# LP Shares (/docs/protocols/v4-hooks/dualpool/concepts/lp-shares)

Understand DualPool's internal share accounting, virtual-shares inflation defense, and deposit locks.

Liquidity providers in a DualPool do not receive ERC-20 share tokens and do not hold v4 positions. Shares are internal, non-transferable accounting entries kept per pool by the hook. A share represents a proportional claim on the pool's [total assets](/docs/protocols/v4-hooks/dualpool/concepts/inventory-and-yield) (vault shares, claims, and tracked ERC-20 together), so LPs can earn swap fees and vault yield without taking any further action.

## Bootstrap
Every pool must be seeded by the owner before it can trade:

```solidity
bootstrap(PoolKey key, uint256 amount0, uint256 amount1) returns (uint256 shares)
```

Bootstrap pulls both tokens, mints `sqrt(received0 * received1)` shares to the owner, and flips the pool live. The owner-supplied amounts set the initial share/asset ratio, which matters for pairs with asymmetric decimals. Amounts below a per-pool floor revert with `BootstrapTooSmall`, so the bootstrapper's economic claim is not meaningfully diluted by the virtual position described below.

## Virtual-Shares Inflation Defense
Share conversion uses the EIP-4626 virtual-offset pattern. Conversions add one virtual asset and `10 ** decimalsOffset` virtual shares to the ratio:

```text
amount = shares * (totalAssets + 1) / (totalShares + 10 ** offset)
```

The offset is derived per pool from the pair's token decimals:

```text
offset = clamp((decimals0 + decimals1) / 2 - 6, 6, 12)
```

For an 18/18-decimal pair the offset is 12; for a 6/6-decimal stablecoin pair it is 6. The virtual position makes post-bootstrap donation attacks uneconomic, at the cost of permanently retaining a dust amount of assets (roughly one token unit per side on a 6/6 pool).

> [!NOTE]
> Interfaces must reproduce this exact math, `totalShares + 10 ** offset` denominators with the rounding below, when displaying redeemable amounts. Naive pro-rata math will not match the contract. Prefer the contract's `previewWithdraw` answer when they differ.

## Deposits and Withdrawals
After bootstrap:

* [`addLiquidity`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/DualPoolHook.sol#L409) mints a requested number of shares and pulls token0/token1 proportional to current total assets. Deposits round up, so new LPs cannot dilute existing LPs.
* [`removeLiquidity`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/DualPoolHook.sol#L437) burns shares and returns proportional token0/token1. Withdrawals round down, so exiting LPs cannot over-withdraw.

Both entry points take caller slippage bounds (`maxAmount0`/`maxAmount1` on deposit, `minAmount0`/`minAmount1` on withdrawal) and a deadline, protecting LPs from ratio changes and vault share-price moves between preview and execution.

Use [`previewDeposit(key, shares)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/base/PoolVault.sol#L283) and [`previewWithdraw(key, shares)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/base/PoolVault.sol#L298) for offchain sizing, and [`sharesOf(key, account)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/DualPoolHook.sol#L656) / [`totalShares(poolId)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/base/PoolVault.sol#L247) to read positions.

## Deposit Lock
Each pool has a [`minDepositBlocks`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/base/PoolVault.sol#L161) parameter, fixed at initialization, that controls how many blocks must elapse after an account's last deposit before it may withdraw:

* `0`: no lock; same-block deposit-then-withdraw is allowed
* `1`: same-block withdrawals revert, preventing single-block fee sniping
* Larger values enforce longer holding periods

A withdrawal inside the lock window reverts with `DepositLocked`.

## External Deposits
`addLiquidity` is owner-only by default. The owner can open a pool to third-party LPs with [`setExternalDeposits(key, true)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/DualPoolHook.sol#L561); the current policy is readable via [`externalDepositsEnabled(poolId)`](https://github.com/Uniswap/v4-hooks-public/blob/main/src/alf/DualPoolHook.sol#L568).

## Where to Go Next
* [Walk through the end-to-end deposit and withdrawal flow](/docs/protocols/v4-hooks/dualpool/guides/provide-liquidity)
* [See what backs your shares across vault shares, claims, and ERC-20](/docs/protocols/v4-hooks/dualpool/concepts/inventory-and-yield)