# Reward Mechanism

### 1. **Overview**

Your points reflect your overall contribution to the aPriori ecosystem. They begin with your **staked MON (aprMON)**, which sets the base speed of how quickly your points grow each day. From there, you can boost this growth by locking your stake, holding $APR consistently, or trading through Swapr. Each of these actions adds additional multipliers to your base points, allowing your daily growth rate to climb.

Every 2 months, the points you’ve accumulated are converted into $**APR rewards**. The distribution is fully proportional: your share depends on how many points you earned compared with the rest of the community during that period. The more you participate, the stronger your growth, and the larger your share of the APR reward pool.

### **2. How Points Turn Into APR Rewards**

At the end of each cycle, we add up all user points and distribute APR based on everyone’s share (pro-rata based):

* Your APR reward = **your points / total points from all users**
* Rewards are paid directly in **APR tokens**
* Points refresh every cycle, so each period is a clean slate
* Your growth rate carries forward unless you change your stake, lock, APR balance, or Swapr activity

### **3. Core Design Principles**

Point growth is determined by four primary inputs: total staked balance, lock duration, the amount of locked $APR, and Swapr trading activity. Together, these inputs define a consistent and compounding trajectory for your points over time.

Key takeaways:

* A transparent, predictable point-growth model
* Large holders earn more, but with diminishing returns to avoid over-concentration
* Only locked stakes receive Duration bonuses
* Holding and staking $APR boosts growth
* Trading through **Swapr** provides an additional multiplier
* Points accumulate **daily**, and rewards are distributed **every 45 days**
* Changing any factor only affects *future* point growth, never past points

## **4. Step-by-Step Formulas**

### **4.1 Total Points Formula**

#### **Concept**

Your daily point increase is determined by your staked amount multiplied by several multipliers:

* Base Points
* Duration Multiplier (only for locked stakes)
* Staked APR Multiplier
* Trading Volume Multiplier

All multipliers are **≥ 1**.

There are **no penalties** and no negative adjustments.

#### **Formula**

Total daily increase:

<p align="center"><span class="math">\Delta TLP_i(t)=\Delta TLP_i^{(liquid)}(t)+\Delta TLP_i^{(lock)}(t)</span></p>

where

<p align="center"><span class="math">\Delta TLP_i^{(liquid)}(t)=B_i^{(liquid)}(t)\cdot S_i(t)\cdot X_i(t)</span></p>

<p align="center"><span class="math">\Delta TLP_i^{(lock)}(t)=\sum_{q}\Bigl[  B_{i,q}^{(lock)}(t)  \cdot D_{i,q}^{(lock)}  \cdot S_i(t)  \cdot X_i(t)\Bigr]</span></p>

Daily changes:

<p align="center"><span class="math">TLP_i(t+1)=TLP_i(t)+\Delta TLP_i(t)</span></p>

#### Variable Annotations

* $$TLP\_i(t)$$: Total Lifetime Points for user $$i$$ at day $$t$$. This is the cumulative point balance.
* $$\Delta TLP\_i(t)$$: Total point increase for user $$i$$ on day $$t$$ (liquid + locked).
* $$\Delta TLP\_i^{(liquid)}(t)$$: Daily points from liquid staking positions for user $$i$$.
* $$\Delta TLP\_i^{(lock)}(t)$$: Daily points from locked staking positions for user $$i$$.
* $$B\_i^{(liquid)}(t)$$: Base points for user $$i$$ from liquid staking on day $$t$$.
* $$B\_{i,q}^{(lock)}(t)$$: Base points from locked position $$q$$ of user $$i$$ on day $$t$$.
* $$D\_{i,q}^{(lock)}$$: Duration multiplier applied to locked position $$q$$ of user $$i$$. Depends on the chosen lock period (15/45/90/180 days).
* $$S\_i(t)$$: $APR multiplier for user $$i$$ on day $$t$$ (defined in Section 4.4).
* $$X\_i(t)$$: Trading volume multiplier for user $$i$$ on day $$t$$ (defined in Section 4.5).

### **4.2 Base Points**

#### **Concept**

Bigger stakes earn more, but growth slows down at higher sizes.

The exponent **0.9** naturally reduces whale dominance while keeping growth smooth.

#### **Formulas**

Liquid staking:

<p align="center"><span class="math">B_i^{(liquid)}(t)=k\cdot\bigl(A_i^{(liquid)}(t)\bigr)^{0.9}</span></p>

Locked staking (each lock position q):

$$
B\_{i,q}^{(lock)}(t)=k\cdot\bigl(A\_{i,q}^{(lock)}(t)\bigr)^{0.9}
$$

#### Variable Annotations

* $$A\_i^{(liquid)}(t)$$: Liquid staked aprMON amount of user $$i$$ at day $$t$$. Includes all stakes that are not locked.
* $$A\_{i,q}^{(lock)}(t)$$: Locked aprMON amount of user $$i$$ in lock position $$q$$ at day $$t$$. Each lock position $$q$$ has its own duration and size.
* $$B\_i^{(liquid)}(t)$$: Base points for user $$i$$ from liquid staking on day $$t$$. This is the pre-multiplier “speed” from liquid staking.
* $$B\_{i,q}^{(lock)}(t)$$: Base points from locked position $$q$$ of user $$i$$ on day $$t$$.
* $$k$$: Global base coefficient controlling system-wide point speed. In this design: k = 0.003

### 4.3 Duration Multiplier

#### **Formulas**

Liquid staking has **no duration multiplier**:

<p align="center"><span class="math">\Delta TLP_i^{(liquid)}(t)=B_i^{(liquid)}(t)\cdot S_i(t)\cdot X_i(t)</span></p>

