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

# Constants and limits

> Current numeric domains, loop bounds, fee settings, and proof limits.

## Price and tick domain

| Constant              | Value                                                          |
| --------------------- | -------------------------------------------------------------- |
| `MIN_TICK`            | `-400000`                                                      |
| `MAX_TICK`            | `400000`                                                       |
| `MIN_TICK_SENTINEL`   | `-400001`                                                      |
| `MAX_TICK_SENTINEL`   | `400001`                                                       |
| `MIN_SQRT_RATIO_X128` | `{ hi: 0, lo: 702075911466779181339691826087 }`                |
| `MAX_SQRT_RATIO_X128` | `{ hi: 484680305, lo: 8756686347225649145659787327114459760 }` |
| Q128.128 unit         | `2^128`                                                        |
| `LIQ_AMOUNT_SAFE_CAP` | `702075911466779181339691826086`                               |

Pool creation accepts `initial_tick >= MIN_TICK` and `initial_tick < MAX_TICK`. A position upper tick can equal `MAX_TICK`.

## Swap execution

| Path       | Hop count | Initialized-tick iterations |
| ---------- | --------: | --------------------------: |
| Single-hop |         1 |                           5 |
| Multi-hop  |    2 or 3 |                   3 per hop |

After the fixed tick-walk loop, `view_bounded_partial` can fill only as far as the nearer next initialized tick or price limit. It returns unconsumed input in `amount_remaining`.

## Fees

The pool fee is a `u16` count of parts per million. Bootstrap registers 100, 500, 3000, and 10000 and binds them to tick spacings 1, 10, 60, and 200.

`fee_protocol` is zero or an integer from 4 through 10. The protocol share is `fee_protocol / 16` of the swap fee. New pools use `DEFAULT_FEE_PROTOCOL = 5`.

## Proof limits

`MerkleProof.siblings` has 16 fields. `MAX_MERKLE_TREE_DEPTH` is 15. Mint validates signer, owner recipient, and withdrawal non-inclusion. Collect validates NFT owner and withdrawal. Claim validates the signer.

## Integer types

Token amounts, liquidity, owed balances, and protocol fees use `u128`. Square-root prices and fee growth use `u256::U256`. Signed liquidity net uses `i128`. Swap deadlines use Aleo block heights in `u32`. Swap nonces use `u64`. Mint nonces use `field`.

The AMM uses native token base units directly. It has no on-chain decimal scale or normalization registry.