Providing in the Bitbon System: Economic and Legal Decentralization of the Bitbon System
The Appendix to the Bitbon System Public Contract “Providing in the Bitbon System: Economic and Legal Decentralization of the Bitbon System” (hereinafter — Appendix) determines the fundamental principles and procedure for performing activities by the Bitbon System Provider[i] in the role of a Registrator[i], regulates his/her rights and obligations in order to ensure the economic and legal decentralization of the Bitbon System[i].
Contents
 SECTION 1. GENERAL PROVISIONS

SECTION 2. OPERATIVE PROVISIONS

Chapter 3. Consensus Building in the Blockchain Network of the
Bitbon System Using the Community PoS Algorithm
 Article 4. Concept of Economic and Legal Decentralization of the Bitbon System
 Article 5. The Main Idea of Community PoS
 Article 6. Concept of the Community PoS Consensus
 Article 7. Network Nodes and Their Role Within the Community PoS Consensus
 Article 8. Supporting the Sortition System
 Article 9. Sortition Procedure
 Article 10. Block Formation
 Article 11. Node Rating

Chapter 4. Scientific and Mathematical Substantiation of the Global
Probability Model of the Block Producer Sequence Formation
Process
 Article 12. Distribution of Assetbox Powers of Registrators Among Network Nodes, Block Producer Candidates
 Article 13. Forming a Block Producer Sequence out of Block Producer Candidates
 Article 14. Events of the Repeated Formation of the Block Producer Sequence
 Article 15. Evaluation of the Probability of Stationarity of the Results of the Block Producer Sequence Formation Process Regarding the Stages of Distribution of Assetbox Powers and Block Producer Sequence Formation

Chapter 5. Role of a Registrator in Consensus Building in the
Bitbon System
 Article 16. Concept of Consensus Building in the Bitbon System
 Article 17. Stages of Providing Aimed at Ensuring Economic and Legal Decentralization of the Bitbon System
 Article 18. Registrator Pool Structure
 Article 19. Connecting to Providing
 Article 20. Mechanism for Implementing the Concept of Economic and Legal Decentralization of the Bitbon System
 Article 21. Assetbox Power
 Article 22. Individual Assetbox Power
 Article 23. Power Increase
 Article 24. Base Assetbox Power
 Article 25. Social Power of Assetboxes and Interlevel Difference
 Article 26. Social Power Blocking
 Article 27. Providing Cycle
 Article 28. Providing Power Protection
 Article 29. Synergy of Remuneration and Principles of Crediting Remuneration
 Article 30. Registrator’s Tools
 Chapter 6. Mathematical Description of Consensus Building

Chapter 3. Consensus Building in the Blockchain Network of the
Bitbon System Using the Community PoS Algorithm
 SECTION 3. CONCLUDING PROVISIONS
SECTION 1. GENERAL PROVISIONS
Chapter 1. Terms and Definitions
Article 1. Use of Terms
1. The terms used in this Appendix shall be interpreted in accordance with the definitions given below:
 1) Registrator’s Assetbox is a Bitbon System component[i] intended for registration of digital asset units[i] in the Bitbon System, which provides access to the storage address of distributed ledger token accounting units[i] in the distributed ledger token accounting system[i]. Access of a Bitbon System User to the Assetbox is provided through the Bitbon System account[i].
 2) UTC (Coordinated Universal Time) is the primary international time standard, which is effectively a successor to GMT (Greenwich Mean Time).
 3) Base power is a parameter of the Registrator’s Assetbox determined by its power and the total power of all Assetboxes of its first line.
 4) Base balance is a parameter that is defined by the total number of Bitbon units[i] in the root Assetbox of a Registrator and the sum of all Assetbox balances of the first line of the Registrator pool.
 5) Assetbox balance is the number of Bitbon units in the Registrator’s Assetbox.
 6) Transaction block (block) is a special structure for recording a group of transactions in the distributed ledger[i] (blockchain[i]).
 7) Block producer is a block producer candidate that was included into the block producer sequence as a result of completing the sortition procedure to sign and announce only one block in a specified time slot within a specific round.
 8) Block producer candidate is any node participating in the quorum that corresponds to the established hardware requirements with the rating above the specified value and the Providing mode turned on.
 9) Root Assetbox is an Assetbox that is at the top of a specific Registrator pool, and all connections in the pool structure lead to this Assetbox.
 10) Providing period is a time window of 72 hours.
 11) Registrator pool is one or several Assetboxes engaged in providing in the Bitbon System[i] that are connected through special transactions and form a structure, which operates in accordance with rules and technical protocols of building consensus in the Bitbon System.
 12) Providing cycle is a combination of three providing periods, when powers (base and social) for each Assetbox of the Registrator pool are calculated and saved as well as when blocks are created and verified with subsequent crediting of remuneration.
 13) Median (from medieval Latin “medianus”, from “medius” — mid) in mathematics is a value denoting a sample (i.e. a set of numbers). If all the elements of the sample are different, the median is a value greater than one half of the sample and lower than the other half. In a more general sense, the median can be determined by arranging the elements of the sample in ascending or descending order and taking the middle element.
 14) Assetbox power is a parameter of a Registrator’s Assetbox that defines the legal weight of a specific Registrator in the Bitbon System Social Network[i] when confirming deals in the Bitbon System[i]. Assetbox power is calculated as a sum of base and social powers of the Registrator’s Assetbox and directly influences the remuneration of the Registrator.
 15) Sortition procedure is an automatic process realized as part of the Community PoS consensus, the purpose of which is to form a sequence of block producers based on the distributed Assetbox powers among block producer candidates that would be the basis for the signing and announcement of blocks by block producers in the following round.
 16) Social power is a parameter of a Registrator’s Assetbox based on the social connections of a Registrator starting from the second line and lower.
 17) Blockchain network node is a hardware and software complex at the disposal of the Bitbon System Provider in the role of a Partitioner, which is connected to the blockchain network of the Bitbon System and stores blockchain data in part or in full.
 18) Synchronization node is a blockchain network node that, when connecting to the network, synchronizes with the other nodes by receiving transaction blocks, transactions and related objects from other network nodes, verifying them and storing in the local blockchain storage.
 19) Node participating in the quorum is any synchronization node, whose network latency to connect to the nodes that participate in the quorum is lower than the threshold.
 20) Level of the Registrator pool is a parameter that depends on base balance of the Registrator’s Assetbox. Providing in the Bitbon System envisions 100 levels.
2. For the correct interpretation of other terms used in this Appendix, it is necessary to be guided by the Appendix Terms and Definitions in the Bitbon System Social Network that is an integral part of the Bitbon System Public Contract.
Chapter 2. Subject and Structure of the Appendix
Article 2. Subject of the Appendix
1. This Appendix regulates relations between Bitbon System Users[i] (hereinafter — User) in the role of a Registrator that arise when engaging in providing in the Bitbon System.
2. This Appendix establishes the fundamental principles and procedure for performing activities by the Bitbon System Provider (hereinafter — Provider) in the role of a Registrator[i], regulates his/her rights and obligations in order to ensure the economic and legal decentralization of the Bitbon System.
Article 3. Structure of the Appendix
1. This Appendix consists of the preamble, sections, chapters, which consist of articles that include parts and paragraphs. The structure of the Appendix also includes links and references to the Provisions of the Bitbon System Public Contract as well as to separate Appendices that are an integral part of the Bitbon System Public Contract.
SECTION 2. OPERATIVE PROVISIONS
Chapter 3. Consensus Building in the Blockchain Network of the Bitbon System Using the Community PoS Algorithm
Article 4. Concept of Economic and Legal Decentralization of the Bitbon System
1. The concept of economic and legal decentralization of the Bitbon System is that Users, through the base services of the Bitbon System[i], can arrange deals regarding accounting of economic relations directly and without intermediaries. While Providers in the role of Registrators, regardless of their citizenship or country of residence, can record such deals in order to confirm a legal fact by achieving consensus using the Community PoS algorithm.
Article 5. Main Idea of Community PoS
1. The main idea of Community PoS lies in organization of the community of Users with the status of Providers by uniting the Assetboxes of Registrators into pools.
2. Registrators provide Bitbon units available in their Assetboxes, which are united into the Registrator pools, for automatic distribution of powers of these Assetboxes among the nodes of the blockchain network of the Bitbon System in order to carry out the voting procedure to form the sequence of block producers, which will sign and announce blocks.
3. A Registrator can involve new Users in order to develop the community of Providers. Each involved User provides Bitbon units available in his/her Assetboxes to form a Registrator pool in order to increase its power.
4. Each new Registrator automatically participates in the validation of blocks generated by other members of the community as well as in formation of new blocks.
5. Each new Registrator lowers the chance of malicious nodes entering the group of block producers, while at the same time increasing the requirements for hardware resources and the number of Bitbon units that the hacker must have in order to carry out an attack on the network.
6. The increase in the number of Registrators leads to a further increase in the ability to withstand attacks on the blockchain network of the Bitbon System, while reducing the possibility of a successful attack on the network.
7. In order to improve the decentralization, reliability, transparency and security of the Bitbon System, the Community PoS consensus algorithm will be further improved in accordance with the development stages described in the Bitbon System Roadmap.
8. Organization of the infrastructure of the Bitbon System blockchain based on the Community PoS consensus algorithm gives an opportunity to build the Bitbon System Social Network, the social, legal, architectural and technical solutions of which will allow for a quick reaction to challenges of the modern world and changes of conditions without decreasing the quality of services of this system.
Article 6. Concept of the Community PoS Consensus
1. The main goal of the Community PoS consensus is to provide true decentralization of the processes of announcing, verifying and storing data of the distributed ledger with a high level of performance of storage network and guaranteed short wait time of transaction confirmation.
2. The achievement of the main goal of Community PoS consensus is ensured by:
 1) using ways of preliminary block production sequence approval by block producers to prevent forks and block collision;
 2) centralizing the network at the moment of block formation by the network node in accordance with the block formation sequence;
 3) introducing a strict synchronized sequence diagram of network node operation to ensure the exact determination of the state of the blockchain network;
 4) introducing the network state “service denied” to register the value of the uncertainty period when business offer cannot qualify the state of the operation carried out by the nodes of the blockchain network;
 5) mutual synchronization of network nodes to ensure adherence to the voting and block formation sequence diagram;
 6) using a fixed maximum amount of time for processing the transaction (with its cancellation in case of failure to complete it within the given timespan);

