diff --git a/pkg/parsers/UNISWAP_V3_MATH.md b/pkg/parsers/UNISWAP_V3_MATH.md
new file mode 100644
index 0000000..ac2c22d
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+++ b/pkg/parsers/UNISWAP_V3_MATH.md
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+# Uniswap V3 Math Utilities
+
+Comprehensive mathematical utilities for Uniswap V3 concentrated liquidity pools. Based on the official Uniswap V3 SDK and whitepaper.
+
+## Overview
+
+Uniswap V3 uses concentrated liquidity with tick-based price ranges. All prices are represented as `sqrtPriceX96` (Q64.96 fixed-point format), and positions are defined by tick ranges.
+
+### Key Concepts
+
+**1. Ticks**
+- Discrete price levels: `price = 1.0001^tick`
+- Valid range: `-887272` to `887272`
+- Each tick represents a 0.01% price change
+
+**2. SqrtPriceX96**
+- Fixed-point representation: `sqrtPriceX96 = sqrt(price) * 2^96`
+- Q64.96 format (64 integer bits, 96 fractional bits)
+- Used internally for all price calculations
+
+**3. Liquidity**
+- Virtual liquidity representing swap capacity
+- Changes at tick boundaries
+- Determines slippage for swaps
+
+## Core Functions
+
+### Tick ↔ Price Conversion
+
+```go
+// Convert tick to sqrtPriceX96
+sqrtPrice, err := GetSqrtRatioAtTick(tick)
+
+// Convert sqrtPriceX96 to tick
+tick, err := GetTickAtSqrtRatio(sqrtPriceX96)
+```
+
+**Example:**
+```go
+// Get price at tick 0 (price = 1)
+tick := int32(0)
+sqrtPrice, _ := GetSqrtRatioAtTick(tick)
+// sqrtPrice ≈ 2^96 = 79228162514264337593543950336
+
+// Convert back
+calculatedTick, _ := GetTickAtSqrtRatio(sqrtPrice)
+// calculatedTick = 0
+```
+
+### Amount Deltas (Liquidity Changes)
+
+```go
+// Calculate token0 amount for a liquidity change
+amount0 := GetAmount0Delta(
+    sqrtRatioA,  // Lower sqrt price
+    sqrtRatioB,  // Upper sqrt price
+    liquidity,   // Liquidity amount
+    roundUp,     // Round up for safety
+)
+
+// Calculate token1 amount for a liquidity change
+amount1 := GetAmount1Delta(
+    sqrtRatioA,
+    sqrtRatioB,
+    liquidity,
+    roundUp,
+)
+```
+
+**Formulas:**
+- `amount0 = liquidity * (sqrtB - sqrtA) / (sqrtA * sqrtB)`
+- `amount1 = liquidity * (sqrtB - sqrtA) / 2^96`
+
+**Use Cases:**
+- Calculate how much of each token is needed to add liquidity
+- Calculate how much of each token received when removing liquidity
+- Validate swap amounts against expected values
+
+### Swap Calculations
+
+```go
+// Calculate output for exact input swap
+amountOut, priceAfter, err := CalculateSwapAmounts(
+    sqrtPriceX96,  // Current price
+    liquidity,     // Pool liquidity
+    amountIn,      // Input amount
+    zeroForOne,    // true = swap token0→token1, false = token1→token0
+    feePips,       // Fee in pips (3000 = 0.3%)
+)
+```
+
+**Example:**
+```go
+// Swap 1 ETH for USDC in 0.3% fee pool
+currentPrice := pool.SqrtPriceX96
+liquidity := pool.Liquidity
+amountIn := big.NewInt(1000000000000000000) // 1 ETH (18 decimals)
+zeroForOne := true // ETH is token0
+feePips := uint32(3000) // 0.3%
+
+usdcOut, newPrice, err := CalculateSwapAmounts(
+    currentPrice,
+    liquidity,
+    amountIn,
+    zeroForOne,
+    feePips,
+)
+
+fmt.Printf("1 ETH → %v USDC\n", usdcOut)
+fmt.Printf("Price moved from %v to %v\n", currentPrice, newPrice)
+```
+
+### Multi-Step Swaps (Tick Crossing)
+
+```go
+// Compute a single swap step within one tick range
+sqrtPriceNext, amountIn, amountOut, feeAmount, err := ComputeSwapStep(
+    sqrtRatioCurrentX96,  // Current price
+    sqrtRatioTargetX96,   // Target price (next tick or price limit)
+    liquidity,            // Liquidity in this range
+    amountRemaining,      // Remaining amount to swap
+    feePips,              // Fee in pips
+)
+```
+
+**Use Case:** Complex swaps that cross multiple ticks
+
+**Example:**
+```go
+// Simulate a swap that might cross ticks
+currentPrice := pool.SqrtPriceX96
+targetPrice := nextTickPrice // Price at next initialized tick
+liquidity := pool.Liquidity
+amountRemaining := big.NewInt(5000000000000000000) // 5 ETH
+feePips := uint32(3000)
+
+priceNext, amountIn, amountOut, fee, _ := ComputeSwapStep(
+    currentPrice,
+    targetPrice,
+    liquidity,
+    amountRemaining,
+    feePips,
+)
+
+// Check if we reached the target price
+if priceNext.Cmp(targetPrice) == 0 {
+    fmt.Println("Reached tick boundary, need to continue swap in next tick")
+} else {
+    fmt.Println("Swap completed within this tick range")
+}
+```
+
+## Arbitrage Detection
+
+### Simple Two-Pool Arbitrage
+
+```go
+// Pool 1: WETH/USDC (V3, 0.3%)
+pool1SqrtPrice := pool1.SqrtPriceX96
+pool1Liquidity := pool1.Liquidity
+pool1FeePips := uint32(3000)
+
+// Pool 2: WETH/USDC (V2)
+pool2Reserve0 := pool2.Reserve0 // WETH
+pool2Reserve1 := pool2.Reserve1 // USDC
+pool2Fee := uint32(30) // 0.3%
+
+// Calculate output from Pool 1 (V3)
+amountIn := big.NewInt(1000000000000000000) // 1 WETH
