> For the complete documentation index, see [llms.txt](https://docs.omnipact.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.omnipact.io/developers/omnipact-technology-white-paper/readme/omni-id-reputation-and-identity-protocol/5.2-reputation-scoring-vector.md).

# 5.2 Reputation Scoring Vector

Omni-Score ($$ $S$ $$) It is a dynamic numerical value between 0 and 1000. It is not a static stored value, but rather based on the user's historical interaction vector $$ $\vec{H}$ $$ The function results are calculated in real time.

#### 5.2.1 The Decay Algorithm: $$ $R(t)$ $$ calculation 

To reflect the "time-sensitive nature of reputation" (i.e., honesty a year ago is not as important as honesty yesterday), all positive behavior integrals are subject to the Half-Life Algorithm.

**Basic Decay Formula:**

The user's current reputation $S(t)$ is defined as:

$$
(t) = \sum\_{i=1}^{n} \left( P\_i \cdot e^{-\lambda(t\_{now} - t\_i)} \right)
$$

* $$ $P\_i$ $$:  $$ $i$ $$ The base points earned from each successful transaction.
* $$ $t\_{now}$ $$: Current block timestamp.
* $$ $t\_i$ $$:  $$ $i$ $$ The timestamp of the completed transaction.
* $$ $\lambda$ $$: Decay Constant. Setting$$ $\lambda \approx 1.8 \times 10^{-7}$ $$,This means that the half-life of the credit score is approximately 6 months.

**Mechanism significance:**

This means users cannot simply rely on their high scores accumulated early on. If a high-scoring user becomes inactive, their score will gradually decline over time, eventually returning to the baseline. This forces business nodes to maintain consistent and stable performance in fulfilling their obligations.

#### 5.2.2 Multi-dimensional Weighting

In addition to the time dimension, the basic points for a single transaction $$ $P\_i$ $$ It is determined by a weighted vector of three core dimensions: transaction volume, interaction frequency, and counterparty quality.

Integral generating function $$ $f(Tx)$ $$：

$$
P\_{Tx} = \underbrace{w\_1 \cdot \ln(1 + V\_{usd})}*{\text{Volume (Logarithmic)}} + \underbrace{w\_2 \cdot \mathbb{I}*{diverse}}*{\text{Diversity Bonus}} - \underbrace{w\_3 \cdot \text{Risk}}*{\text{Risk Factor}}
$$

**1. Volume: Logarithmic Growth**

We are concerned about the transaction amount$$ $V\_{usd}$ $$ Using natural logarithm $$ $\ln$ $$ Processing, rather than nonlinear processing.

* Reason: To prevent "whale hegemony." The reputation boost from a single $1 million transaction should be far less than that from 1 million $1 transactions. Reputation comes from proven honesty, not simply from displays of wealth.
* Example: A transaction of 100 U earns 10 points, while a transaction of 10,000 U earns 20 points (instead of 1,000 points).

**2. Frequency & Diversity** 

To defend against "Sybil Washing" (i.e., creating two separate accounts to trade and inflate scores), a counterparty diversity coefficient was introduced($$ $\mathbb{I}\_{diverse}$ $$).

* The algorithm constructs a local social graph $$ $G(V, E)$ $$。
* If a user always transacts with the same address,$$ $\mathbb{I}\_{diverse}$ $$ It will decay exponentially to 0.
* You can only earn the full credits by trading with new, high-reputation counterparties.

**3. The "Glass Cannon" Penalty Logic** 

In the Omni-ID model, building reputation is like hiking up a mountain, while destroying reputation is like falling from a great height.

Once a user is determined to be "fraudulent" in DAN arbitration (i.e., loses the arbitration and is marked as malicious), their reputation score will trigger a nullifier:

$$
S\_{new} = S\_{old} \times (1 - \text{SeverityFactor})
$$

* SeverityFactor: For serious fraud (such as providing false logistics), this factor is 1.0 (directly reduced to zero); for minor breaches of contract (such as delays), this factor may be 0.2 (subtracted by 20%).
* This asymmetrical design ensures that the cost of wrongdoing is extremely high, making rational users cherish their Omni-Score as much as they would their feathers.