7) introducing three types of network node operation protocols:
 — protocol for quorum control and ensuring time synchronization of nodes that is essentially a background process based on the poll of the blockchain network and keeps the information on the availability of the nodes, which can participate in the voting and block formation procedures, up to date;
 — sortition protocol, within which the network node sequence is formed, according to which network nodes will act as block producers;
 — block formation protocol, which includes the creation of the block by the block producer, its verification by other network nodes and a node rating system, which provides the accuracy of carrying out the block producer functions by the network nodes;
 8) using the algorithm of the random distribution of Assetbox powers of Registrators among the network nodes prior to sortition of the nodes, the rating of which allows them to be candidates for block producers. Such a decision allows increasing the difficulty of predicting the block producer sequence;
 9) the mechanism of decentralized sortition when determining the sequence of taking on the role of block producers by the nodes, which is conducted by sorting the list of nodes according to the powers allocated in favor of these nodes, defining the sequence limits and observing the nodes’ compliance with the rules of participating in the formed sequence of block producers;
 10) a decentralized verification of the block by all the nodes of the blockchain network and sending out the message on the increase or decrease of the rating of the block producer that generated the block depending on the verification results.
Article 7. Network Nodes and Their Role Within the Community PoS Consensus
1. Network node is a hardware and software complex at the disposal of the Provider in the role of a Partitioner[i], which is connected to the blockchain network of the Bitbon System and stores blockchain data in part of in full. The blockchain network node of the Bitbon System can have the following roles: synchronization node; node participating in the quorum; block producer candidate; block producer.
2. Synchronization node is a blockchain network node that, when connecting to the network, synchronizes with the other nodes by receiving transaction blocks, transactions and objects related to them from the other network nodes, verifying them and storing in the local blockchain storage. Synchronization of the node time is conducted in accordance with the timestamp of the last valid block and the latency metric to the block producer that formed this block as well as the timestamps from the other network nodes. After synchronization, the node conducts the verification and storage of transactions and blocks it receives. If the metric of distributing the block for this node is less than the specified value, then this blockchain network node must accept transactions from client applications and/or services for processing and, after verifying them, rebroadcast them to all the other network nodes. Otherwise, or if the quorum of the blockchain network nodes has not been reached, the node does not accept transactions for processing, displaying the “service denied” error.
3. Node participating in the quorum is a synchronization node, whose latency for nodes that are part of the quorum does not exceed the threshold. To implement the protocol of operation of the Community PoS consensus in the blockchain network, the number of nodes has to be higher than the size of the quorum determined by the Bitbon System Operators[i] (no less than 2/3 of the number of blockchain network nodes). The node participating in the quorum takes part in the rating formation procedure in accordance with the node rating system. If, while processing transactions and blocks, the quorum participant notices a violation of the processing rules, they send all the network nodes the relevant message on the decrease of the rating of sources of invalid data. If the data is valid, then the message contains the information on the increase of the rating of the relevant block producers.
4. Block producer candidate is a node participating in the quorum that complies with established hardware requirements, has the rating above the specified value and the Providing mode turned on. In this case, such a node will be included in the procedure of distributing powers of Assetboxes of the Registrator pool.
5. Block producer is a block producer candidate, which was included in the block producer sequence as a result of conducting the sortition to sign and announce only one block in the specified time period (timeslot) within a specific round.
Article 8. Supporting the Sortition System
1. To automate the voting procedure of Registrators[i] and eliminate the threats of the Bitbon System centralization, the Community PoS consensus protocol envisions a procedure of automatic redistribution of Assetbox powers of Registrators among block producer candidates.
2. All that is required in order for an Assetbox to participate in automatic voting is to transfer the Registrator’s Assetbox power to the Registrator pool in the manner specified in Part 1 of Article 19 of this Appendix.
3. Assetbox powers of Registrators, which participate in automatic distribution, randomly associate among all blockchain network nodes of the Bitbon System with the corresponding rating, which meet the relevant requirements for the performance and quality of the connection channel (node in the role of a block producer candidate) at the time of voting.
Article 9. Sortition Procedure
1. Sortition procedure is a process, the goal of which is to form the sequence of block producers based on Assetbox powers of Registrators, which are distributed among block producer candidates, according to which said block producers will sign and announce blocks in the next round.
2. The sortition procedure is conducted in accordance with the voting and block formation sequence diagram and contains the rounds, the duration of which is equal to the number of block producers multiplied by the 1second time interval.
3. The number of block producers is determined by Bitbon System Operators.
4. The sortition procedure starts after the end of each round and is conducted over the entire duration of the round. The final block of the round or the message of the timestamp instead of it, if this timeslot had no transactions, can serve as an indicator of the end of the round.
5. Voting under the sortition procedure is carried out in the following order:
 1) within the first 2 seconds, every node, based on Assetbox powers of Registrators, which are distributed among block producer candidates, must randomly form a list of possible positions (sequence) from 1 to n for each block producer candidate node with power higher than the lower limit and a corresponding rating and then send the hash of this list (sequence) to all the nodes participating in the quorum;
 2) out of the nodes that can be included in the sequence, the block producer, which is the last to form a block in this round, is excluded;
 3) sequence elements with identical positions are not allowed;
 4) it is forbidden to include 2 elements with the same identifier in the sequence;
 5) on the 5th second, each node participating in the quorum, based on the number of votes for each unique sequence hash, must determine whether or not the sequence it formed collected the maximum amount of votes. If not, the node goes into the standby mode awaiting the block producer sequence. Otherwise, the node checks if the number of votes exceeds or equals 2/3 of the quorum. If the number of votes exceeds or equals 2/3 of the quorum, the node announces the sequence. If not, the node announces the message about the sequence forming error and goes into the standby mode until the start of the next round;
 6) each node receives either the block production sequence or the error from the other nodes by the 9th second.
6. Each node, regardless of its role, verifies the received blocks in accordance with the calculated/received sequence of block producers.
7. The block producer candidate specified in the resultant sequence takes on the role of a block producer during its timeslot.
Article 10. Block Formation
1. The block producer forms the block out of transactions that are in its transaction pool with the timestamp of the latest transaction in the last valid formed block and the moment of block formation in the next timeslot, which it serves according to the rules:
 1) if no transactions were received in the processed timeslot, the block will not be formed, but all the nodes will be sent the timestamp of the ending of the timeslot;
 2) the node in the role of a block producer forms a block based on the hash code of the previous valid block out of transactions in its transaction pool;
 3) during the round, the block producer can form a block only once;
 4) the block producer cannot under any circumstances form 2 blocks in a row;

