Alpha Vault Formulas

Alpha Vault accounting is proportional: the vault buys as one account, then users receive token claims and quote refunds based on their escrow deposit share. All on-chain arithmetic uses integer token amounts. Division rounds down.

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Key Terms

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Max Swappable Amount

The max swappable amount is mode-dependent. $$\text{Pro Rata Max Swappable} = \min(\text{total\_deposit}, \text{max\_buying\_cap})$$ $$\text{FCFS Max Swappable} = \text{total\_deposit}$$ Each fill instruction also takes a max_amount, so the actual amount for that fill is: $$\text{Fill Swappable Amount} = \min(\text{Max Swappable Amount} - \text{swapped\_amount}, \text{max\_amount})$$

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User Deposit Share

Most user-facing amounts use the escrow’s share of total vault deposits. $$\text{User Share} = \frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}$$ Because this is integer math on-chain, the program multiplies before dividing and rounds down.

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Linear Vesting

The program treats both endpoints as inclusive by adding 1 to the numerator and denominator. $$\text{Vesting Duration} = \text{end\_vesting\_point} - \text{start\_vesting\_point} + 1$$ $$\text{Elapsed Duration} = \min(\text{current\_point}, \text{end\_vesting\_point}) - \text{start\_vesting\_point} + 1$$ $$\text{Total Claimable Token} = \text{bought\_token} \times \frac{\text{Elapsed Duration}}{\text{Vesting Duration}}$$ Claims are not allowed before start_vesting_point.

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User Claimable Token

$$\text{Escrow Dripped Token} = \text{Total Claimable Token} \times \frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}$$ $$\text{User Claimable Token} = \text{Escrow Dripped Token} - \text{escrow.claimed\_token}$$ After a claim, the program increments both the escrow’s claimed_token and the vault’s total_claimed_token.

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Pro Rata Overflow Refund

Overflow is the part of total deposits that cannot be included in max swappable amount. $$\text{Deposit Overflow} = \text{total\_deposit} - \text{Max Swappable Amount}$$ $$\text{Escrow Overflow Refund} = \text{Deposit Overflow} \times \frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}$$ An escrow can withdraw this overflow after last_join_point and through last_buying_point. The program tracks withdrawn_deposit_overflow so repeated withdrawals only receive the remaining overflow amount.

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Final Remaining Quote Refund

After the pool’s last_buying_point, an escrow can withdraw its share of quote left in the vault. $$\text{Remaining Quote} = \text{total\_deposit} - \text{swapped\_amount}$$ $$\text{Escrow Total Refund Quote} = \text{Remaining Quote} \times \frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}$$ $$\text{Final Refund Transfer} = \text{Escrow Total Refund Quote} - \text{escrow.withdrawn\_deposit\_overflow}$$ The escrow is then marked as refunded so the final remaining quote path cannot be used twice.

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FCFS Accepted Deposit

In FCFS mode, the program limits the accepted deposit amount before transfer. $$\text{Remaining Vault Capacity} = \text{max\_depositing\_cap} - \text{total\_deposit}$$ $$\text{Remaining User Quota} = \text{User Cap} - \text{escrow.total\_deposit}$$ $$\text{Accepted Deposit} = \min( \text{requested net amount}, \text{Remaining Vault Capacity}, \text{Remaining User Quota} )$$ If the accepted amount is 0, the deposit fails.

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Token 2022 Transfer Fees

When the quote mint has a Token 2022 transfer fee, the vault records the fee-excluded amount as the deposit. It transfers the fee-included amount from the user so that the vault receives the intended net amount. $$\text{Recorded Deposit} = \text{Transfer Amount} - \text{Transfer Fee}$$ For outbound claims and refunds, emitted event amounts are fee-excluded when a transfer fee applies.