’s creator.
+
+2. Solving this challenge takes a certain amount of time, which depends
+   on the calculating power of the whole network. This provides a common
+   ground for defining the needed time reference. A block time is set
+   (ie: 1 block = 5 min) and Duniter adapts the challenge difficulty to
+   get an average duration corresponding to this block time.
+
+4.2. Only members can “mine”
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+One of Duniter’s major differences with other PoW-based cryptocurrencies
+is that only members are allowed to author blocks. Each block is signed
+with the member’s private key, allowing the algorithm to determine a
+personalised difficulty.
+
+This personalised difficulty eliminates the rat-race for the most
+sophisticated and powerful mining equipment. Another benefit is the fact
+that no “supercomputer” can take control of the blockchain. Lastly,
+Duniter implements a rotation in forging members thanks to this
+personalized difficulty.
+
+This lightweight PoW is much less energy-consuming than other PoW
+cryptocurrencies. Members can mine with anything from a raspberry pi to
+a privacy-first internet cube.
+
+.. _how-does-duniter-pow-work:
+
+4.3. How does it work ?
+~~~~~~~~~~~~~~~~~~~~~~~
+
+.. _the-hash:
+
+4.3.1. The hash (aka digest)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Example of a valid hash:
+
+::
+
+   00000276902793AA44601A9D43099E7B63DBF9EBB55BCCFD6AE20C729B54C653
+
+As you can see this hash starts with five zeros which was very hard to
+achieve and took a lot of work for someone’s computer. Hence the term
+“proof of work”.
+
+.. _common-difficulty:
+
+4.3.2. The common difficulty
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+A common difficulty is needed to settle on a yardstick for our time
+reference. Its role is to make sure the blockchain moves forward at a
+steady pace - one block every ``avgGenTime`` seconds, ``avgGenTime``
+being one of the 20 parameters behind the Duniter protocol-.
+
+This difficulty’s initial value can be set to any arbitrary value
+(``70`` in Duniter ``v1.5.x``) and then acts as a spring, regulating
+blocktime creation by increasing itself if the creation interval drops
+under ``avgGenTime`` and vice-versa.
+
+4.3.2.1. How is difficulty applied ?
+''''''''''''''''''''''''''''''''''''
+
+The numeric value of difficulty is taken from an array of possible
+hashes out of all possible hashes. In DUBPv13 the hash of a block is its
+sha256 hexadecimal hash.
+
+To understand the difficulty, we make a euclidiean division of the
+difficulty by 16.
+
+Here’s an example with a difficulty value of 70 :
+
+..   70 // 16 = 4 with a remainder of 6. 
+
+   70 / 16 = 4 with a remainder of 6. 
+
+The valid hashes are the ones starting with four zeros and with the
+fifth character less than or equal to 9 (6 in hexadecimal notation). The
+valid hashes are then written as starting with : ``0000[0-9]``. This is
+a bit different from Bitcoin, where the difficulty is only ruled by the
+number of zeroes.
+
+4.3.2.2. The Nonce
+''''''''''''''''''
+
+When a member is forging a new block, his computer freezes the block’s
+content and changes the Nonce until the hash reaches the required number
+of zeroes.
+
+The nonce allows us to mine a new block by finding a hash. The hash
+value allows us to determine the difficulty level of the proof-of-work
+performed. Examples of possible Nonce values:
+
+-  10100000112275
+-  10300000288743
+-  10400000008538
+-  10700000079653
+-  10300000070919
+
+In reality the ``Nonce`` value follows a pre-determined format akin to
+``XYY00000000000``. The Nonce’s value isn’t the number of attempts but
+rather a value within a set of possible ones. This is how the Nonce is
+built:
+
+-  X is a number assigned to a specific peer. Let’s assume that someone
+   has several nodes each with the same private key, this would lead to
+   possible collisions if this person were to mine the same block with
+   different nodes. Each [STRIKEOUT:block] **node ?** will therefore
+   have its own unique X to prevent this from happening.
+
+-  Y is the number of cores of the processor. The Nonce starting with
+   ``107[…]`` belongs to a seven cores processor, while ``199[...]``
+   could be the proof generated by a 99 cores processor.
+
+The rest of the Nonce, the part that follows after the XYY, is the
+numerical space for this individual node and is unique to each of the
+CPU’s core. This space is comprised of eleven digits (``00000000000``).
+For the sake of accuracy, we use the term CPU in the wider sense, it can
+be understood as a bi-CPU for example. We take into consideration the
+number of cores for the resulting PoW.
+
+4.4. Personalised difficulty
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Earlier in this article, we explained that the personalised difficulty
+is the new and key concept that sets Duniter apart from other PoW-based
+cryptocurrencies.