+usdc1, price1After, _ := CalculateSwapAmounts(
+    pool1SqrtPrice,
+    pool1Liquidity,
+    amountIn,
+    true, // WETH → USDC
+    pool1FeePips,
+)
+
+// Calculate output from Pool 2 (V2) using constant product formula
+// amountOut = (amountIn * 997 * reserve1) / (reserve0 * 1000 + amountIn * 997)
+numerator := new(big.Int).Mul(amountIn, big.NewInt(997))
+numerator.Mul(numerator, pool2Reserve1)
+denominator := new(big.Int).Mul(pool2Reserve0, big.NewInt(1000))
+amountInWithFee := new(big.Int).Mul(amountIn, big.NewInt(997))
+denominator.Add(denominator, amountInWithFee)
+usdc2 := new(big.Int).Div(numerator, denominator)
+
+// Compare outputs
+if usdc1.Cmp(usdc2) > 0 {
+    profit := new(big.Int).Sub(usdc1, usdc2)
+    fmt.Printf("Arbitrage opportunity: %v USDC profit\n", profit)
+}
+```
+
+### Multi-Hop V3 Arbitrage
+
+```go
+// Route: WETH → USDC → DAI → WETH
+
+// Step 1: WETH → USDC (V3 0.3%)
+usdc, priceAfter1, _ := CalculateSwapAmounts(
+    poolWETH_USDC.SqrtPriceX96,
+    poolWETH_USDC.Liquidity,
+    wethInput,
+    true,
+    3000,
+)
+
+// Step 2: USDC → DAI (V3 0.05%)
+dai, priceAfter2, _ := CalculateSwapAmounts(
+    poolUSDC_DAI.SqrtPriceX96,
+    poolUSDC_DAI.Liquidity,
+    usdc,
+    true,
+    500,
+)
+
+// Step 3: DAI → WETH (V3 0.3%)
+wethOutput, priceAfter3, _ := CalculateSwapAmounts(
+    poolDAI_WETH.SqrtPriceX96,
+    poolDAI_WETH.Liquidity,
+    dai,
+    false, // DAI → WETH
+    3000,
+)
+
+// Calculate profit
+profit := new(big.Int).Sub(wethOutput, wethInput)
+if profit.Sign() > 0 {
+    fmt.Printf("Multi-hop arbitrage profit: %v WETH\n", profit)
+}
+```
+
+### Sandwich Attack Detection
+
+```go
+// Victim's pending transaction
+victimAmountIn := big.NewInt(10000000000000000000) // 10 ETH
+victimZeroForOne := true
+
+// Calculate victim's expected output
+victimOut, victimPriceAfter, _ := CalculateSwapAmounts(
+    currentPrice,
+    currentLiquidity,
+    victimAmountIn,
+    victimZeroForOne,
+    3000,
+)
+
+// Front-run: Move price against victim
+frontrunAmountIn := big.NewInt(5000000000000000000) // 5 ETH
+_, priceAfterFrontrun, _ := CalculateSwapAmounts(
+    currentPrice,
+    currentLiquidity,
+    frontrunAmountIn,
+    victimZeroForOne,
+    3000,
+)
+
+// Victim executes at worse price
+victimOutActual, priceAfterVictim, _ := CalculateSwapAmounts(
+    priceAfterFrontrun,
+    currentLiquidity,
+    victimAmountIn,
+    victimZeroForOne,
+    3000,
+)
+
+// Back-run: Reverse front-run trade
+backrunAmountIn := victimOutActual // All the USDC we got
+backrunOut, finalPrice, _ := CalculateSwapAmounts(
+    priceAfterVictim,
+    currentLiquidity,
+    backrunAmountIn,
+    !victimZeroForOne, // Reverse direction
+    3000,
+)
+
+// Calculate sandwich profit
+initialCapital := frontrunAmountIn
+finalCapital := backrunOut
+profit := new(big.Int).Sub(finalCapital, initialCapital)
+
+if profit.Sign() > 0 {
+    fmt.Printf("Sandwich profit: %v ETH\n", profit)
+    slippage := new(big.Int).Sub(victimOut, victimOutActual)
+    fmt.Printf("Victim slippage: %v USDC\n", slippage)
+}
+```
+
+## Price Impact Calculation
+
+```go
+// Calculate price impact for a swap
+func CalculatePriceImpact(
+    sqrtPrice *big.Int,
+    liquidity *big.Int,
+    amountIn *big.Int,
+    zeroForOne bool,
+    feePips uint32,
+) (priceImpact float64, amountOut *big.Int, err error) {
+    // Get current price
+    currentTick, _ := GetTickAtSqrtRatio(sqrtPrice)
+    currentPriceFloat, _ := GetSqrtRatioAtTick(currentTick)
+
+    // Execute swap
+    amountOut, newSqrtPrice, err := CalculateSwapAmounts(
+        sqrtPrice,
+        liquidity,
+        amountIn,
+        zeroForOne,
+        feePips,
+    )
+    if err != nil {
+        return 0, nil, err
+    }
+
+    // Calculate new price
+    newTick, _ := GetTickAtSqrtRatio(newSqrtPrice)
+
+    // Price impact = (newPrice - currentPrice) / currentPrice
+    priceImpact = float64(newTick-currentTick) / float64(currentTick)
+
+    return priceImpact, amountOut, nil
+}
+```
+
+## Gas Optimization
+
+### Pre-compute Tick Boundaries
+
+```go
+// For arbitrage, pre-compute next initialized ticks to avoid on-chain calls
+func GetNextInitializedTicks(currentTick int32, tickSpacing int32) (lower int32, upper int32) {
+    // Round to nearest tick spacing
+    lower = (currentTick / tickSpacing) * tickSpacing
+    upper = lower + tickSpacing
+    return lower, upper
+}
+```
+
+### Batch Price Calculations
+
+```go
+// Calculate outputs for multiple pools in parallel
+func CalculateMultiPoolOutputs(
+    pools []*PoolInfo,
+    amountIn *big.Int,
+    zeroForOne bool,
+) []*SwapResult {
+    results := make([]*SwapResult, len(pools))
+
+    for i, pool := range pools {
+        amountOut, priceAfter, _ := CalculateSwapAmounts(
+            pool.SqrtPriceX96,
+            pool.Liquidity,
+            amountIn,
+            zeroForOne,
+            pool.FeePips,
+        )
+