5) all the nodes (including block producers in this round) take on the
role of the synchronization node receiving transactions, carrying them out
and checking the received blocks:
 — if the block is valid, then both it and the transactions it includes are registered in the storage;
 — if the block is invalid, the node ignores it and awaits a valid block with the same number;
 6) if a block producer was unable to verify the previous block at the time of serving its timeslot, it forms a new one with the same number, which includes all transactions in the transaction pool, with the ones that arrived in the previous timeslots, filtered by the time of creation (excluding the ones that ran out of processing time). The block producer sends out a message on the decrease of the rating of the previous block producer.
Article 11. Node Rating
1. The rating of each node is formed through messages that are sent out via the blockchain network of the Bitbon System by all the nodes as a result of verifying another block formation.
2. The changes in the rating are accepted by all the network nodes in favor of all the network nodes, in particular in favor of the block producer, and are applied after a time period equal to the duration of three timeslots after block formation, on condition that the number of messages exceeds or equals the quorum (at the same time, the number of messages from each node is being monitored). Only one message from a node for each block is included.
3. Below are the main factors that influence the rating of the nodes:

1) rating is increased:
 — for the correctly formed block;
 — for fulfilling the terms of participating in the quorum (issued by the Bitbon System Operator);
 — if a block producer formed at least one block during the day and did not receive the rating decrease;

