# Senior Reward Calculation Rules

When the n-th tip occurs:

* **Payment amount:** X<sub>N</sub>
* **Time:** t<sub>N</sub>

The system processes it as follows:

#### Fund Split

* **Creator income:** Creator<sub>N</sub> = 0.2 × X<sub>N</sub>
* **Total senior reward pool:** Pool<sub>N</sub> = 0.8 × X<sub>N</sub>

Split into four layers:

Pool<sub>N,1</sub> = 0.4 × X<sub>N</sub>

Pool<sub>N,2</sub> = 0.3 × X<sub>N</sub>

Pool<sub>N,3</sub> = 0.2 × X<sub>N</sub>

Pool<sub>N,4</sub> = 0.1 × X<sub>N</sub>

#### Determining the Four Senior Sets by Time

Based on time differences, we determine four sets of seniors from historical tips:

* **L**<sub>**1**</sub>**&#x20;(≤ 1 day)**\
  S<sub>N,1</sub> = { i | i < N, 0 < t<sub>N</sub> − t<sub>i</sub> ≤ 1 day }
* **L**<sub>**2**</sub>**&#x20;(1–7 days)**\
  S<sub>N,2</sub> = { i | i < N, 1 < t<sub>N</sub> − t<sub>i</sub> ≤ 7 days }
* **L**<sub>**3**</sub>**&#x20;(8–30 days)**\
  S<sub>N,3</sub> = { i | i < N, 7 < t<sub>N</sub> − t<sub>i</sub> ≤ 30 days }
* **L**<sub>**4**</sub>**&#x20;(31–365 days)**\
  S<sub>N,4</sub> = { i | i < N, 30 < t<sub>N</sub> − t<sub>i</sub> ≤ 365 days }

#### Proportional Distribution Within Each Layer

For each layer k ∈ {1,2,3,4}:

* Total historical payment in that layer:\
  H<sub>N,k</sub> = Σ (Xⱼ), for all j ∈ S<sub>N,k</sub>
* If the layer is not empty, senior i receives:\
  Reward<sub>i,N,k</sub> = Pool<sub>N,k</sub> × (X<sub>i</sub> / H<sub>N,k</sub>)
* Total reward for senior i from this **n-th** tip is:\
  Reward<sub>i,N</sub> = Σ Reward<sub>i,N,k</sub>

#### Missing Layer Handling Rules

To keep the system simple, closed-loop, and waste-free:

* If **one layer** is empty:
  * Its share is merged into the nearest layer that has seniors.
  * Example case: if the empty layer is L2, its share goes to L1.
* If **three layers** are empty:
  * All rewards go to the remaining layer.
* If **all four layers** are empty (i.e., no one has tipped in the past 365 days):
  * The entire 80% goes to the **creator**.
  * This effectively starts a **new cycle**: this tip becomes the **first tip of a new reward era** for this content.

This ensures:

* No rewards are left hanging;
* No systemic “reward debt” accumulates;
* The mechanism is self-consistent at all times.


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