# Effective Shares & Reward Accrual
#### Definitions
Let:
* = a specific position
* = time
* = the current epoch
* = total Nova emissions allocated to the pool for epoch 
* = USD-denominated value of the burn or forfeiture at entry
* = base shares assigned to position 
* = multiplier applied to position (if applicable)
* = effective shares of position 
* = time position is active during epoch 
* = total length of epoch 
***
#### Base Share Assignment
At position creation, a base share value is assigned using the USD value at entry:
\
This ensures:
* All inputs are normalized across assets
* Share assignment is deterministic and non-reflexive
* Future price changes do not affect share weight
***
#### Effective Shares
Effective Shares represent the reward weight of a position.
If no additional multipliers apply:
\
If protocol-defined multipliers apply (e.g. loyalty or referral):
\
Where:
\
Multipliers:
* Are applied at position creation or epoch boundaries
* Do not compound
* Do not affect principal or base shares
***
#### Time-Weighted Accrual
Rewards accrue continuously and linearly based on time-weighted effective shares.
The time-weighted share contribution of position during epoch is:
\
Where:
* 
* Late entry or partial participation reduces proportionally
***
#### Total Epoch Weight
The total effective weight for epoch is:
\
***
#### Reward Allocation
At epoch settlement, rewards are finalized and distributed pro-rata.
The Nova reward allocated to position for epoch is:
\
Substituting:
\
This guarantees:
* No advantage from timing entry near epoch end
* Fair distribution based on value and time
* Deterministic, audit-friendly settlement
***
#### Claimability
* Rewards are not claimable mid-epoch
* At epoch completion:
* becomes finalized
* Claimable balance increases
* Unclaimed rewards remain claimable indefinitely
***
#### Irreversibility Constraints
For all payout pool positions:
* , , and are immutable after creation
* Positions cannot be exited early
* Burned or forfeited assets are never returned
* Only rewards may be claimed
***
#### Summary
Effective Shares convert irreversible economic actions into deterministic reward weight.\
Time-weighted accrual ensures fairness, prevents manipulation, and aligns rewards with sustained participation.
The payout pool system:
* Uses USD-normalized base shares
* Applies deterministic multipliers
* Accrues rewards linearly over time
* Settles discretely at epoch boundaries
This preserves simplicity, auditability, and long-term incentive alignment.
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