2) rating is decreased:
 — if a block producer included more than 10 transactions related to the previous timeslot;
 — if a block producer formed a block in a timeslot that is not its own;
 — if a block producer did not form and send the package with a timestamp in its timeslot;
 — if the node sent more than 2 messages on the increase/decrease of the rating for one block (pause);
 — if the node broadcasted an invalid transaction or the same transaction once again (for each repetition);
 — rating reduction to zero if a block producer formed an invalid block (included an invalid transaction).
4. The calculation of the network node rating may also be influenced by other events and metric values.
Chapter 4. Scientific and Mathematical Substantiation of the Global Probability Model of the Block Producer Sequence Formation Process
Article 12. Distribution of Assetbox Powers of Registrators Among Network Nodes, Block Producer Candidates
1. The source data is represented by the group of Assetboxes . Each Assetbox e(j) is characterized by a unique identifier a out of the multitude A and a power (positive numeric characteristic) b(j)
,
,
where N is a number of Assetboxes of Registrators, which participate in providing.
Assetbox powers are transferred randomly (quasirandomly) in favor of a set of network nodes (block producer candidates). The power of each Assetbox is transferred to only one node. Depending on the state of the group , there is a number of positive probabilities
of transferring the power of j Assetbox to the i block producer candidate. For each Assetbox, the sum of probabilities of transferring the power of this Assetbox to a specific node, a block producer candidate, for all the nodes, equals one
.
The probability of distributing powers of the Assetbox group with the numbers in favor of the i node equals
.
Whereas the probability of transferring powers of only these Assetboxes to the i node equals
.
If the i node receives the precise set of Assetbox powers , and the other nodes, block producer candidates, receive other, unrelated sets of Assetbox powers, while combining such sets with all the nodes amounts to the entire multitude of Assetbox powers, the probability that all the nodes will receive the powers of their own unique sets of Assetboxes is defined as a product of probabilities for all the blockchain network nodes
,
which means
.
Article 13. Forming a Block Producer Sequence out of Block Producer Candidates
1. Each node with its own set of Assetbox powers out of the total set of n blockchain network nodes can be selected into the block producer group out of k nodes .
The probability p(i)[H] of choosing the i node into the selected group depends on the state of the nodes H=(E^{1},E^{2},...,E^{n}) where the state of the nodes is determined by the Assetbox powers distributed in their favor
.
V(i) is a random value that shows the number of entrances of the i node into the chosen group, which means that V(i) is an indicator of the i node entering the chosen group, i=1,2,...,n, which receives the values of 0 or 1. denotes the number of nodes in the chosen group.
The probability of the i node entering the chosen group of k block producers equals
the conditional probability of the i node entering the chosen group on condition that the number of nodes in the chosen group equals k.
This conditional probability is determined as a relation of the probability of the product P(V(i)=1,V=k) of these two events to the probability of the P(V=k) condition.
The probability of the condition equals
the total of the probability of the products of events of the specific node’s membership in a group (chosen or not chosen) of events when the chosen group consists of k nodes.
Then we calculate the probability of the product P(V(i)=1, V=k), i.e. distinguish the summands out of this total, in which V(i)=1 and the total of other indicators equals k1. This probability is determined as follows
.
The probability of the i node entering the chosen group of k block producers equals
the conditional probability of the i node entering the chosen group on condition that the number of the nodes in the chosen group equals k and
or
,
where
.
Article 14. Events of the Repeated Formation of the Block Producer Sequence
1. The conditional probability of the i node entering the chosen group of block producers at the r position on condition that the size of the group of block producers is k nodes equals .
The conditional probability of repeating the fragment of the sequence out of the determined w nodes in the group of block producers of k nodes on condition that the nodes, which participated in the selection procedure are already included in the sequence equals the probability
that this sequence fragment is positioned at the beginning of the sequence of block producers multiplied by the number of positions in the sequence (kw+1), in which this sequence fragment can be placed, in the group of block producers of k nodes
.
The probability of the condition of forming the i(1),i(2),...,i(w) sequence fragment equals the product of the probabilities p(i(1)),p(i(2)),...p(i(w)). The probability of the sequence fragment i(1),i(2),...,i(w) occurring at another step in the group of block producers equals the product of the conditional probability P^{(r)}(w,k) and the probability of the condition p(i(1))p(i(2))...p(i(w)) and equals
.
Article 15. Evaluation of the Probability of Stationarity of the Results of the Block Producer Sequence Formation Process Regarding the Stages of Distribution of Assetbox Powers and Block Producer Sequence Formation
1. As the evaluation of the solution options, we can determine the number of possible ways to divide the multitude out of N elements into the unrelated subsets A^{(i)}, A=A^{(1)}+A^{(2)}+ ... +A=^{(K)} , where i=1,2,...,K and K < N, which equals K^{N} . The first element a(1) of the multitude A can enter any of K subsets, the second element a(2) of the multitude A can enter any of K subsets... and so on N times. The division of the source multitude A into the unrelated subsets A^{(i)} , where i=1,2,...,K is a result of the stage of distributing Assetbox powers in favor of network nodes, block producer candidates.
Now let us calculate the power distribution.
This way, each subset A^{(i)} takes on the condition E^{i} that is defined by the elements a(i(s)), s=1,2,...,l=l(i) within it,
.
Generally, the states of subsets will change. The result of implementing the power distribution stage is shown as a number of shifts N_{sh} of subsets of the multitude A (assuming that the shift, in this case, means the arrangement A^{(i)} by the value of the condition E^{i} ), which equals
N_{sh}=K!
Each shift is the source data for the process of forming the sequence of block producers, with the help of which the privileged subsets A^{(i)} are selected out of subsets A^{(v)} , where v=1,2,...,П. The total number of selections N_{select} of privileged unordered subsets out of block producer groups equals
.
Generally, the probability of the element e(i) entering a specific subset A^{j} (event X), for example, for the first j=1, equals . The probability of selecting the subset A^{1} into the privileged group (group of block producers) on condition that the event X has occurred (in the subset A^{1} there is an element e(i^{1}) , event Y) equals . The probability of the repeated entering by the element of the sequence, which will then enter the privileged group into the same spot, equals
.
u elements were selected into the subset and this subset entered the privileged group into a specific position in a group of block producers, the event X will be the selection of the same number u of elements into the same subset during the next step, and the event Y is a selection of this subset into the privileged group into the same position. We calculate
and
.
Based on the abovementioned, we determine the value of the probability of distributing Assetbox powers into a specific network node and the probability of distributing a specific network node, a block producer candidate, into a privileged group of nodes that produce blocks.
The probability of the events described above will be low with high values of variables.
Chapter 5. Role of a Registrator in Consensus Building in the Bitbon System
Article 16. Concept of Consensus Building in the Bitbon System
1. The concept of consensus building in the Bitbon System[i] is based on the effectiveness of the activity of the Provider[i] in the role of a Registrator[i] as a participant in the social network of economic relations who is interested in its development, reliability and security.
2. Under the concept of consensus building in the Bitbon System, the person and his/her resources, which include social connections and Bitbon units[i], acquire value.
3. Consensus in the Bitbon System is ensured by using the Community PoS algorithm in the distributed ledger of the Bitbon System.
4. Consensus building in the Bitbon System is the priority of the entire community of the Bitbon System Social Network[i].
5. The activity of the Provider in the role of a Registrator is aimed at recording deals in the Bitbon System[i] in order to confirm a legal fact by achieving consensus using the Community PoS algorithm.
6. The Provider participates in consensus building using the functionality of the Bitbon System infrastructure[i].
7. In order to participate in providing in the role of a Registrator, the User shall connect his/her Assetbox to the Registrator pool.
8. By participating in providing, Registrators provide Bitbon units available in their Assetboxes for automatic distribution of powers of these Assetboxes among the blockchain network nodes of the Bitbon System for voting.
9. The powers of Registrator pools participate in sortition procedure in order to form a sequence of network nodes that will sign and announce blocks.
10. Registrators accumulate their Bitbon units on Assetboxes, which they connect to the Registrator pool, as well as form and develop their own pools, thereby increasing the power of their pool and its legal weight when confirming deals by achieving consensus in the Bitbon System. The Bitbon System, through the providing fund[i] as one of its components, distributes remuneration among Registrators depending on the number of Bitbon units allocated by each Registrator as well as on the social connections formed by them.
Article 17. Stages of Providing Aimed at Ensuring Economic and Legal Decentralization of the Bitbon System
1. Providing[i] aimed at ensuring economic and legal decentralization of the Bitbon System is implemented according to the stages specified in the Decentralization Roadmap.
Article 18. Registrator Pool Structure
1. Registrator pool consists of one or several Assetboxes engaged in providing, which are connected through special transactions. The Registrator pool operates in accordance with rules and technical protocols of Community PoS consensus building.
2. Each Registrator pool has a root Assetbox. All Assetboxes directly connected to the root Assetbox are called the first connection line.
3. Registrator pools can be of several types:
 1) Registrator pool with one Assetbox that connected to providing;
 2) Registrator pool with the 1st connection line;
 3) Registrator pool with the 2nd and more connection lines.
Article 19. Connecting to Providing
1. In order to connect to providing, the User shall transfer 0.0001 Bitbon units with a comment /providing to the Assetbox he/she wants to connect to.
Article 20. Mechanism for Implementing the Concept of Economic and Legal Decentralization of the Bitbon System
1. Providers in the role of Registrators, by allocating their Bitbon units for participating in providing, acquire a certain legal weight, which allows them to record deals in the Bitbon System by achieving consensus using the Community PoS algorithm in order to confirm their legal fact. The Registrator receives remuneration for his/her activities, the amount of which depends on the method of participation of a specific Registrator in economic and legal decentralization of the Bitbon System.
2. The participation of a specific Registrator in economic and legal decentralization of the Bitbon System is implemented by one of three methods.
3. The first method is implemented when the Registrator initially connects his/her Assetbox to providing. Thus, the Registrator acquires his/her own legal weight in the Bitbon System Social Network in order to participate in confirming deals in the Bitbon System. The legal weight of this Registrator depends on the number of bitbons[i] in his/her Assetbox.
4. The second method is implemented when this Registrator connects new Registrators to the first line of his/her pool. This Registrator pool uses a larger number of Bitbon units in providing, receives a greater legal weight and consists of the root Assetbox and the total number of Assetboxes of all pool participants, the first connection line.
5. The third method is implemented when the participants of the first connection line of the pool of this Registrator also connect new participants to their pools, which became a part of the initial structure of the Registrator pool. This pool has social connections of a larger scale, acquires greater legal weight and consists of the root Assetbox, Assetboxes of Registrators of the first line and Assetboxes of Registrators of the second line and lower.
Article 21. Assetbox Power
1. The main parameter of the root Assetbox of the Registrator is its power that defines the legal weight of a specific Registrator in the Bitbon System Social Network when confirming deals in the Bitbon System and is calculated as a sum of base and social powers of the Registrator’s Assetbox.
2. Power of the Registrator’s Assetbox is measured in power units.
3. Assetbox power is a key indicator used to calculate the Registrator’s remuneration.
Article 22. Individual Assetbox Power
