# dDAFI Claiming

## Fragmented timeframes

As the weight accumulates, when a user decides to claim their rewards, we can extract it from the weight.

Where DPS = Distribute per second, US = User Stake, TS = Total Network Stake, UR = User Reward, and n = Time in seconds

$$
UR1 = (DPS1 \* US1 / TS1) + (DPS2 \* US1 / TS2) + (DPSn \* US1 / TSn)
$$

We can calculate the user reward within a timeframe, as a to b where b > a

Where n = 1 to a, 

$$
UR1 = US \* ∑DPSn / TSn
$$

$$
UR = US1 \* (DPS1 / TS1 + DPS2 / TS2 + DPSx / TSx)
$$

Where n = 1 to b, 

$$
UR2 = US \* ∑DPSn / TSn
$$

When a user initiates an action in the network, where a = n > 1, we calculate n from 1 to a. When the same user initiates an action again, we calculate from 1 to b, and subtract the previous 1 to a. This can be represented as :

$$
UR = US \* ∑ DPSn / TSn, (n = 1 : ∞)
$$

A user's reward between timeframe a and b can be calculated accurately as:

$$
URab = UR2 - UR1 = (US \* ∑DPSn / TSn)
$$

where n = 1 to b, and

$$

* (US \* ∑DPSn / TSn)
  $$

where n = 1 to a

$$
\= US \* ((∑DPSn / TSn, (n=1:b)) - (∑DPSn / TSn,  (n = 1:a)))
$$


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