# Official Interpretation of “Nebulas Rank Yellow Paper”

The Nebulas Rank Yellow Paper was published on June 30, and it has generated productive discussion in the blockchain community. We are publishing this official interpretation to provide the Nebulas perspective on some of the core questions and issues raised so far.

**Q: What is Nebulas Rank?**

In short, Nebulas Rank is a value measurement system for the blockchain world.

**Q: Why is Nebulas Rank important?**

- Because of decentralization, blockchains lack an effective, comprehensive data measurement and ranking system.
- Many value measurement standards in the traditional internet era (represented by Google PageRank and its iteration versions) cannot be well-adapted to the specific situation of the blockchain.

**Q：What is the key innovation of “Nebulas Rank”?**

- Nebulas Rank firstly achieves a quantitative understanding of the contribution of a particular account to the blockchain economy. In one way, it is to blockchain what Boolean algebra in mathematics. And by quantifying the contribution of each account to the blockchain economy, it provides a foundation for measuring and determining the correct incentives.
- The classic monetary theory of economics holds that the value of a currency system stems from its liquidity. We believe the same holds for digital currencies. In a crypto economy, the main unit of the economy is the asset-holding account, and the aggregate economy is derived from the transactions (value circulation) carried out by all accounts. As such, the contribution of a particular account to the output of the entire economy provides the “Nebulas Rank”.

**Q: What is “Core Nebulas Rank”?**

Core Nebulas Rank is used to measure the contribution of a specific account to the economy during a time period, and it is related to the three concepts of “Median Account Stak “, “ In-and-Out Degree” and the “ Wilbur function”. In other words, the “ Core Nebulas Rank” is the sum of “ asset median” and the “discrepancy index”.

**Median Account Stake:**It is used to guarantee the validity of the transaction. For example, a normal transaction in the blockchain economy is from a to b, for example, a transfers 100 RMB to b. However, in reality, there is a widespread situation in which a malicious actor increases nodes in order to make more contributions (for example, a first turns 100 to A, then A turns 100 to B). The “Median Account Stake” takes the ascending/descending order of the assets held at different times (t1/t2/t3), and takes a median to indicate the status of the assets. The “asset median” represents the “token age”, that is, the account needs to hold at least half of the time of the asset to ensure the validity of the transaction.**In-and-Out Degree:**As mentioned earlier, the value of the economy stems from asset liquidity. Therefore, the ranking system values the assets to go “in and out” and truly flowing. We derive a system to mitigate against a malicious actor that makes use “circular transfers” to improve it is in and out degrees. To calculate the in and out degree, it needs first to remove the “circular transfer” process, and then sum the in and out the amount in the node, and based on this, calculate the in and out degree via a specific function.**Wilbur function:**The core of it is to prevent sybil attacks. For example, an account a can trade 1000 RMB in one transaction, however, in order to get higher NR value, a will split 1000 RMB into several units for multiple transactions. The Nebulas Rank is something like a specific function based on the Wilbur function, making this splitting cheating not worthwhile: no matter how a malicious actor splits the transaction, the total gained will be less than the one-time transaction without splitting; likewise, after the split unit reaches a certain threshold, the return will be much smaller than the NR value of the same unit.

In short, the calculation of the Median Account Stake and In-and-Out Degree can give the Core Nebulas Rank. And the Wilbur Function guarantees the security of this calculation.

**Q: How can “Core Nebulas Rank” guarantee fairness?**

Fairness of Nebulas Rank is mainly achieved by the algorithms resistance to manipulation. Manipulation can be understood the potential benefit a malicious actor has in attacking the system by transferring assets that it and its allies control.

Due to the de-circular algorithm and the Wilbur function, the cheating of the NR value of a single account and sybil attacks have an upper limit of the NR score calculation. This makes cheating uneconomical and strengthens the resistance of Nebulas Rank.

**Q: Can the Core Nebulas Rank evolve, and if so, how?**

We will update the block structure. The new block structure will contain the algorithm and parameters of the Core Nebulas Rank (in the form of LLVM IR). The Nebulas virtual machine (NVM) is used as the execution engine of the algorithm to obtain the algorithms and parameters of the Core Nebulas Rank from the block. We then execute the algorithm to obtain the core Nebulas Rank of the account within the node.

When the algorithm or parameters need to be updated, we will work with the community to include the latest algorithms and parameters in the new block, thus ensuring the timeliness and smoothness of the entire update process, and avoiding possible forks.

**Q: What is the Extended Nebulas Rank?**

This is another concept of the Core Nebulas Rank” proposed in the Yellow Paper. The Core Nebulas Rank measures the devotion of the account to the total economic volume. From this same basis, the “Extended Nebulas Rank” is a measure of value that satisfies more application scenarios.

For example, you can sort the smart contracts (mainly looking at two indicators: the call of the account address to the smart contract, and the call between the smart contract). The Extended Nebulas Rank is multi-dimensional and depends on the specific application scenario. Its calculation method is also based on the Core Nebulas Rank.