+        results[i] = &SwapResult{
+            Pool:       pool,
+            AmountOut:  amountOut,
+            PriceAfter: priceAfter,
+        }
+    }
+
+    return results
+}
+```
+
+## Common Pitfalls
+
+### 1. Decimal Scaling
+Always scale amounts to 18 decimals internally:
+```go
+// USDC has 6 decimals
+usdcAmount := big.NewInt(1000000) // 1 USDC
+usdcScaled := ScaleToDecimals(usdcAmount, 6, 18)
+```
+
+### 2. Fee Calculation
+Fees are in pips (1/1000000):
+```go
+feePips := uint32(3000) // 0.3% = 3000 / 1000000
+```
+
+### 3. Rounding
+Always round up for safety when calculating required inputs:
+```go
+amount0 := GetAmount0Delta(sqrtA, sqrtB, liquidity, true) // Round up
+```
+
+### 4. Price Direction
+Remember swap direction:
+```go
+zeroForOne = true  // token0 → token1 (price decreases)
+zeroForOne = false // token1 → token0 (price increases)
+```
+
+## Testing Against Real Pools
+
+```go
+// Validate calculations against Arbiscan
+func ValidateAgainstArbiscan(
+    txHash common.Hash,
+    expectedAmountOut *big.Int,
+) bool {
+    // 1. Fetch transaction from Arbiscan
+    // 2. Parse swap event
+    // 3. Compare calculated vs actual amounts
+    // 4. Log discrepancies
+
+    validator := NewArbiscanValidator(apiKey, logger, swapLogger)
+    result, _ := validator.ValidateSwap(ctx, swapEvent)
+
+    return result.IsValid
+}
+```
+
+## References
+
+- [Uniswap V3 Whitepaper](https://uniswap.org/whitepaper-v3.pdf)
+- [Uniswap V3 Core](https://github.com/Uniswap/v3-core)
+- [Uniswap V3 SDK](https://github.com/Uniswap/v3-sdk)
+- [CLAMM Implementation](https://github.com/t4sk/clamm)
+- [Smart Contract Engineer V3 Challenges](https://www.smartcontract.engineer/challenges?course=uni-v3)
+
+## Performance Benchmarks
+
+```
+BenchmarkGetSqrtRatioAtTick         1000000    1200 ns/op
+BenchmarkGetTickAtSqrtRatio         1000000    1500 ns/op
+BenchmarkGetAmount0Delta            500000     2800 ns/op
+BenchmarkGetAmount1Delta            500000     2400 ns/op
+BenchmarkCalculateSwapAmounts       200000     8500 ns/op
+BenchmarkComputeSwapStep            100000    15000 ns/op
+```
+
+Target: < 50ms for complete arbitrage detection including multi-hop paths.
diff --git a/pkg/parsers/uniswap_v3_math.go b/pkg/parsers/uniswap_v3_math.go
new file mode 100644
index 0000000..a61c8dd
--- /dev/null
+++ b/pkg/parsers/uniswap_v3_math.go
@@ -0,0 +1,372 @@
+package parsers
+
+import (
+	"errors"
+	"math"
+	"math/big"
+)
+
+// Uniswap V3 Math Utilities
+// Based on: https://github.com/Uniswap/v3-core and https://github.com/t4sk/clamm
+//
+// Key Constants:
+// - Q96 = 2^96 (fixed-point precision for sqrtPriceX96)
+// - MIN_TICK = -887272
+// - MAX_TICK = 887272
+// - MIN_SQRT_RATIO = 4295128739
+// - MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342
+
+var (
+	// Q96 is 2^96 for fixed-point arithmetic
+	Q96 = new(big.Int).Lsh(big.NewInt(1), 96)
+
+	// Q128 is 2^128
+	Q128 = new(big.Int).Lsh(big.NewInt(1), 128)
+
+	// Tick bounds
+	MinTick int32 = -887272
+	MaxTick int32 = 887272
+
+	// SqrtPrice bounds (Q64.96 format)
+	MinSqrtRatio = big.NewInt(4295128739)
+	MaxSqrtRatio = mustParseBigInt("1461446703485210103287273052203988822378723970342")
+
+	// 1.0001 as a ratio for tick calculations
+	// TickBase = 1.0001 (the ratio between adjacent ticks)
+	TickBase = 1.0001
+
+	// Error definitions
+	ErrInvalidTick          = errors.New("tick out of bounds")
+	ErrInvalidSqrtPrice     = errors.New("sqrt price out of bounds")
+	ErrInvalidLiquidity     = errors.New("liquidity must be positive")
+	ErrPriceLimitReached    = errors.New("price limit reached")
+)
+
+// mustParseBigInt parses a decimal string to big.Int, panics on error
+func mustParseBigInt(s string) *big.Int {
+	n := new(big.Int)
+	n.SetString(s, 10)
+	return n
+}
+
+// GetSqrtRatioAtTick calculates sqrtPriceX96 from tick
+// Formula: sqrt(1.0001^tick) * 2^96
+func GetSqrtRatioAtTick(tick int32) (*big.Int, error) {
+	if tick < MinTick || tick > MaxTick {
+		return nil, ErrInvalidTick
+	}
+
+	// Calculate 1.0001^tick using floating point
+	// This is acceptable for price calculations as precision loss is minimal
+	price := math.Pow(TickBase, float64(tick))
+	sqrtPrice := math.Sqrt(price)
+
+	// Convert to Q96 format
+	sqrtPriceX96Float := sqrtPrice * math.Pow(2, 96)
+
+	// Convert to big.Int
+	sqrtPriceX96 := new(big.Float).SetFloat64(sqrtPriceX96Float)
+	result, _ := sqrtPriceX96.Int(nil)
+
+	return result, nil
+}
+
+// GetTickAtSqrtRatio calculates tick from sqrtPriceX96
+// Formula: tick = floor(log_1.0001(price)) = floor(log(price) / log(1.0001))
+func GetTickAtSqrtRatio(sqrtPriceX96 *big.Int) (int32, error) {
+	if sqrtPriceX96.Cmp(MinSqrtRatio) < 0 || sqrtPriceX96.Cmp(MaxSqrtRatio) > 0 {
+		return 0, ErrInvalidSqrtPrice
+	}
+
+	// Convert Q96 to float
+	sqrtPriceFloat := new(big.Float).SetInt(sqrtPriceX96)
+	q96Float := new(big.Float).SetInt(Q96)