1. Each Assetbox has an individual power that depends on the number of Bitbon units stored in the Assetbox and is equal to 25% of the balance of this Assetbox.
Article 23. Power Increase
1. The power increase process starts from the second providing period after an Assetbox connects to the Registrator pool. Over the course of 10 providing periods, the Assetbox power increases until it reaches its nominal value.
2. If you add funds to the Registrator’s Assetbox while increasing the power, then, starting from the next period after that, a parallel process of increasing the power of this Assetbox takes place.
3. If, during the power increase, the balance of the Registrator’s Assetbox decreases, the increase in power is calculated and performed according to the number of Bitbon units remaining in the Assetbox, not to its initial balance.
4. Bitbon units that are sent to the Registrator’s Assetbox from the providing fund as remuneration are engaged in providing right after the Registrator receives them without going through the power increase process.
5. When the root Assetbox of the Registrator is increasing its power, there may be no power to calculate remuneration for the root Assetbox of the Registrator for several providing periods if Bitbon units are withdrawn from the Assetboxes of the first connection line.
Article 24. Base Assetbox Power
1. Base Assetbox power is formed when other Assetboxes connect to the Registrator’s Assetbox.
2. Base power is determined by the individual power of the Registrator’s Assetbox and Assetbox powers of its first connection line.
Article 25. Social Power of Assetboxes and Interlevel Difference
1. Social power of an Assetbox is formed using social connections of a Registrator starting from the second line and lower.
2. All Assetboxes of the Registrator pool are divided into levels. The level depends on the base balance of the Registrator pool: the more Bitbon units there are in the Registrator’s Assetbox and its first connection line, the higher the level of the pool.
3. Assetboxes of Registrators involved in providing have a 100level scale used to distribute the base balances of such Assetboxes. The value of the limit of level 100 depends on the median of distributing Assetbox balances in providing. Therefore, the base balance of an Assetbox that it needs to achieve to get level 100 is calculated relative to this median.
4. Assetboxes of Registrators are divided into levels according to the calculated base balance and the value in Bitbon units that needs to be achieved to get level 100.
5. An interlevel difference of the Registrator pool is formed as follows: the bigger the difference between the level of the Registrator’s Assetbox and that of the Assetbox below it in the pool, the higher share of social power the Assetbox of this Registrator will receive.
Article 26. Social Power Blocking
1. If the structure of the Registrator pool has an Assetbox with the base balance (level) equal to or higher than the base balance (level) of the Assetbox of this Registrator, the blocking of social power takes place.
2. As a result of blocking, your Assetbox loses its social power and does not participate in calculating remuneration for the following providing period in this branch of the Registrator pool.
3. If the structure of the Registrator pool contains an Assetbox with the balance lower than 0.001, this Assetbox is not involved in providing and does not receive remuneration, while social connections in the structure of the pool through this Assetbox are maintained, but quality and quantity indicators for it are not calculated.
4. Providing in the Bitbon System envisions a power blocking indicator, which is displayed in the Registrator’s analytical dashboard and is a tool used to control the levels of base balances of Assetboxes of the Registrator pool.
Article 27. Providing Cycle
1. A providing cycle contains three providing periods, during which the powers (base and social) are calculated and saved for each Assetbox of the Registrator pool, and the blocks are being created and verified followed by the crediting of remuneration.
2. Providing cycles for each Registrator’s Assetbox participating in providing are calculated simultaneously.
3. During the 1st period of the providing cycle, base and social powers for each Assetbox of the Registrator pool are calculated and saved. The minimum balance throughout the providing period is always used for calculating the Assetbox powers.
4. During the 2nd period of the providing cycle, the Assetbox powers that are part of Registrator pools participate in creating transaction blocks and their subsequent verification.
5. During the 3rd period of the providing cycle, remuneration for the powers calculated during the first period of the providing cycle is credited to the Assetboxes of Registrators.
6. When the Registrator’s Assetbox connects to the pool, the first providing cycle consists of four providing periods:
 1) the first providing period envisions the inclusion of the Assetbox into the Registrator pool;
 2) the minimum balance of this Assetbox at the time of its connection is zero, the power increase process will be implemented in accordance with the calculated indicators for the second providing period. The Assetbox power will increase over 10 providing periods until it reaches its nominal value;
 3) during the third providing period, the powers calculated for the second period will participate in creating transaction blocks and their subsequent verification;
 4) during the fourth providing period, remuneration will be credited for the powers calculated for the second providing period and that participated in signing transaction blocks and their subsequent verification during the third providing period.
7. Remuneration and the entire providing system are linked to the server time (UTC).
Article 28. Providing Power Protection
1. Providing power protection was developed in order to create the conditions for a stable operation of the providing service and optimal distribution of powers among Providers in the role of Registrators.
2. Providing power protection implies that:
 1) when a providing period ends (i.e. after 72 hours), transfers of Bitbon units to the Assetboxes of Registrators over the given period are analyzed;
 2) if the Assetbox balance, based on which the power for this providing period is calculated, is lower than for the previous providing period, the power of this Assetbox is reduced by the difference of powers calculated before and after the decrease in the balance of this Assetbox multiplied by four. The power value that the power of this Assetbox was reduced by will go back to the value that corresponds to the new balance over the course of 10 providing periods: 10% for each providing period;
 3) if the balance reduces during one of the following periods, another providing power protection process is created, which is added to unfinished power protection processes that occurred before.
3. The providing power protection process does not cover Bitbon units received as remuneration on condition that these Bitbon units were transferred from the Registrator’s Assetbox during the same period when the remuneration was received (before they start participating in the next providing period).
Article 29. Synergy of Remuneration and Principles of Crediting Remuneration
1. The received remuneration will be credited to the Registrator’s Assetbox in the corresponding providing period. The transaction with remuneration will specify what part of remuneration the Registrator received for the base power, and what part of remuneration was for social power.
2. If the Registrator does not accept the transaction with remuneration within 30 days, this transaction is returned to the providing fund for further redistribution among Registrators. If the Registrator does not accept the transaction with remuneration in the specified period, such remuneration cannot be credited again.
3. The main principles of crediting remuneration include the following:
 1) the higher the balance of the Registrator’s Assetbox involved in providing, the higher the remuneration received by the Registrator;
 2) remuneration of the Registrator is proportional to his/her contribution to forming a Registrator pool;
 3) providing is a cyclical process, one period of which equals 72 hours. Every 72 hours, all Registrators receive remuneration from the providing fund for participating in providing. The size of remuneration directly depends on the base and social powers of the Registrator’s Assetbox.
Article 30. Registrator’s Tools
1. The Bitbon System[i] has the following Registrator’s tools: Registrator’s[i] analytical dashboard; Registrator pool virtual modeling application; “Adjusted Base Balance of Level 100” chart; “Number of Bitbons in Providing” chart; “Power of Assetboxes” chart; “Changes in the Pool Structure” chart; Registrator’s calculator; adviser bot.
2. Registrator’s analytical dashboard is the main tool of the Registrator that displays detailed information on all Assetboxes in all the lines of the Registrator pool: base balance, total power, Assetbox level and other data. Registrator’s analytical dashboard shows expanded and detailed statistics of distributing remuneration among Assetboxes of Registrators.
3. Registrator pool virtual modeling application was created in order to teach the basics of providing[i] in the Bitbon System and the main principles of the Registrator’s activity. A set of tools of the application that includes charts and various settings allows for a better understanding of the principles of building Registrator pools with different combinations of Assetboxes that are part of the Registrator pool and their balances.
4. The “Adjusted Base Balance of Level 100” chart is a line chart where Yaxis represents the value in Bitbon units that needs to be achieved for the Assetbox to get level 100. Xaxis represents 90 providing periods.
5. The “Number of Bitbons in Providing” chart is a line chart where Yaxis represents the total balance of all Assetboxes of Registrators, which participate in providing, and Xaxis represents 90 providing periods.
6. The “Power of Assetboxes” chart is a line chart where Yaxis represents the sum of powers of all Assetboxes of Registrators, which participate in providing, and Xaxis represents 90 providing periods.
7. The “Changes in the Pool Structure” chart is a line chart that shows the calculated indicator of proximity of the total power of all Assetboxes of Registrators, which participate in providing, to the power of an “ideal pool” (theoretically achievable power of all Registrator pools in the Bitbon System).
8. Registrator’s calculator is one of the main tools developed in order to provide Registrators with the ability to conduct preliminary calculation of remuneration for participating in building consensus in the Bitbon System. This application automatically predicts the ways of receiving remuneration based on the entered parameters with the option of choosing the period and one of the three main prediction models:
 1) 1st model: the prediction is made based on the fact that a Registrator has only his/her own Assetbox, and only its individual power participates in providing;
 2) 2nd model: the prediction is made based on the fact that a Registrator has a connected first line, i.e. base power;
 3) 3rd model: the prediction is made based on the fact that a Registrator has the second line and more, i.e. social power.
9. Adviser bot is a tool created for timely notification of a Registrator about the key events in his/her pool through Telegram messenger. Adviser bot will inform the Registrator about incoming transactions with remuneration, connection of new Assetboxes to the pool, recalculations of levels and powers and so on. In addition, the adviser bot provides recommendations on increasing the effectiveness of managing the pool. Messages sent by the bot in the messenger are doubled in the Registrator’s analytical dashboard in a special “Adviser Bot” tab.
Chapter 6. Mathematical Description of Consensus Building
Article 31. Analytical Expressions to Perform a Sequence of Actions Related to Calculating Remuneration to Registrators for Participating in Providing
1. Source data:
N — number of Assetboxes of Registrators, which participate in providing,
B(n) — balance of Assetbox number n, n=1,2,3,...,N,
BB(n)=B(n)+B^{(1)}(n) — base balance where is the sum total of Assetbox balances of its first connection line, B(n(i)) is the balance of the i Assetbox of the first line number n(i).
2. Let us calculate the (common value)
B^{avg} — average of Assetbox balances of Registrators, which participate in providing,
.
3. Let us calculate the (individual value) for each Assetbox number n
b^{r}(n) — relative balance of the Assetbox,
.
4. Let us assign z > 0, an influence coefficient of the first connection line and function f(b^{o}(n)), an influence regulator of the first line, by selecting its parameters
a > d > 0, c > 0.
It sets the value of entering the level of zero Assetboxes to zero.
It depends on the relative balance b^{o}(n) of Assetbox number n.
It is continuous on the positive semiaxis and f(0)=0, f(∞)=1:
.
5. Based on the total balance B^{(1)}(n) of the first connection line for each Assetbox number n, we calculate R(n), the value of bringing Assetbox number n to a certain level (adjusted base balance) determined by the value
R(n)=B(n)+z*B^{(1)}(n)*f(b^{o}(n)),
that depends on the balance B(n) of Assetbox number n, as well as the total balance of its first connection line. This formula contains:
z > 0, an influence coefficient of the first connection line and function f(b^{o}(n)), an influence regulator of the first line, which depends on the relative balance of Assetbox number n.
6. The issue of selecting the left boundary of the top (100th) level is solved using the generalized exponential distribution (Weibull distribution).