+
+Here is how this personalised difficulty is calculated and assigned:
+
+It is determined by a combination of two different constraints with
+complimentary roles: the **exclusion factor** and the **handicap**.
+
+Let ``powMin`` be the common difficulty, ``exFact`` a member’s exclusion
+factor and ``handicap`` their handicap. This member’s personalised
+difficulty ``diff`` is:
+
+..   diff = powMin*exFact + handicap
+
+.. math:: {\textrm{diff} = \textrm{powMin} \times \textrm{exFact} + \textrm{handicap}}
+
+.. _the-exclusion-factor:
+
+4.4.1. Understanding ``exFact``, the exclusion factor
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Members who have never produced blocks or haven’t for quite some time
+are assigned an exclusion factor of ``1``. Their personalised difficulty
+is therefore simply the sum of ``powMin + handicap``.
+
+Before reading on, let’s precise the role of this exclusion factor. When
+a member adds a block to the chain, his ``exFact`` jumps up from one to
+a very high value, to prevent them from forging other blocks immediately
+after and taking control of the blockchain.
+
+The exclusion factor will then rapidly return to one. This delay is
+expressed as a number of blocks. It is calculated as a proportion of the
+number of members forging. In the Ğ1’s case, this proportion is 1/3,
+meaning that if there are fifteen members currently forging, the
+member’s exclusion factor will drop down to one after five blocks.
+
+4.4.1.1. What is intended by “the number of members forging” ?
+''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
+
+We mean the number of members trying to create the next block. In
+reality, there is no way to precisely know how many members are
+calculating at any given time, because it is impossible to view the
+entire network. But we need this information, whithout which assigning a
+personalised difficulty is impossible. To achieve this, Duniter looks
+back at the blockchain and assumes that there is as much members forging
+as those who have found at least one block in the last blocks in the
+current window, minus the very last one.
+
+4.4.1.2. Current window
+'''''''''''''''''''''''
+
+We use the concept of **current window**. The current window is the
+number of blocks we look back at to determine how many members are
+forging. Let’s see how it works:
+
+-  ``issuersFrame`` is the size of the current window in blocks.
+
+-  ``issuersCount`` the number of members who have calculated at least
+   one block during the current window.
+
+Both ``issuersFrame`` and ``issuersCount`` are block fields. When first
+starting a blockchain, the very first block has an ``issuersFrame=1``
+and an ``issuersCount=0``. The genesis block is excluded as there are no
+members in the current window!
+
+From the second block onwards (block #1) we track the variation of
+``issuersCount``. The member having mined block #0 enters the current
+window and in block #1 we will therefore mention ``issuersCount=1``.
+
+``issuersFrame`` then varies as follows:
+
+-  if ``issuersCount`` increases by N (with a maximum step of N = 1),
+   then ``issuersFrame`` will increase by one unit over a period of 5N
+   blocks.
+-  Conversely, if ``issuersCount`` decreases by Y (with a maximum step
+   of Y = 2 = current window inching forward + loss of one calculating
+   member), then ``issuersFrame`` will decrease by one unit during 5Y
+   blocks.
+-  When such events overlap, ``issuersFrame`` evolves as so :
+
+======= ============================================ ===============
+bloc    event                                        issuersFrame
+======= ============================================ ===============
+T       Babar writes a block and enters issuersCount 160
+T+1     Celeste leaves issuersCount                  160 +1 = 161
+T+2     N/a                                          161 +1 -1 = 161
+T+3/4/5 N/a                                          161 +1 -1 = 161
+T+6     N/a                                          161 -1 = 160
+======= ============================================ ===============
+
+The calculation can be found under rules
+`BR_G05 <https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g05-headissuersframe>`__
+and
+`BR_G06 <https://git.duniter.org/nodes/common/doc/blob/master/rfc/0009_Duniter_Blockchain_Protocol_V11.md#br_g06-headissuersframevar>`__
+of the DUP protocol.
+
+4.4.1.3. exFact and the personalised difficulty
+'''''''''''''''''''''''''''''''''''''''''''''''
+
+We explained that ``exFact`` spikes immediately after the member has
+found a block. It decreases then rapidly to ``1`` after a number of
+blocks equal to ``1/3 * issuersCount``. Let’s see precisely how we
+calculate ``exFact``:
+
+-  ``nbPreviousIssuers`` is the value of issuersCount at the last block
+   ``N`` found by the member.
+
+-  ``nbBlocksSince`` is the number of blocks found by the rest of the
+   network since block ``N``.