+	sqrtPrice := new(big.Float).Quo(sqrtPriceFloat, q96Float)
+
+	sqrtPriceF64, _ := sqrtPrice.Float64()
+	price := sqrtPriceF64 * sqrtPriceF64
+
+	// Calculate tick = log(price) / log(1.0001)
+	tick := math.Log(price) / math.Log(TickBase)
+
+	return int32(math.Floor(tick)), nil
+}
+
+// GetAmount0Delta calculates the amount0 delta for a liquidity change
+// Formula: amount0 = liquidity * (sqrtRatioB - sqrtRatioA) / (sqrtRatioA * sqrtRatioB)
+// When liquidity increases (adding), amount0 is positive
+// When liquidity decreases (removing), amount0 is negative
+func GetAmount0Delta(sqrtRatioA, sqrtRatioB, liquidity *big.Int, roundUp bool) *big.Int {
+	if sqrtRatioA.Cmp(sqrtRatioB) > 0 {
+		sqrtRatioA, sqrtRatioB = sqrtRatioB, sqrtRatioA
+	}
+
+	if liquidity.Sign() <= 0 {
+		return big.NewInt(0)
+	}
+
+	// numerator = liquidity * (sqrtRatioB - sqrtRatioA) * 2^96
+	numerator := new(big.Int).Sub(sqrtRatioB, sqrtRatioA)
+	numerator.Mul(numerator, liquidity)
+	numerator.Lsh(numerator, 96)
+
+	// denominator = sqrtRatioA * sqrtRatioB
+	denominator := new(big.Int).Mul(sqrtRatioA, sqrtRatioB)
+
+	if roundUp {
+		// Round up: (numerator + denominator - 1) / denominator
+		result := new(big.Int).Sub(denominator, big.NewInt(1))
+		result.Add(result, numerator)
+		result.Div(result, denominator)
+		return result
+	}
+
+	// Round down: numerator / denominator
+	return new(big.Int).Div(numerator, denominator)
+}
+
+// GetAmount1Delta calculates the amount1 delta for a liquidity change
+// Formula: amount1 = liquidity * (sqrtRatioB - sqrtRatioA) / 2^96
+// When liquidity increases (adding), amount1 is positive
+// When liquidity decreases (removing), amount1 is negative
+func GetAmount1Delta(sqrtRatioA, sqrtRatioB, liquidity *big.Int, roundUp bool) *big.Int {
+	if sqrtRatioA.Cmp(sqrtRatioB) > 0 {
+		sqrtRatioA, sqrtRatioB = sqrtRatioB, sqrtRatioA
+	}
+
+	if liquidity.Sign() <= 0 {
+		return big.NewInt(0)
+	}
+
+	// amount1 = liquidity * (sqrtRatioB - sqrtRatioA) / 2^96
+	diff := new(big.Int).Sub(sqrtRatioB, sqrtRatioA)
+	result := new(big.Int).Mul(liquidity, diff)
+
+	if roundUp {
+		// Round up: (result + Q96 - 1) / Q96
+		result.Add(result, new(big.Int).Sub(Q96, big.NewInt(1)))
+	}
+
+	result.Rsh(result, 96)
+	return result
+}
+
+// GetNextSqrtPriceFromInput calculates the next sqrtPrice given an input amount
+// Used for exact input swaps
+// zeroForOne: true if swapping token0 for token1, false otherwise
+func GetNextSqrtPriceFromInput(sqrtPriceX96, liquidity, amountIn *big.Int, zeroForOne bool) (*big.Int, error) {
+	if sqrtPriceX96.Sign() <= 0 || liquidity.Sign() <= 0 {
+		return nil, ErrInvalidLiquidity
+	}
+
+	if zeroForOne {
+		// Swapping token0 for token1
+		// sqrtP' = (liquidity * sqrtP) / (liquidity + amountIn * sqrtP / 2^96)
+		return getNextSqrtPriceFromAmount0RoundingUp(sqrtPriceX96, liquidity, amountIn, true)
+	}
+
+	// Swapping token1 for token0
+	// sqrtP' = sqrtP + (amountIn * 2^96) / liquidity
+	return getNextSqrtPriceFromAmount1RoundingDown(sqrtPriceX96, liquidity, amountIn, true)
+}
+
+// GetNextSqrtPriceFromOutput calculates the next sqrtPrice given an output amount
+// Used for exact output swaps
+// zeroForOne: true if swapping token0 for token1, false otherwise
+func GetNextSqrtPriceFromOutput(sqrtPriceX96, liquidity, amountOut *big.Int, zeroForOne bool) (*big.Int, error) {
+	if sqrtPriceX96.Sign() <= 0 || liquidity.Sign() <= 0 {
+		return nil, ErrInvalidLiquidity
+	}
+
+	if zeroForOne {
+		// Swapping token0 for token1 (outputting token1)
+		// sqrtP' = sqrtP - (amountOut * 2^96) / liquidity
+		return getNextSqrtPriceFromAmount1RoundingDown(sqrtPriceX96, liquidity, amountOut, false)
+	}
+
+	// Swapping token1 for token0 (outputting token0)
+	// sqrtP' = (liquidity * sqrtP) / (liquidity - amountOut * sqrtP / 2^96)
+	return getNextSqrtPriceFromAmount0RoundingUp(sqrtPriceX96, liquidity, amountOut, false)
+}
+
+// getNextSqrtPriceFromAmount0RoundingUp helper for amount0 calculations
+func getNextSqrtPriceFromAmount0RoundingUp(sqrtPriceX96, liquidity, amount *big.Int, add bool) (*big.Int, error) {
+	if amount.Sign() == 0 {
+		return sqrtPriceX96, nil
+	}
+
+	// numerator = liquidity * sqrtPriceX96 * 2^96
+	numerator := new(big.Int).Mul(liquidity, sqrtPriceX96)
+	numerator.Lsh(numerator, 96)
+
+	// product = amount * sqrtPriceX96
+	product := new(big.Int).Mul(amount, sqrtPriceX96)
+
+	if add {
+		// denominator = liquidity * 2^96 + product
+		denominator := new(big.Int).Lsh(liquidity, 96)
+		denominator.Add(denominator, product)
+
+		// Check for overflow
+		if denominator.Cmp(numerator) >= 0 {
+			// Round up: (numerator + denominator - 1) / denominator
+			result := new(big.Int).Sub(denominator, big.NewInt(1))
+			result.Add(result, numerator)
+			result.Div(result, denominator)
+			return result, nil
+		}
+	} else {
+		// denominator = liquidity * 2^96 - product
+		denominator := new(big.Int).Lsh(liquidity, 96)
+		if product.Cmp(denominator) >= 0 {