1) First, we need to express the parameter of the generalized exponential distribution through its median. The generalized exponential distribution is as follows
F(x)=1−exp[−λx)^{α}], x>0 .
Let us solve the equation 𝐹(𝑥) = 1⁄2. Then, write down an equivalent equation
1⁄2 = 1 − exp[−(𝜆𝑥)^{𝛼}] .
Let us find
exp[−(𝜆𝑥) ^{𝛼}] = 1⁄2
and𝜆𝑥 = (ln2)^{(1⁄𝛼)} .
Therefore
𝑥^{(𝑚𝑒𝑑)} = (ln2) ^{(1⁄𝛼)}⁄𝜆 .

2) The next step is to express the quantile for the probability 0.99 through the parameter of the exponential distribution. Let us find the left boundary of level 100. We solve the equation
F(x)=0.99,
or
0.99=1−exp[−(λx)^{α}],
or
exp[−(λx)^{α}]=0.01.
Therefore
𝜆𝑥 = (ln100)^{(1⁄𝛼)}
and
𝑥^{(0.99)} = (ln100) ^{(1⁄𝛼)}⁄𝜆.
From the relation
𝑥^{(med)} = (ln2) ^{(1⁄𝛼)}⁄𝜆
we find
𝜆 = (ln2)^{(1⁄𝛼)}⁄𝑥^{(med)}
and apply it to the expression
𝑥^{(0.99)} = (ln100)^{(1⁄𝛼)}⁄𝜆.
We obtain
𝑥^{(0.99)} = (ln100)^{(1⁄𝛼)}⁄𝜆 = 𝑥^{(med)}(ln100/ln2)^{(1⁄𝛼)} = 𝑥 ^{(med)} * [(log100)/(log2)]^{(1⁄𝛼)} ,
or
,
or
.
The left boundary of level 100 is expressed through the median of the exponential distribution as
.