**Q: How to understand the “Core Nebulas Rank” from a deeper meaning?**

A deep understanding of the concept of Nebulas Rank requires the repeated reading of the Yellow Paper. Nebulas Rank Yellow Paper is the first research result released by the Nebulas Research Institute of blockchain technology innovation team. The author is Dr. T of the Nebulas Research Institute. He wrote an article about his understanding of the Yellow Paper and may offer some help to understand it in depth. The full text is as follows:

**To understand Nebulas Rank, begin from three of its features:**

From Dr. T of Nebulas research team: At the beginning of designing the Nebulas Rank, we hoped that it can meet three characteristics: authenticity, fairness, and diversity. Therefore, this article attempts to interpret the Yellow Paper from the above three characteristics.

Authenticity is the primary characteristic and also represents the ultimate goal of Nebulas Rank: to build a value measurement that accurately reflects the blockchain economic system. From Bitcoin to Ethereum, we have witnessed the development of blockchain technology.

From simple digital assets to more complex application scenarios, blockchain has gradually become a self-evolving ecosystem. In essence, a healthy blockchain system can be seen as an economy, and the encrypted digital currency itself has basic monetary attributes, therefore, we try to introduce the monetary model from the economic perspective to give Nebulas Rank the true meaning.

In the Yellow Paper, we introduce the Nebulas Rank as a measure of the devotion of account addresses to the blockchain economic system. More directly, Nebulas Rank measures the contribution of each account to the economic system at the micro level. Then we try to imagine whether the Nebulas Rank can reflect changes in the total economic system at the macro level.

In Section 3, we describe the relationship between currency volume, currency value, the rate of circulation, and productivity in the blockchain using the classical equation of the quantity of currency in economics. An interesting argument is that we do not deny that the value of many encrypted digital currencies in the market at this stage is affected by many factors (such as user investment expectations and other unknown factors), but in the long run, the balance of supply and demand of currency is still the important factor that determines the currency’s value, and our experimental results also support the above conclusions.

The understanding of fairness is more straightforward: Nebulas Rank must be effective against manipulation or cheating. This design idea is also reflected in the fourth and fifth sections of the Yellow Paper. The ranking algorithm we designed in the white paper is based on the LeaderRank strategy, however, we have modified the algorithm after nearly a year of thinking and verification.

In recent years, many papers have pointed out that the PageRank ranking strategy has defects in dealing with the “sybil attack”, and we have also verified the above problems. So we jumped out of our existing mindset and tried to design a more effective anti-cheating algorithm.

When designing the Core Nebulas Rank, we considered many factors, adhering to the “Occam razor” rule, and finally we chose the “median account stake “ and “weighted in and out degree”. The former reflects the “token age” of the account, while the latter reflects the location information in the trading network. It should be noted that for both practical and anti-manipulation considerations, the above two indicators are statistical data over a period of time.

Median Account Stake is actually the median of the account balance in ascending order over a period of time, which means that the account needs to hold at least half of the asset to get the median value of the corresponding asset, so transfer between multiple accounts to improve the ranking of the multiple accounts becomes more difficult.

Compared to the median account stake, the calculation of the weighted in and out degree is more difficult. Generally, in the case of non-joint manipulation, the operator itself is subject to hard constraints and cannot obtain more capital, as compared to the degree of trade access.

Considering that malicious controllers use “circular transfer” to improve their in and out degrees, therefore, in the calculation of the in and out degree, the “de-transaction loop” process is needed. The processed transaction graph can reflect the real transaction between accounts. At the same time, in the Nebulas Rank, we encourage normal trading between accounts.

We have designed a two-dimensional accessibility calculation function, in which the unilateral transfer in or out gain in a time period will not be higher than both in and out transactions, even if the transaction amount of the former is twice that of the latter.

Finally, we need to design a function to integrate the above two features and so there is the Nebulas Rank. Given that we hope the Nebulas Rank can effectively protect against Sybil Attack, then we name this function the Wilbur function, which is also named after the movie Sybil.

A sybil attack targets the evaluation system and destroys the peer-to-peer network by creating a large number of pseudonym accounts, thereby obtaining a false high importance score. In the blockchain system, this type of attack is manifested by the attacker creating a large number of accounts and splitting the assets separately for transactions to obtain higher returns.

Therefore, the Wilbur function should prevent the user from achieving a transaction behavior by controlling multiple accounts with a greater benefit than executing the transactions through a single account. At the same time, when the user’s median value and the in and out degree are large enough, we believe that the proceeds from the normal trading behavior should not be subject to additional losses. We give these two features a mathematical description in the Yellow Paper, and we give a function that satisfies this property.

For diversity, we hope that the Nebulas Rank can be applied to a variety of data and digital asset measurement scenarios. Therefore, the Nebulas Rank is divided into a Core Nebulas Rank and an Extended Nebulas Rank at the designing stage. We are also able to leave out the complex application scenarios and focus on solving the core problems.

The Core Nebulas Rank is designed to measure the contribution of accounts to the economic system and is also a core factor in Proof of Devotion (PoD) and Developer Incentive Program (DIP). The Extended Nebulas Rank will play a role in other application scenarios, such as in the multidimensional application scenario like the extended NR of smart contracts and the advertising recommendation system, etc.

Learn more about Nebulas:

- Github: github.com/nebulasio/go-nebulas
- Slack: nebulasio.herokuapp.com
- Telegram(EN): t.me/nebulasio
- Twitter: @nebulasio

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