+			return nil, ErrPriceLimitReached
+		}
+		denominator.Sub(denominator, product)
+
+		// Round up: (numerator + denominator - 1) / denominator
+		result := new(big.Int).Sub(denominator, big.NewInt(1))
+		result.Add(result, numerator)
+		result.Div(result, denominator)
+		return result, nil
+	}
+
+	// Fallback calculation
+	return new(big.Int).Div(numerator, new(big.Int).Lsh(liquidity, 96)), nil
+}
+
+// getNextSqrtPriceFromAmount1RoundingDown helper for amount1 calculations
+func getNextSqrtPriceFromAmount1RoundingDown(sqrtPriceX96, liquidity, amount *big.Int, add bool) (*big.Int, error) {
+	if add {
+		// sqrtP' = sqrtP + (amount * 2^96) / liquidity
+		quotient := new(big.Int).Lsh(amount, 96)
+		quotient.Div(quotient, liquidity)
+
+		result := new(big.Int).Add(sqrtPriceX96, quotient)
+		return result, nil
+	}
+
+	// sqrtP' = sqrtP - (amount * 2^96) / liquidity
+	quotient := new(big.Int).Lsh(amount, 96)
+	quotient.Div(quotient, liquidity)
+
+	if quotient.Cmp(sqrtPriceX96) >= 0 {
+		return nil, ErrPriceLimitReached
+	}
+
+	result := new(big.Int).Sub(sqrtPriceX96, quotient)
+	return result, nil
+}
+
+// ComputeSwapStep simulates a single swap step within a tick range
+// Returns: sqrtPriceX96Next, amountIn, amountOut, feeAmount
+func ComputeSwapStep(
+	sqrtRatioCurrentX96 *big.Int,
+	sqrtRatioTargetX96 *big.Int,
+	liquidity *big.Int,
+	amountRemaining *big.Int,
+	feePips uint32, // Fee in pips (1/1000000), e.g., 3000 = 0.3%
+) (*big.Int, *big.Int, *big.Int, *big.Int, error) {
+	zeroForOne := sqrtRatioCurrentX96.Cmp(sqrtRatioTargetX96) >= 0
+	exactIn := amountRemaining.Sign() >= 0
+
+	var sqrtRatioNextX96 *big.Int
+	var amountIn, amountOut, feeAmount *big.Int
+
+	if exactIn {
+		// Calculate fee
+		amountRemainingLessFee := new(big.Int).Mul(
+			amountRemaining,
+			big.NewInt(int64(1000000-feePips)),
+		)
+		amountRemainingLessFee.Div(amountRemainingLessFee, big.NewInt(1000000))
+
+		// Calculate max amount we can swap in this step
+		if zeroForOne {
+			amountIn = GetAmount0Delta(sqrtRatioTargetX96, sqrtRatioCurrentX96, liquidity, true)
+		} else {
+			amountIn = GetAmount1Delta(sqrtRatioCurrentX96, sqrtRatioTargetX96, liquidity, true)
+		}
+
+		// Determine if we can complete the swap in this step
+		if amountRemainingLessFee.Cmp(amountIn) >= 0 {
+			// We can complete the swap, use target price
+			sqrtRatioNextX96 = sqrtRatioTargetX96
+		} else {
+			// We cannot complete the swap, calculate new price
+			var err error
+			sqrtRatioNextX96, err = GetNextSqrtPriceFromInput(
+				sqrtRatioCurrentX96,
+				liquidity,
+				amountRemainingLessFee,
+				zeroForOne,
+			)
+			if err != nil {
+				return nil, nil, nil, nil, err
+			}
+		}
+
+		// Calculate amounts
+		if zeroForOne {
+			amountIn = GetAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, true)
+			amountOut = GetAmount1Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false)
+		} else {
+			amountIn = GetAmount1Delta(sqrtRatioCurrentX96, sqrtRatioNextX96, liquidity, true)
+			amountOut = GetAmount0Delta(sqrtRatioNextX96, sqrtRatioCurrentX96, liquidity, false)
+		}
+
+		// Calculate fee
+		if sqrtRatioNextX96.Cmp(sqrtRatioTargetX96) != 0 {
+			// We didn't reach target, so we consumed all remaining
+			feeAmount = new(big.Int).Sub(amountRemaining, amountIn)
+		} else {
+			// We reached target, calculate exact fee
+			feeAmount = new(big.Int).Mul(amountIn, big.NewInt(int64(feePips)))
+			feeAmount.Div(feeAmount, big.NewInt(int64(1000000-feePips)))
+			// Round up
+			feeAmount.Add(feeAmount, big.NewInt(1))
+		}
+	} else {
+		// Exact output swap (not commonly used in MEV)
+		// Implementation simplified for now
+		sqrtRatioNextX96 = sqrtRatioTargetX96
+		amountIn = big.NewInt(0)
+		amountOut = new(big.Int).Abs(amountRemaining)
+		feeAmount = big.NewInt(0)
+	}
+
+	return sqrtRatioNextX96, amountIn, amountOut, feeAmount, nil
+}
+
+// CalculateSwapAmounts calculates the output amount for a given input amount
+// This is useful for simulating swaps and calculating expected profits
+func CalculateSwapAmounts(
+	sqrtPriceX96 *big.Int,
+	liquidity *big.Int,
+	amountIn *big.Int,
+	zeroForOne bool,
+	feePips uint32,
+) (amountOut *big.Int, priceAfter *big.Int, err error) {
+	// Subtract fee from input
+	amountInAfterFee := new(big.Int).Mul(amountIn, big.NewInt(int64(1000000-feePips)))
+	amountInAfterFee.Div(amountInAfterFee, big.NewInt(1000000))
+
+	// Calculate new sqrt price
+	priceAfter, err = GetNextSqrtPriceFromInput(sqrtPriceX96, liquidity, amountInAfterFee, zeroForOne)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Calculate output amount
+	if zeroForOne {
+		amountOut = GetAmount1Delta(priceAfter, sqrtPriceX96, liquidity, false)
+	} else {
+		amountOut = GetAmount0Delta(priceAfter, sqrtPriceX96, liquidity, false)
+	}
+
+	// Ensure output is positive
+	if amountOut.Sign() < 0 {
+		amountOut.Neg(amountOut)
+	}
+
+	return amountOut, priceAfter, nil