Locked staking receives duration multipliers

<p align="center"><span class="math">\Delta TLP_i^{(lock)}(t)=\sum_{q}\Bigl[  B_{i,q}^{(lock)}(t)  \cdot D_{i,q}^{(lock)}  \cdot S_i(t)  \cdot X_i(t)\Bigr]</span></p>

<p align="center"><span class="math">D_{i,q}^{(lock)}=\begin{cases}1.0,&#x26; \text{no lock} \\1.2,&#x26; 15\ \text{days} \\1.5,&#x26; 45\ \text{days} \\2.0,&#x26; 90\ \text{days} \\2.5,&#x26; 180\ \text{days}\end{cases}</span></p>

| Lock Period            | Multiplier |
| ---------------------- | ---------- |
| No lock                | 1.0        |
| 15 days                | 1.2        |
| 45 days (coming soon)  | 1.5        |
| 90 days (coming soon)  | 2.0        |
| 180 days (coming soon) | 2.5        |

#### Variable Annotations

* $$\Delta TLP\_i(t)$$: Total point increase for user $$i$$ on day $$t$$ (liquid + locked).
* $$\Delta TLP\_i^{(liquid)}(t)$$: Daily points from liquid staking positions for user $$i$$ .
* $$\Delta TLP\_i^{(lock)}(t)$$: Daily points from locked staking positions for user $$i$$.
* $$D\_{i,q}^{(lock)}$$: Duration multiplier applied to locked position $$q$$ of user $$i$$ . Depends on the chosen lock period (15/45/90/180 days).
* $$S\_i(t)$$: $APR multiplier for user $$i$$ on day $$t$$ (defined in Section 4.4).
* $$X\_i(t)$$: Trading volume multiplier for user $$i$$ on day $$t$$ (defined in Section 4.5).

### 4.4 Staked APR Multiplier

#### **Concept**

We use a simple rule: the more $APR you **consistently** hold, the higher your daily multiplier.

This removes “snapshot gaming” because the system uses a **7-day rolling average**.

#### **Formula**

Time-weighted 7-day APR balance

<p align="center"><span class="math">W_i(t) = \frac{\sum_{t=0}^{6} APR_i(d)}{7}</span></p>

APR multiplier based on the average

<p align="center"><span class="math">S_i =\begin{cases}1.05, &#x26;0 &#x3C; W_i &#x3C; 300 \\1.1, &#x26; 300 \le W_i &#x3C; 3{,}000 \\1.2, &#x26; 3{,}000 \le W_i &#x3C; 15{,}000 \\1.3, &#x26; 15{,}000 \le W_i &#x3C; 30{,}000 \\1.4, &#x26; W_i \ge 30{,}000\end{cases}</span></p>

#### Variable Annotations

* $$APR\_i(d)$$: Snapshot of user $$i$$'s APR token balance on day *d*. Taken once per day and stored.
* $$W\_i(t)$$: 7-day rolling average APR balance for user $$i$$ evaluated on day $$t$$. It is the average of the last 7 daily snapshots.
* $$S\_i$$: APR multiplier for user $$i$$ on day $$t$$. Determined by which range $$W\_i$$ falls into.

Notes:

* Only holding APR consistently boosts the average
* Selling APR reduces future multiplier but **never reduces existing points**

### **4.5 Trading Volume Multiplier**

#### **Concept**

This multiplier rewards real on-chain trading on Swapr over a **30-day rolling window**.

* Only trades executed through **Swapr** count.
* Major stable pairs are excluded from the calculation.
* Major pairs excluded:
  * MON
  * WMON
  * WBTC
  * WSOL
  * USDC
  * WETH

#### **Formula**

30-day volume (USDT value):

<p align="center"><span class="math">Q_i(t) = \sum_{t=0}^{29} \text{SwaprVol}_i</span></p>

Multiplier:

<p align="center"><span class="math">X_i =\begin{cases}1.00, &#x26; Q_i &#x3C; 2{,}000 \\1.05, &#x26; 2{,}000 \le Q_i &#x3C; 10{,}000 \\1.10, &#x26; 10{,}000 \le Q_i &#x3C; 50{,}000 \\1.20, &#x26; 50{,}000 \le Q_i &#x3C; 200{,}000 \\1.35, &#x26; 200{,}000 \le Q_i &#x3C; 500{,}000 \\1.50, &#x26; Q_i \ge 500{,}000\end{cases}</span></p>

#### Variable Annotations

* $${SwaprVol}\_i$$: USDT-denominated trading volume for user $$i$$ on Swapr during day d excluding major pairs.
* $$Q\_i(t)$$: 30-day rolling cumulative Swapr trading volume for user $$i$$ used on day $$t$$.
* $$X\_i$$: Trading Volume Multiplier for user $$i$$ on day $$t$$, based on $$Q\_i$$.

### **4.6 Reward Distribution**

#### **Concept**

Points accumulate **daily**, and rewards are distributed every 2 months. **The points are cleared and recalculated in each epoch.**

Your share of the reward pool is proportional to your overall TLP.

#### Formula

<p align="center"><span class="math">Reward_i = \frac{TLP_i}{\sum_j TLP_j} \times E_{period} </span></p>

#### Variable Annotations

* $$Reward\_i$$: Token reward allocated to user i for that emission period.
* $$TLP\_i$$: Total Lifetime Points of user i at the end of the period.
* $${\sum\_j TLP\_j}$$: Sum of the Total Lifetime Points of all users at the end of the period.
* $$E\_{period}$$: Total emission (token amount) allocated to this 2-month period.


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