> ## Documentation Index
> Fetch the complete documentation index at: https://docs.meteora.ag/llms.txt
> Use this file to discover all available pages before exploring further.

# Alpha Vault Formulas

> Review Alpha Vault allocation, swappable amount, refund, vesting, cap, and Token 2022 transfer-fee 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.

## Key Terms

| Term                         | Meaning                                                 |
| ---------------------------- | ------------------------------------------------------- |
| `total_deposit`              | Total net quote amount recorded across all escrows.     |
| `escrow.total_deposit`       | Net quote amount recorded for one escrow.               |
| `max_buying_cap`             | Pro Rata quote amount cap for vault fills.              |
| `max_depositing_cap`         | FCFS total accepted deposit cap.                        |
| `swapped_amount`             | Total quote amount already used by vault fills.         |
| `bought_token`               | Total launch token bought by the vault.                 |
| `claimed_token`              | Launch token already claimed by an escrow.              |
| `withdrawn_deposit_overflow` | Pro Rata overflow quote already withdrawn by an escrow. |

## Max Swappable Amount

The max swappable amount is mode-dependent.

```math theme={"system"}
\text{Pro Rata Max Swappable} =
\min(\text{total\_deposit}, \text{max\_buying\_cap})
```

```math theme={"system"}
\text{FCFS Max Swappable} =
\text{total\_deposit}
```

Each fill instruction also takes a `max_amount`, so the actual amount for that fill is:

```math theme={"system"}
\text{Fill Swappable Amount} =
\min(\text{Max Swappable Amount} - \text{swapped\_amount}, \text{max\_amount})
```

## User Deposit Share

Most user-facing amounts use the escrow's share of total vault deposits.

```math theme={"system"}
\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.

## Linear Vesting

The program treats both endpoints as inclusive by adding `1` to the numerator and denominator.

```math theme={"system"}
\text{Vesting Duration} =
\text{end\_vesting\_point} - \text{start\_vesting\_point} + 1
```

```math theme={"system"}
\text{Elapsed Duration} =
\min(\text{current\_point}, \text{end\_vesting\_point})
- \text{start\_vesting\_point} + 1
```

```math theme={"system"}
\text{Total Claimable Token} =
\text{bought\_token}
\times
\frac{\text{Elapsed Duration}}{\text{Vesting Duration}}
```

Claims are not allowed before `start_vesting_point`.

## User Claimable Token

```math theme={"system"}
\text{Escrow Dripped Token} =
\text{Total Claimable Token}
\times
\frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}
```

```math theme={"system"}
\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`.

## Pro Rata Overflow Refund

Overflow is the part of total deposits that cannot be included in max swappable amount.

```math theme={"system"}
\text{Deposit Overflow} =
\text{total\_deposit} - \text{Max Swappable Amount}
```

```math theme={"system"}
\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.

## Final Remaining Quote Refund

After the pool's `last_buying_point`, an escrow can withdraw its share of quote left in the vault.

```math theme={"system"}
\text{Remaining Quote} =
\text{total\_deposit} - \text{swapped\_amount}
```

```math theme={"system"}
\text{Escrow Total Refund Quote} =
\text{Remaining Quote}
\times
\frac{\text{escrow.total\_deposit}}{\text{total\_deposit}}
```

```math theme={"system"}
\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.

## FCFS Accepted Deposit

In FCFS mode, the program limits the accepted deposit amount before transfer.

```math theme={"system"}
\text{Remaining Vault Capacity} =
\text{max\_depositing\_cap} - \text{total\_deposit}
```

```math theme={"system"}
\text{Remaining User Quota} =
\text{User Cap} - \text{escrow.total\_deposit}
```

```math theme={"system"}
\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.

## 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.

```math theme={"system"}
\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.

<Warning>
  Formula examples describe the accounting path. Actual token balances can also be affected by Token 2022 transfer fees and transfer-memo requirements on destination accounts.
</Warning>