+
+-  ``percentRot`` is the number of *not excluded* peers we want. It is a
+   monetary parameter, its value is 0.67 for Ğ1 currency.
+
+..   a = FLOOR (percentRot * nbPreviousIssuers / (1 + nbBlocksSince))
+..   exFact = MAX [ 1 ; a ]
+
+.. math:: exFact = MAX[ 1 ; FLOOR ({{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}}) ]
+
+
+The FLOOR is a simple truncate function. For ``exFact`` to exclude the
+member, we need :
+
+..   (percentRot * nbPreviousIssuers / (1 + nbBlocksSince)) >= 2
+
+.. math:: {{percentRot \times nbPreviousIssuers} \over {1 + nbBlocksSince}} >= 2
+
+We can see that the member is not excluded if ``nbBlocksSince`` is
+greater than 1/3 of the calculating members. Take as an example
+``nbPreviousIssuers = 6`` and ``nbBlocksSince = 3``:
+
+..   (0.67* 6 / (1 + 3)) = 1.005 -> exFact = 1
+
+.. math:: {0.67 \times {6 \over {1 + 3}} = 1.005} \Rightarrow exFact = 1
+
+
+However, if the member computed a block one block ago (nbBlocksSince =
+1), exFact = 2 and the forging peer is excluded:
+
+
+..   (0.67 * 6 / (1 + 1)) = 2.01 -> exFact = 2
+
+.. math:: {0.67 \times {6 \over {1 + 1}} = 2.01} \Rightarrow exFact = 2
+
+
+Moreover if the last block was authored by the said member, then:
+
+..   nbBlocksSince=0   and 
+..   exFact = 0.67 * nbPreviousIssuers
+
+.. math:: nbBlocksSince = 0  
+.. math:: exFact = 0.67 \times nbPreviousIssuers
+
+
+ExFact value increases according to the number of members calculating.
+Thus, if there is enough members calculating, even mining farms would be
+excluded. We have therefore succeeded in our intent to deter attempts to
+seize the blockchain and its currency.
+
+However, at any time ``t``, the two-thirds of calculating members all
+have an exclusion factor of ``1``, even though they might not all have
+the same computational power at hand. If the personalised difficulty
+only took into account the exclusion factor, then only the members with
+the highest computational power from the remaining third would be able
+to author new blocks and the other 2/3s would almost always be excluded.
+Lesser machines wouldn’t stand a chance…
+
+4.4.2. The handicap
+^^^^^^^^^^^^^^^^^^^
+
+The handicap is the second parameter of the personalised difficulty. Its
+main role is to improve the rotation of forging peers. A higher handicap
+is assigned to members with higher calculating power, so lesser machines
+can also compute blocks. As a consequence, there is no incentive on
+forging with powerful computers. Security can be achieved with less
+computing power than with pure PoW.
+
+The aim is to handicap the half that has authored most blocks (the most
+powerful half) to favour the other one. So, the handicap formula will
+use the median number of blocks authored by peers within the current
+window.
+
+-  ``nbPersonalBlocksInFrame`` is the number of blocks authored by a
+   single member within the current window.
+
+-  ``medianOfBlocksInFrame`` is the median number of blocks written by
+   the calculating members during the same timeframe.
+
+
+..   a = (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame
+..   handicap = FLOOR(LN(MAX( 1 ; a )) / LN(1.189))
+
+.. math:: handicap = FLOOR( {\ln({ \max({ 1 ; {{nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame} )} )} \over \ln{1.189} })
+
+
+Let’s unwrap the formula:
+
+..   (nbPersonalBlocksInFrame + 1) / medianOfBlocksInFrame)
+
+.. math:: { {nbPersonalBlocksInFrame + 1} \over medianOfBlocksInFrame}
+
+is simply the ratio between the number of blocks authored by the peer
+and the median number of blocks. For example, if a peer has authored
+``9`` blocks in the current window and the median is ``5``, then the
+ratio will be ``(9+1)/5 = 2``. 
+
+- The MAX function allows us to ensure that
+the handicap has a value at least equal to ``1``.
+
+- The Napierian Logarithm of this ratio prevents the handicap from
+becoming excluding. We want the handicap to level the calculating field
+so that all peers stand a chance, not to exclude peers.
+
+- If we wanted the handicap to be applied as soon as the median is
+reached, we would divide it by ``LN(1)``. The problem is that we have
+already set a minimum value of ``1`` with the MAX function. If we were
+to divide the ratio by ``LN(1)`` all calculating peers would have a
+handicap ``\>= 1``. In addition, is it really fair to handicap a member
+who is right on the median?