3) The next step is to determine the exponent of the distribution.
In order to determine the exponent of the generalized exponential distribution, we use the expression for the expected value of a random variable with this distribution:
F(x) = 1  exp[(λx^{α})], x > 0.
It equals
.
The expression for the median is
𝑥^{(𝑚𝑒𝑑)} = (ln2)^{(1⁄𝛼)}⁄𝜆,
we find
.
Let us calculate
.
Let us solve the equation
of the relatively known exponent ɑ.
Here
is the value of gamma function in the point 1+1⁄α.
Let us create the process of finding the expression
with the previously assigned accuracy, the equation
is solved using bisection or the method of golden section.
Let us use ɑ=1⁄3 for the initial structure.
As an example.
If x^{med} = 30,
𝛥 = 𝑥^{left}(1) is the left boundary of the first level, the value the crediting of remuneration starts from,
A(1) — length of the first level interval,
L — number of levels (in this case L = 100),
𝐷 = 𝑥^{left}(𝐿) — left boundary of the top level.
Let us determine:
the range extender of level intervals (starting from the second one).
For all levels, starting from level 2 (2 ≤ k ≤ L)), the left interval boundary of level k equals:
𝑥^{left}(𝑘) = 𝑥^{left}(1) + 𝐴(1) ∗ 𝑆^{(𝑘−2)} = 𝛥 + 𝐴(1) ∗ 𝑆^{(𝑘−2)}, 2 ≤ k ≤ L.
To illustrate this
Let us calculate the length Δ(k) of the level interval k, 1 ≤ k ≤ L.
If k = 1, the length of the first level interval equals A(1):
𝛥(1) = 𝑥^{left}(2) − 𝑥^{left}(1) = [𝑥^{left}(1) + 𝐴(1) ∗ 𝑆^{(2−2)}] − 𝑥^{left}(1) = 𝐴(1).
If k = 2, the length of the second level interval equals:
𝛥(2) = 𝑥^{left}(3) − 𝑥^{left}(2) = 𝐴(1) ∗ 𝑆(3−2) − 𝐴(1) = 𝐴(1) ∗ (𝑆 − 1).
If k = 3, the length of the third level interval equals:
𝛥(3) = 𝑥^{left}(4) − 𝑥^{left}(3) = 𝐴(1) ∗ 𝑆^{(4−2)} − 𝐴(1) ∗ 𝑆^{(3−2)} = 𝐴(1) ∗ (𝑆^{2} − 𝑆).
If k = 4, the length of the fourth level interval equals:
𝛥(4) = 𝑥^{left}(5) − 𝑥^{left}(4) = 𝐴(1) ∗ 𝑆^{(5−2)} − 𝐴(1) ∗ 𝑆^{(4−2)} = 𝐴(1) ∗ (𝑆^{3} − 𝑆^{2}).
If k = L  1, the length of the L  1st level interval equals:
𝛥(𝐿 − 1) = 𝑥^{left}(𝐿) − 𝑥^{left}(𝐿 − 1) = 𝐴(1) ∗ 𝑆^{(𝐿−2)} − 𝐴(1) ∗ 𝑆^{(𝐿−3)} = 𝐴(1) ∗(𝑆^{(𝐿−2)} − 𝑆^{(𝐿−3)}).
The left boundary of the L level interval equals:
𝑥^{left}(𝐿) = 𝑥^{left}(1) + 𝐴(1) ∗ 𝑆^{(𝐿−2)} = 𝛥 + 𝐴(1) ∗ 𝑆^{(𝐿−2)} = 𝛥 +𝐴(1)[(𝐷 − 𝛥)⁄𝐴 (1)] = 𝐷.
The relation of lengths of adjacent intervals:
, 2 ≤ k ≤ L  2,
starting from the second and ending with L  2nd equals S:
for all 2 ≤ k ≤ L  2.
7. We calculate level percentage coefficients r(k) (level percentages 100*r(k)) for each level k, k = 1, ..., L:
,
k = 1, ..., L, while the power parameter β > 0 determines the growth speed near small and big level values (downward or upward convexity of the level coefficients chart). If β = 1, the growth speed is constant (points on the chart are in a straight line).
8. Let us calculate the base power W ^{b}(n) of Assetbox n for each Assetbox number n using the formula:
W ^{b}(n) = max[0,25 * B(n);W],
where
W = min[B(n);0,25 * X]
is a minimum of the balance B(n) of the Assetbox number n and the sum of minimums min[B(n); B^{1}(n(i))] of its balance B(n) and balances B^{1}(n(i)) = B(n(i)) of all the nodes of the first line of connection to Assetbox n multiplied by the coefficient 0.25:
In order to do that, let us perform the following sequence of actions.
 1) Using the superscripts 1,..., we assign numbers to the levels (lines) of Assetboxes connected to the researched Assetbox.

2) We calculate the secondary variable:
,
where l — number of Assetboxes in the first line of the Assetbox;
B^{1}(n(i)) — balance of the i Assetbox of the first line number n(i).

3) We calculate the secondary variable:
W = min[B(n);0,25 * X].