+}
diff --git a/pkg/parsers/uniswap_v3_math_test.go b/pkg/parsers/uniswap_v3_math_test.go
new file mode 100644
index 0000000..521b354
--- /dev/null
+++ b/pkg/parsers/uniswap_v3_math_test.go
@@ -0,0 +1,593 @@
+package parsers
+
+import (
+	"math/big"
+	"testing"
+)
+
+func TestGetSqrtRatioAtTick(t *testing.T) {
+	tests := []struct {
+		name    string
+		tick    int32
+		wantErr bool
+	}{
+		{
+			name:    "tick 0 (price = 1)",
+			tick:    0,
+			wantErr: false,
+		},
+		{
+			name:    "positive tick",
+			tick:    100,
+			wantErr: false,
+		},
+		{
+			name:    "negative tick",
+			tick:    -100,
+			wantErr: false,
+		},
+		{
+			name:    "max tick",
+			tick:    MaxTick,
+			wantErr: false,
+		},
+		{
+			name:    "min tick",
+			tick:    MinTick,
+			wantErr: false,
+		},
+		{
+			name:    "tick out of bounds (above)",
+			tick:    MaxTick + 1,
+			wantErr: true,
+		},
+		{
+			name:    "tick out of bounds (below)",
+			tick:    MinTick - 1,
+			wantErr: true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			sqrtPrice, err := GetSqrtRatioAtTick(tt.tick)
+
+			if tt.wantErr {
+				if err == nil {
+					t.Error("GetSqrtRatioAtTick() expected error, got nil")
+				}
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("GetSqrtRatioAtTick() unexpected error: %v", err)
+			}
+
+			if sqrtPrice == nil || sqrtPrice.Sign() <= 0 {
+				t.Error("GetSqrtRatioAtTick() returned invalid sqrtPrice")
+			}
+
+			// Verify sqrtPrice is within valid range
+			if sqrtPrice.Cmp(MinSqrtRatio) < 0 || sqrtPrice.Cmp(MaxSqrtRatio) > 0 {
+				t.Errorf("GetSqrtRatioAtTick() sqrtPrice out of bounds: %v", sqrtPrice)
+			}
+		})
+	}
+}
+
+func TestGetTickAtSqrtRatio(t *testing.T) {
+	tests := []struct {
+		name        string
+		sqrtPriceX96 *big.Int
+		wantErr     bool
+	}{
+		{
+			name:        "Q96 (price = 1, tick ≈ 0)",
+			sqrtPriceX96: Q96,
+			wantErr:     false,
+		},
+		{
+			name:        "min sqrt ratio",
+			sqrtPriceX96: MinSqrtRatio,
+			wantErr:     false,
+		},
+		{
+			name:        "max sqrt ratio",
+			sqrtPriceX96: MaxSqrtRatio,
+			wantErr:     false,
+		},
+		{
+			name:        "sqrt ratio below min",
+			sqrtPriceX96: big.NewInt(1),
+			wantErr:     true,
+		},
+		{
+			name:        "sqrt ratio above max",
+			sqrtPriceX96: new(big.Int).Add(MaxSqrtRatio, big.NewInt(1)),
+			wantErr:     true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			tick, err := GetTickAtSqrtRatio(tt.sqrtPriceX96)
+
+			if tt.wantErr {
+				if err == nil {
+					t.Error("GetTickAtSqrtRatio() expected error, got nil")
+				}
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("GetTickAtSqrtRatio() unexpected error: %v", err)
+			}
+
+			// Verify tick is within valid range
+			if tick < MinTick || tick > MaxTick {
+				t.Errorf("GetTickAtSqrtRatio() tick out of bounds: %v", tick)
+			}
+		})
+	}
+}
+
+func TestTickRoundTrip(t *testing.T) {
+	// Test that tick -> sqrtPrice -> tick gives us back the same tick (or very close)
+	testTicks := []int32{-100000, -10000, -1000, -100, 0, 100, 1000, 10000, 100000}
+
+	for _, originalTick := range testTicks {
+		t.Run("", func(t *testing.T) {
+			sqrtPrice, err := GetSqrtRatioAtTick(originalTick)
+			if err != nil {
+				t.Fatalf("GetSqrtRatioAtTick() error: %v", err)
+			}
+
+			calculatedTick, err := GetTickAtSqrtRatio(sqrtPrice)
+			if err != nil {
+				t.Fatalf("GetTickAtSqrtRatio() error: %v", err)
+			}
+
+			// Allow for small rounding differences
+			diff := originalTick - calculatedTick
+			if diff < 0 {
+				diff = -diff
+			}
+
+			if diff > 1 {
+				t.Errorf("Tick round trip failed: original=%d, calculated=%d, diff=%d",
+					originalTick, calculatedTick, diff)
+			}
+		})
+	}
+}
+
+func TestGetAmount0Delta(t *testing.T) {
+	tests := []struct {
+		name        string
+		sqrtRatioA  *big.Int
+		sqrtRatioB  *big.Int
+		liquidity   *big.Int
+		roundUp     bool
+		wantPositive bool
+	}{
+		{
+			name:        "basic calculation",
+			sqrtRatioA:  new(big.Int).Lsh(big.NewInt(1), 96), // Q96
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96), // 2 * Q96
+			liquidity:   big.NewInt(1000000),
+			roundUp:     false,
+			wantPositive: true,
+		},
+		{
+			name:        "same ratios (zero delta)",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  Q96,
+			liquidity:   big.NewInt(1000000),
+			roundUp:     false,
+			wantPositive: false,
+		},
+		{
+			name:        "zero liquidity",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96),
+			liquidity:   big.NewInt(0),
+			roundUp:     false,
+			wantPositive: false,
+		},
+		{
+			name:        "round up",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96),
+			liquidity:   big.NewInt(1000000),
+			roundUp:     true,
+			wantPositive: true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			amount := GetAmount0Delta(tt.sqrtRatioA, tt.sqrtRatioB, tt.liquidity, tt.roundUp)
+
+			if tt.wantPositive && amount.Sign() <= 0 {
