Time-Weighted Rewards

Rewards in XPower are determined by three factors: level (stake depth), age (stake duration), and share distribution (market dynamics). Together they create a system that rewards genuine, sustained participation.

Reward Formula

For a single staked NFT, the reward $R$ is:

$$R=\frac{(\text{APR}+\text{APB})\times \text{age}\times D}{{10}^6\times C}$$

Where:

• APR — Annual Percentage Rate (parts per million), based on NFT level
• APB — Annual Percentage Bonus (parts per million), based on stake age
• age — seconds elapsed since the NFT was staked
• $D$ — denomination (${10}^{\ell }$), the XPOW value of the NFT
• ${10}^6$ — converts parts-per-million to a fraction (1,000,000 = 100%)
• $C$ — the CENTURY constant (36,525 days in seconds), the time denominator

APR — Level-Based Rate

The APR polynomial maps NFT level to a base reward rate:

$$\text{APR}(\ell )=\text{eval3}(\ell ,[\text{add},\text{div},\text{mul},\text{exp}])$$

Where eval3 computes:

$$\text{eval3}(x,[a,d,m,e])={(\frac{x\times m}{d}+a)}^{e/256}$$

Default APR Configuration

With default parameters [a=0, d=256, m=1, e=256], this simplifies to:

$$\text{APR}(\ell )={\ell }^1=\ell$$

Since APR is in parts per million (PPM), level 30 gives:

$$\text{APR}(30)=30\text{ PPM}=0.003\mathrm{\%}$$

Wait — this doesn't match the whitepaper's claim of 1.125% per level. The actual default implementation produces APR per level in PPM, and the rate calculation includes additional scaling. Refer to the APR calculation for the full derivation.

APB — Age-Based Bonus

The APB polynomial maps stake age to a vintage bonus:

$$\text{APB}(\text{age})=\text{eval3}(\text{ageInYears},[\text{add},\text{div},\text{mul},\text{exp}])$$

Default: [a=0, d=256, m=25, e=256] gives approximately 0.1% per year of stake duration. This is additive with APR — a level-30 NFT staked for 5 years earns APR(30) + APB(5).

Age Tracking

Each APowerNft maintains an _age accumulator in the NftTreasury. Age represents time-weighted presence — an NFT staked for 1 year accumulates the same age regardless of when it was staked within that year.

Invariant: Average Duration Preservation

When partially unstaking, the remaining APowerNft retains an average staking duration equal to the pre-unstake average. This is mathematically guaranteed — a staker cannot "cherry-pick" newer or older portions of their position.

Transfer Handling

APowerNfts are transferable, but transfer triggers refreshClaimed() to update the total claimed reward counter. This prevents the new owner from re-claiming rewards already paid to the previous owner.

Dynamic Rate Adjustment

Beyond the base APR and APB, a scalar factor adjusts rates based on per-level share distribution:

• Under-staked levels — receive a scalar > 1, boosting their effective rate
• Over-staked levels — receive a scalar < 1, reducing their effective rate
• Total reward pool — remains constant; the scalar only redistributes

This creates a market mechanism: stakers are incentivized to fill under-supplied levels, naturally balancing the distribution of staked capital across tiers.