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: