> ## 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

Alpha Vault implements a sophisticated vesting and token distribution mechanism with support for both pro-rata and first-come-first-served (FCFS) allocation modes.

# Linear Vesting Formula

The core vesting mechanism follows a linear time-based release schedule:

```math theme={"system"}
\text{claimable\_tokens} = \frac{\text{elapsed\_time} \times \text{total\_bought\_tokens}}{\text{total\_vesting\_duration}}
```

**Where:**

* `elapsed_time` = time since vesting start
* `total_bought_tokens` = total tokens purchased by all users
* `total_vesting_duration` = total duration of vesting period

***

# Individual Token Claim Formula

```math theme={"system"}
\text{user\_claimable} = \frac{\text{total\_claimable} \times \text{user\_deposit}}{\text{total\_vault\_deposit}} - \text{already\_claimed}
```

**Where:**

* `total_claimable` = total tokens available for claiming at current time
* `user_deposit` = individual user's deposit amount
* `total_vault_deposit` = sum of all user deposits in the vault
* `already_claimed` = tokens already claimed by the user

***

# Refund Calculation Formulas

## Base Refund Calculation

```math theme={"system"}
\text{refund} = \frac{\text{unswapped\_amount} \times \text{user\_deposit}}{\text{total\_deposit}}
```

## Deposit Overflow Refund (Pro-rata Vaults)

```math theme={"system"}
\text{overflow\_refund} = \frac{\text{excess\_deposit} \times \text{user\_deposit}}{\text{total\_deposit}}
```

**Where:**

* `excess_deposit` = total deposits exceeding the maximum buying cap
* `unswapped_amount` = tokens that weren't successfully swapped

***

# Swappable Amount Calculation

## Pro-rata Mode

```math theme={"system"}
\text{max\_swappable} = \min(\text{total\_deposit}, \text{max\_buying\_cap})
```

## FCFS Mode

```math theme={"system"}
\text{max\_swappable} = \text{total\_deposit}
```

**Where:**

* `max_buying_cap` = maximum tokens that can be purchased (for pro-rata mode only)
* `total_deposit` = sum of all user deposits

***

# Vault Mode Specifications

## Pro-rata Mode

* No maximum buying cap restriction
* Distributes tokens proportionally among all participants
* Provides refunds for excess deposits
* Suitable for unlimited token sales

## FCFS Mode

* Enforces maximum buying cap
* Tokens distributed on first-come-first-served basis
* No overflow refunds (all deposits are valid)
* Suitable for fair distribution with limited token supply