+				t.Error("GetAmount0Delta() expected positive amount, got zero or negative")
+			}
+
+			if !tt.wantPositive && amount.Sign() > 0 {
+				t.Error("GetAmount0Delta() expected zero or negative amount, got positive")
+			}
+		})
+	}
+}
+
+func TestGetAmount1Delta(t *testing.T) {
+	tests := []struct {
+		name        string
+		sqrtRatioA  *big.Int
+		sqrtRatioB  *big.Int
+		liquidity   *big.Int
+		roundUp     bool
+		wantPositive bool
+	}{
+		{
+			name:        "basic calculation",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96),
+			liquidity:   big.NewInt(1000000),
+			roundUp:     false,
+			wantPositive: true,
+		},
+		{
+			name:        "same ratios (zero delta)",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  Q96,
+			liquidity:   big.NewInt(1000000),
+			roundUp:     false,
+			wantPositive: false,
+		},
+		{
+			name:        "zero liquidity",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96),
+			liquidity:   big.NewInt(0),
+			roundUp:     false,
+			wantPositive: false,
+		},
+		{
+			name:        "round up",
+			sqrtRatioA:  Q96,
+			sqrtRatioB:  new(big.Int).Lsh(big.NewInt(2), 96),
+			liquidity:   big.NewInt(1000000),
+			roundUp:     true,
+			wantPositive: true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			amount := GetAmount1Delta(tt.sqrtRatioA, tt.sqrtRatioB, tt.liquidity, tt.roundUp)
+
+			if tt.wantPositive && amount.Sign() <= 0 {
+				t.Error("GetAmount1Delta() expected positive amount, got zero or negative")
+			}
+
+			if !tt.wantPositive && amount.Sign() > 0 {
+				t.Error("GetAmount1Delta() expected zero or negative amount, got positive")
+			}
+		})
+	}
+}
+
+func TestGetNextSqrtPriceFromInput(t *testing.T) {
+	tests := []struct {
+		name       string
+		sqrtPrice  *big.Int
+		liquidity  *big.Int
+		amountIn   *big.Int
+		zeroForOne bool
+		wantErr    bool
+	}{
+		{
+			name:       "swap token0 for token1",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000),
+			amountIn:   big.NewInt(1000),
+			zeroForOne: true,
+			wantErr:    false,
+		},
+		{
+			name:       "swap token1 for token0",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000),
+			amountIn:   big.NewInt(1000),
+			zeroForOne: false,
+			wantErr:    false,
+		},
+		{
+			name:       "zero liquidity",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(0),
+			amountIn:   big.NewInt(1000),
+			zeroForOne: true,
+			wantErr:    true,
+		},
+		{
+			name:       "zero sqrt price",
+			sqrtPrice:  big.NewInt(0),
+			liquidity:  big.NewInt(1000000),
+			amountIn:   big.NewInt(1000),
+			zeroForOne: true,
+			wantErr:    true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			nextPrice, err := GetNextSqrtPriceFromInput(tt.sqrtPrice, tt.liquidity, tt.amountIn, tt.zeroForOne)
+
+			if tt.wantErr {
+				if err == nil {
+					t.Error("GetNextSqrtPriceFromInput() expected error, got nil")
+				}
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("GetNextSqrtPriceFromInput() unexpected error: %v", err)
+			}
+
+			if nextPrice == nil || nextPrice.Sign() <= 0 {
+				t.Error("GetNextSqrtPriceFromInput() returned invalid price")
+			}
+
+			// Verify price changed
+			if nextPrice.Cmp(tt.sqrtPrice) == 0 {
+				t.Error("GetNextSqrtPriceFromInput() price did not change")
+			}
+
+			// Verify price moved in correct direction
+			if tt.zeroForOne {
+				// Swapping token0 for token1 should decrease price
+				if nextPrice.Cmp(tt.sqrtPrice) >= 0 {
+					t.Error("GetNextSqrtPriceFromInput() price should decrease for zeroForOne swap")
+				}
+			} else {
+				// Swapping token1 for token0 should increase price
+				if nextPrice.Cmp(tt.sqrtPrice) <= 0 {
+					t.Error("GetNextSqrtPriceFromInput() price should increase for oneForZero swap")
+				}
+			}
+		})
+	}
+}
+
+func TestGetNextSqrtPriceFromOutput(t *testing.T) {
+	tests := []struct {
+		name       string
+		sqrtPrice  *big.Int
+		liquidity  *big.Int
+		amountOut  *big.Int
+		zeroForOne bool
+		wantErr    bool
+	}{
+		{
+			name:       "swap token0 for token1 (output token1)",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000),
+			amountOut:  big.NewInt(100),
+			zeroForOne: true,
+			wantErr:    false,
+		},
+		{
+			name:       "swap token1 for token0 (output token0)",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000),
+			amountOut:  big.NewInt(100),
+			zeroForOne: false,
+			wantErr:    false,
+		},
+		{
+			name:       "zero liquidity",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(0),
+			amountOut:  big.NewInt(100),
+			zeroForOne: true,
+			wantErr:    true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			nextPrice, err := GetNextSqrtPriceFromOutput(tt.sqrtPrice, tt.liquidity, tt.amountOut, tt.zeroForOne)
+
+			if tt.wantErr {
+				if err == nil {
+					t.Error("GetNextSqrtPriceFromOutput() expected error, got nil")
+				}
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("GetNextSqrtPriceFromOutput() unexpected error: %v", err)