4) We determine the base power:
W ^{b}(n) = max[0,25 * B(n);W].
Using this way of calculating base power, on condition that the first line of the researched Assetbox contains four Assetboxes with the balances equal to that of the researched one, this Assetbox will receive the maximum possible base power. There are other possible ways of structuring that would give the Assetbox the maximum possible base power for its balance.
9. Let us enter the adjusted social power W ^{ns}(n) for each Assetbox number n, which is determined by the source contents of the node n, Assetboxes numbers n(1), n(2), ..., n(l^{[1]}) of the first line of connection L^{[1]}n to the node n (they provide the base power for entering a level) and contents of the Assetboxes of all its connection branches below the first line connected to the Assetbox with the level percentage lower than that of the Assetbox number n (common value П(n)).
,
where Z(n) = l^{[1]} + П(n). Here, the variable C^{*}(n(i),n^{[1]}(π), n) is determined as follows. There is a singular connection path from the node n(i), located below the first line of connection to the Assetbox n, to the node n:
π(n^{[s]}(i), n)
that equals:
,
or simplified as:
that starts at the node n(i) = n^{[s]}(i) at the bottom level [s] and ends at the node
at the top one, at level 0 from its point of view.
While
is the maximum of all level percentage coefficients
r(n^{[1]}), r(n^{[2]}), r(n^{[3]}), ..., r(n^{[s1]}), r(n^{[s]})
of the nodes
n^{[1]}, n^{[2]}, n^{[3]}... n^{[s1]}, n^{[s]}
on the path
of connections from the node n(i) = n ^{[s]}(i) = n ^{[s]} to the node .
The sum total is calculated using all the branches below the first line of connection to Assetbox number n, the level percentage of which is lower than that of Assetbox number n. No branches of the Assetbox with the level percentage lower than that of Assetbox number n are used in calculations.
10. Let us calculate the majorizing social power W ^{ms}(n) for Assetbox number n:
.
The majorizing social power of node n is different from the adjusted social power due to the use of the variable r ^{max} = 1 instead of the variable r(n).
11. Then we calculate the social power W ^{s}(n) of the node n based on the adjusted social power W ^{ns}(n) using the formula:
W ^{s}(n) = W ^{ns}(n) * g(C ^{o}(n)).
Here we introduce the social normalizing function g(x) to ensure the social direction of providing, which equals:
g(x) = [h + (1  h)(1 + px^{η}) q ^{1x}],
0 < h < 1, q > 1, p ≥ 0, η ≥ 0.
Here h — level of unachievable minimum of the social normalizing function;
p — regulator of the wavelet of the social normalizing function chart;
η — indicator of the power that ensures the wavelet of the function chart;
q — base of an exponential social normalizing function, which ensures its movement towards an unachievable minimum h.
The argument x of the social normalizing function is represented by the variable:
,
which equals the relation between the majorizing social power W ^{ms}(n) and the average B^{avg} of the Assetbox balances.
12. Let us calculate the power W(n) for each Assetbox number n as a sum of base and social powers of the node n:
W(n) = W^{b}(n) + W^{s}(n).
13. The received sum S is split among all Assetboxes
in direct proportion to their powers using the formula for calculating remuneration S(n) for the nth Assetbox:
,
where
is the sum of powers of all Assetboxes.
The values of parameters in the realized model.
 1) z = 1
 2) ɑ = 1
 3)
 4) c = 0.8
 5)
 6) r ^{min} = 0.3, L = 100, β = 0.5
 7) q = 2, p = 1.5, η = 1.46, Δ = 10^{3},A(1)=1, h = 0.05
Article 32. Parameters of the Formulas for Calculating Remuneration to Registrators for Participating in Providing
1. Δ = 10^{3} — minimum Assetbox balance required to receive remuneration.
2. I(1) = 1 — length of the first level interval.
3. k = 1 — first line value coefficient.
4. ɑ = 1 — power of the main summands in an endless asymptotic.
5. с = 0.8 — coefficient that regulates the value of the function in unity.
6. d = 1/3 — exponent that allows setting the value of entering the level of zero Assetboxes to zero.
7. r ^{min} = 0.3 — minimum value of level percentage coefficients.
8. L = 100 — tables of rank percentages of Assetbox powers and correspondence of the Assetbox power and the first line to a certain rank are calculated in a dynamic manner based on the maximum power in the system. As the number of levels changes, the boundaries of level intervals also change.
9. β = 0.5 — power parameter that determines the level of growth near small and big level values; must be higher than 0.
10. h = 0.05 — level of an unachievable minimum (bottom boundary) of a social function; must be higher than 0, but lower than 1.
11. p = 1.5 — regulator of the wavelet of the normalizing function.
12. r = 1.46 — power for the argument of the social function.
13. q = 2 — base of an exponential social normalizing function q , which ensures its movement towards an unachievable minimum h.
SECTION 3. CONCLUDING PROVISIONS
Chapter 7. General and Other Terms and Conditions
Article 33. General Terms and Conditions
1. Amendments and additions to this Appendix may be made solely under the rules stipulated by the Appendix Making Amendments and/or Additions to the Bitbon System Public Contract.
2. If there is any discrepancy between various forms (printed, electronic, etc.) of this Appendix, its electronic version published on the official information resources of the Bitbon System[i] shall be deemed official.
3. This Appendix is translated into other languages only for convenience of Bitbon System Users[i]. In case of differences in understanding and/or interpretation of this Appendix, the Russian version shall prevail.
4. In accordance with Provision 2 of the Bitbon System Public Contract, this Appendix is an integral part of the Bitbon System Public Contract and comes into force after its publication on the official information resources of the Bitbon System.
5. In accordance with paragraph 3 of Provision 2 of the Bitbon System Public Contract, amendments and/or additions may be made to this Appendix only if such amendments and/or additions do not contradict the Provisions of the Bitbon System Public Contract and Appendices, which are an integral part of the Bitbon System Public Contract. Amendments and/or additions made to this Appendix shall be published on the official information resources of the Bitbon System and come into force in accordance with the Appendix to the Bitbon System Public Contract “Making Amendments and/or Additions to the Bitbon System Public Contract”.
Article 34. Other Terms and Conditions
1. The Bitbon System Operators[i] strive to maintain uninterrupted operation of the Bitbon System infrastructure[i]. By participating in providing, the User agrees that there is a possibility of disruptions in the operation of the services and/or components of the Bitbon System, which may lead to a temporary restriction of the rights and opportunities of the Provider[i] in whole or in any part.
2. Remuneration of the Provider that is not accrued due to a disruption in the operation of the services and/or components of the Bitbon System shall not be accrued again and/or reimbursed.
3. The User shall not participate in providing if he/she does not accept the terms and conditions established by the Bitbon System Public Contract and/or this Appendix in whole or in any part.
4. The participation of the User in providing shall mean agreement with the terms and conditions established by the Bitbon System Public Contract and this Appendix.