+
+That’s why we went for ``1.189`` rather than ``1``. A member has to be
+at least ``18.9%`` above the median to be assigned a handicap. 18.9% is
+actually 16^(1/16), the difficulty factor between two levels of the
+proof work (hexadecimal hash).
+
+To conclude, you have to remember that :
+
+-  The handicap is indexed on the logarithm of the ratio to the median,
+-  Handicap is only applied on members whose ratio to the median is
+   greater than the ratio between two levels of the proof-of-work’s
+   difficulty.
diff --git a/source/parts/en/6_conclusion.rst b/source/parts/en/6_conclusion.rst
new file mode 100644
index 0000000000000000000000000000000000000000..b60770d62d1f981c1a046fc9411879459363a208
--- /dev/null
+++ b/source/parts/en/6_conclusion.rst
@@ -0,0 +1,40 @@
+Conclusion
+----------
+
+.. raw:: html
+
+   <!-- source : https://duniter.org/en/theoretical/ -->
+
+Duniter’s Blockchain can be compared to Bitcoin’s : a common document
+retracing the history of the currency. However, Duniter registers not
+only trades, but also the history of relationships in the community as a
+mean to identify a human to a digital account. This way, Duniter has
+information about the fondamental reference of RTM : living humans. A
+libre Currency can be issued thanks to the Universal Dividend.
+
+More than that, Duniter proposes a new model for securing a Blockchain
+in an efficient and decentralized way. Basing the security on a Web of
+Trust with an individualised security makes the calculation rules more
+fair. A side-effect of this choice is a network consisting mostly of
+low-end computers, maintaining a good security and helping
+decentralization of calculation.
+
+The ultimate goal of Duniter project is to allow people to participate
+in a libre economy, thanks to a libre currency. What is a libre economy
+? The Relative Theory of Money defines it through four economic
+liberties :
+
+-  The freedom to choose your currency system: because money should not
+   be imposed.
+-  The freedom to access resources: because we all should have access to
+   economic & monetary resources.
+-  The freedom to estimate and produce value: because value is a purely
+   relative to each individual.
+-  The freedom to trade with the money: because we should not be limited
+   by the avaible money supply.
+
+Those 4 economic freedoms should be understood together, not
+exclusively. Plus, “freedom” has to be understood as “non-nuisance”. So
+here, freedom does not mean the right to take all of a resource (like
+water source in a desert) so no more is available to the others. Now you
+get it, this is the goal: free economy through free currency.
diff --git a/source/parts/en/9_sources.rst b/source/parts/en/9_sources.rst
new file mode 100644
index 0000000000000000000000000000000000000000..feb0ca9fafd35f8758aa437aa55925d1c1cf9701
--- /dev/null
+++ b/source/parts/en/9_sources.rst
@@ -0,0 +1,25 @@
+
+Sources :
+---------
+
+-  Relative Theory of Money, S.Laborde, 2010:
+   `en.trm.creationmonetaire.info/ <http://en.trm.creationmonetaire.info/>`__
+-  Bitcoin Whitepaper, S.Nakamoto, 2008:
+   `bitcoin.org/bitcoin.pdf <https://bitcoin.org/bitcoin.pdf>`__
+-  The Bitcoin Lightning Network, J.Poon & T.Dryja, 2016 :
+   `lightning.network/lightning-network-paper.pdf <http://lightning.network/lightning-network-paper.pdf>`__
+-  The GNU Privacy Handbook, M.Ashley, 1999 :
+   `www.gnupg.org/gph/en/manual.html#AEN335 <https://www.gnupg.org/gph/en/manual.html#AEN335>`__
+-  High-speed high-security signatures, D.J.Bernstein, N.Duif, T.Lange,
+   P.Schwabe, B-Y.Yang. Journal of Cryptographic Engineering 2 (2012),
+   77–89.
+   `cr.yp.to/papers.html#ed25519 <https://cr.yp.to/papers.html#ed25519>`__.
+-  PPCoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake, S.King &
+   S.Nadal, 2012 :
+   `archive.org/details/PPCoinPaper <https://archive.org/details/PPCoinPaper>`__
+-  Duniter Blockchain Protocol, v13, draft by Elois :
+   `git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md <https://git.duniter.org/nodes/common/doc/blob/dubp_v13/rfc/0011_Duniter_Blockchain_Protocol_V13.md>`__
+-  The Sibyl Attack, J.R.Douceur:
+   `www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf <https://www.microsoft.com/en-us/research/wp-content/uploads/2002/01/IPTPS2002.pdf>`__
+-  Neocortex size as a constraint on group size in primates,
+   R.I.M.Dunbar, Journal of Human Evolution, 1992
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