# Score & Boost

This section covers:

* how xULAB becomes a **Score**, and
* how that Score determines your boosted effective amount `new_a` for rewards.

***

#### Score

Score represents your share of the total xULAB pool.

Definitions:

* $$\text{xULAB}\_i$$ : xULAB balance of user $$i$$
* $$∑\_j \text{xULAB}\_j$$ : total xULAB across all users

Score formula:

$$
\text{Score}\_i = \frac{\text{xULAB}\_i}{\sum\_j \text{xULAB}\_j}
$$

* Range: 0–1 (0%–100%)
* Interpretation: your percentage ownership of the Locker (xULAB system).

**Example**

* Your xULAB:  $$\text{xULAB}\_i = 50$$
* Total xULAB: $$∑j​xULABj​=5,000$$

$$
\text{Score}\_i = \frac{50}{5{,}000} = 0.01 = 1%
$$

Quick reference:

| Concept     | Description                          |
| ----------- | ------------------------------------ |
| xULABᵢ      | Your ve-style balance from locked LP |
| ΣxULAB      | Sum of xULAB from all users          |
| Scoreᵢ      | xULABᵢ ÷ ΣxULAB                      |
| High Scoreᵢ | Larger effect on boosts & flows      |

***

#### Boost Multiplier (new\_a)

The **Boost Multiplier** uses your Score to convert your raw position `a` into a boosted effective amount `new_a`.

This `new_a` is used to split ULAB emissions in that market.

Per market:

* $$a$$ : your liquidity in that market (USD)
  * e.g. your Supply amount
* $$A$$ : total liquidity of that market (USD)
  * sum of all users’ liquidity
* $$\text{Score}$$ : your Score from above

Boost formula:

$$
\text{new\_a} = \min\Big( 3 \times a,;; a + (1.5 \times A \times \text{Score}) \Big)
$$

* `a` = your original position
* `1.5 × A × Score` = bonus amount from your share of the system and total market size
* `3 × a` = hard cap (max 3× boost)

**Example**

Let:

*  $$a = 1{,}000$$
* $$A = 100{,}000$$
*  $$\text{Score} = 0.01$$ (1%)

1. Cap term:

$$
3 \times a = 3 \times 1{,}000 = 3{,}000
$$

2. Score term:

$$
a + (1.5 \times A \times \text{Score}) = 1{,}000 + (1.5 \times 100{,}000 \times 0.01) = 1{,}000 + 1{,}500 = 2{,}500
$$

3. Take minimum:

$$
\text{new\_a} = \min(3{,}000,; 2{,}500) = 2{,}500
$$

→ effective **2.5×** boost on your original `a`.

***

#### From new\_a to Rewards (Concept)

For each market:

* Total ULAB emissions for the epoch:

$$
\text{Emissions}\_{\text{market}}
$$

* Sum all users’ `new_a`:

$$
\sum\_j \text{new\_a}\_j
$$

* User $$i$$’s reward:

$$
\text{Reward}*i = \text{Emissions}*{\text{market}} \times \frac{\text{new\_a}\_i}{\sum\_j \text{new\_a}\_j}
$$

Chain of logic:

> Lock ULAB LP → xULAB → Score → new\_a → share of ULAB emissions

If you are not Emission Eligible (LockedLPValue < 3% × SupplyValue for that market), your effective reward is **0**, regardless of Score or `new_a`.


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