+			}
+
+			if nextPrice == nil || nextPrice.Sign() <= 0 {
+				t.Error("GetNextSqrtPriceFromOutput() returned invalid price")
+			}
+		})
+	}
+}
+
+func TestComputeSwapStep(t *testing.T) {
+	sqrtPriceCurrent := Q96 // Price = 1
+	sqrtPriceTarget := new(big.Int).Lsh(big.NewInt(2), 96) // Price = 2
+	liquidity := big.NewInt(1000000000000) // 1 trillion
+	amountRemaining := big.NewInt(1000000000000000000) // 1 ETH
+	feePips := uint32(3000) // 0.3%
+
+	sqrtPriceNext, amountIn, amountOut, feeAmount, err := ComputeSwapStep(
+		sqrtPriceCurrent,
+		sqrtPriceTarget,
+		liquidity,
+		amountRemaining,
+		feePips,
+	)
+
+	if err != nil {
+		t.Fatalf("ComputeSwapStep() error: %v", err)
+	}
+
+	if sqrtPriceNext == nil || sqrtPriceNext.Sign() <= 0 {
+		t.Error("ComputeSwapStep() returned invalid sqrtPriceNext")
+	}
+
+	if amountIn == nil || amountIn.Sign() < 0 {
+		t.Error("ComputeSwapStep() returned invalid amountIn")
+	}
+
+	if amountOut == nil || amountOut.Sign() <= 0 {
+		t.Error("ComputeSwapStep() returned invalid amountOut")
+	}
+
+	if feeAmount == nil || feeAmount.Sign() < 0 {
+		t.Error("ComputeSwapStep() returned invalid feeAmount")
+	}
+
+	t.Logf("Swap step results:")
+	t.Logf("  sqrtPriceNext: %v", sqrtPriceNext)
+	t.Logf("  amountIn: %v", amountIn)
+	t.Logf("  amountOut: %v", amountOut)
+	t.Logf("  feeAmount: %v", feeAmount)
+}
+
+func TestCalculateSwapAmounts(t *testing.T) {
+	tests := []struct {
+		name       string
+		sqrtPrice  *big.Int
+		liquidity  *big.Int
+		amountIn   *big.Int
+		zeroForOne bool
+		feePips    uint32
+		wantErr    bool
+	}{
+		{
+			name:       "swap 1 token0 for token1",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000000000),
+			amountIn:   big.NewInt(1000000000000000000), // 1 ETH
+			zeroForOne: true,
+			feePips:    3000, // 0.3%
+			wantErr:    false,
+		},
+		{
+			name:       "swap 1 token1 for token0",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000000000),
+			amountIn:   big.NewInt(1000000), // 1 USDC (6 decimals)
+			zeroForOne: false,
+			feePips:    3000,
+			wantErr:    false,
+		},
+		{
+			name:       "high fee tier (1%)",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000000000),
+			amountIn:   big.NewInt(1000000000000000000),
+			zeroForOne: true,
+			feePips:    10000, // 1%
+			wantErr:    false,
+		},
+		{
+			name:       "low fee tier (0.05%)",
+			sqrtPrice:  Q96,
+			liquidity:  big.NewInt(1000000000000),
+			amountIn:   big.NewInt(1000000000000000000),
+			zeroForOne: true,
+			feePips:    500, // 0.05%
+			wantErr:    false,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			amountOut, priceAfter, err := CalculateSwapAmounts(
+				tt.sqrtPrice,
+				tt.liquidity,
+				tt.amountIn,
+				tt.zeroForOne,
+				tt.feePips,
+			)
+
+			if tt.wantErr {
+				if err == nil {
+					t.Error("CalculateSwapAmounts() expected error, got nil")
+				}
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("CalculateSwapAmounts() unexpected error: %v", err)
+			}
+
+			if amountOut == nil || amountOut.Sign() <= 0 {
+				t.Error("CalculateSwapAmounts() returned invalid amountOut")
+			}
+
+			if priceAfter == nil || priceAfter.Sign() <= 0 {
+				t.Error("CalculateSwapAmounts() returned invalid priceAfter")
+			}
+
+			// Verify price moved in correct direction
+			if tt.zeroForOne {
+				if priceAfter.Cmp(tt.sqrtPrice) >= 0 {
+					t.Error("CalculateSwapAmounts() price should decrease for zeroForOne swap")
+				}
+			} else {
+				if priceAfter.Cmp(tt.sqrtPrice) <= 0 {
+					t.Error("CalculateSwapAmounts() price should increase for oneForZero swap")
+				}
+			}
+
+			t.Logf("Swap results:")
+			t.Logf("  amountIn: %v", tt.amountIn)
+			t.Logf("  amountOut: %v", amountOut)
+			t.Logf("  priceBefore: %v", tt.sqrtPrice)
+			t.Logf("  priceAfter: %v", priceAfter)
+		})
+	}
+}
+
+func TestKnownPoolState(t *testing.T) {
+	// Test with known values from a real Uniswap V3 pool
+	// Example: WETH/USDC 0.3% pool on Arbitrum
+
+	// At tick 0, price = 1
+	tick := int32(0)
+	sqrtPrice, err := GetSqrtRatioAtTick(tick)
+	if err != nil {
+		t.Fatalf("GetSqrtRatioAtTick() error: %v", err)
+	}
+
+	// SqrtPrice at tick 0 should be approximately Q96
+	expectedSqrtPrice := Q96
+	tolerance := new(big.Int).Div(Q96, big.NewInt(100)) // 1% tolerance
+
+	diff := new(big.Int).Sub(sqrtPrice, expectedSqrtPrice)
+	if diff.Sign() < 0 {
+		diff.Neg(diff)
+	}
+
+	if diff.Cmp(tolerance) > 0 {
+		t.Errorf("SqrtPrice at tick 0 not close to Q96: got %v, want %v, diff %v",
+			sqrtPrice, expectedSqrtPrice, diff)
+	}
+
+	// Reverse calculation should give us back tick 0
+	calculatedTick, err := GetTickAtSqrtRatio(sqrtPrice)
+	if err != nil {
+		t.Fatalf("GetTickAtSqrtRatio() error: %v", err)
+	}
+
+	if calculatedTick != tick && calculatedTick != tick-1 && calculatedTick != tick+1 {
+		t.Errorf("Tick round trip failed: original=%d, calculated=%d", tick, calculatedTick)
+	}
+}