# 2️⃣ Staking & Yield Engine

#### Staking Model

*Each pool defines lock period (T), base rate (r), and duration bonus (B). Rewards (continuous compounding):*

$$
\mathrm{Reward} = A \left( e^{(r + B),\frac{t}{365}} - 1 \right)
$$

where (A) is stake amount and (t) is days.

Example: (A=10{,}000), (r=0.18), (B=0.03), (t=180) ⇒ approximately 1,020 ROCA.

#### Yield Sources

* Platform / transaction fees
* External liquidity revenues
* Treasury low-risk strategies
* AI-guided rotations favoring higher risk-adjusted returns

Sharpe-like score used for scoring again:

$$
SR\_i = \frac{\mathbb{E}\[R\_i] - R\_f}{\sigma\_i}
$$

#### Epoch Distribution

Total income (I) allocated to pools by weights (W\_j):

$$
Y\_j = \frac{W\_j}{\sum\_i W\_i}, I
$$

Then streamed proportionally to user stakes inside each pool.