# Uniswap V3 Pricing Documentation

This document explains the Uniswap V3 pricing model and how it's implemented in the MEV bot.

## Core Concepts

### Ticks
In Uniswap V3, prices are represented as ticks. A tick is defined as:

```
tick = log√1.0001(√P)
```

Where P is the price of token1 in terms of token0.

Ticks are integers that range from -887272 to 887272.

### sqrtPriceX96
Prices are stored internally as sqrtPriceX96, which is:

```
sqrtPriceX96 = √P * 2^96
```

This allows for precise fixed-point arithmetic without floating-point operations.

### Liquidity
Liquidity in a pool is represented as a uint128 value that determines the depth of the pool at a given price.

## Mathematical Relationships

### Converting between representations

1. Tick to sqrtPriceX96:
   ```
   sqrtPriceX96 = 1.0001^(tick/2) * 2^96
   ```

2. sqrtPriceX96 to Tick:
   ```
   tick = log_1.0001(sqrtPriceX96 / 2^96)^2
   ```

3. Price to Tick:
   ```
   tick = log_1.0001(price)
   ```

## Implementation Details

Our Go implementation uses the math/big package for precision and handles the fixed-point arithmetic required for Uniswap V3 calculations.

Key functions:
- `SqrtPriceX96ToPrice`: Converts sqrtPriceX96 to a floating-point price
- `PriceToSqrtPriceX96`: Converts a floating-point price to sqrtPriceX96
- `TickToSqrtPriceX96` : Converts a tick to sqrtPriceX96
- `SqrtPriceX96ToTick` : Converts sqrtPriceX96 to a tick