mev-beta/docs/MATHEMATICAL_AUDIT_DETAILED_20251101.md

# MEV Bot Mathematical Audit Report
## Comprehensive Review of Calculation Correctness

**Date**: November 1, 2025  
**Scope**: All mathematical calculations in MEV bot  
**Status**: CRITICAL ISSUES IDENTIFIED

---

## Executive Summary

The MEV bot contains **multiple critical mathematical errors** that could lead to:
- Incorrect profit calculations (overestimation)
- Invalid arbitrage execution decisions  
- Gas cost underestimation
- Price impact miscalculations
- Precision loss and rounding errors
- Potential for negative profits despite calculations showing positive

**Severity**: HIGH - Immediate fixes required before production execution

---

## CRITICAL ISSUES FOUND

### 1. PROFIT CALCULATION - ROUNDING ERROR IN profit_calc.go

**Location**: `/home/administrator/projects/mev-beta/pkg/profitcalc/profit_calc.go:199-210`

**Issue**: Profit margin calculation uses integer division which truncates decimal places

```go
// PROBLEMATIC CODE (Line 199-210)
if amountOut.Sign() > 0 && amountOut.Cmp(big.NewFloat(0)) != 0 {
    profitMargin := new(big.Float).Quo(netProfit, amountOut)
    profitMarginFloat, _ := profitMargin.Float64()
    // Ensure the profit margin is reasonable and not extremely high
    if profitMarginFloat > 1.0 { // 100% profit margin is unrealistic
        opportunity.ProfitMargin = 0.0 // Set to 0 if profit margin is unrealistic
        opportunity.IsExecutable = false
        opportunity.RejectReason = "unrealistic profit margin"
        opportunity.Confidence = 0.0
    } else {
        opportunity.ProfitMargin = profitMarginFloat
    }
}
```

**Problem**:
- The condition `profitMarginFloat > 1.0` is checking if profit margin exceeds 100%
- However, this is mathematically incorrect: a 1:1 profit (100% margin) IS possible in arbitrage
- This check REJECTS valid opportunities with 100%+ margins
- The code incorrectly assumes profitable arbitrage cannot exceed 100% margin

**Impact**: HIGH - Rejects all highly profitable arbitrage opportunities

**Fix Required**: Remove the artificial 100% profit margin cap and implement proper validation

---

### 2. SLIPPAGE CALCULATION ERROR - slippage_protection.go

**Location**: `/home/administrator/projects/mev-beta/pkg/profitcalc/slippage_protection.go:59-67`

**Issue**: Slippage formula is oversimplified and incorrect for actual AMM pools

```go
// PROBLEMATIC CODE (Line 59-67)
// Estimate slippage using simplified AMM formula
// For constant product AMMs: slippage ≈ trade_size / (2 * liquidity)
estimatedSlippage := tradeSizeFloat / 2.0

// Apply curve adjustment for larger trades (non-linear slippage)
if tradeSizeFloat > 0.1 { // > 10% of pool
    // Quadratic increase for large trades
    estimatedSlippage = estimatedSlippage * (1 + tradeSizeFloat)
}
```

**Problems**:
1. Formula `tradeSize / (2 * liquidity)` is NOT the correct slippage formula
   - Actual formula for Uniswap V2: `slippage = tradeSize / (2 * liquidity + tradeSize)` (more complex)
   
2. The curve adjustment `(1 + tradeSizeFloat)` is arbitrary
   - When tradeSizeFloat = 0.5 (50% of pool), multiplier = 1.5
   - This doesn't match actual AMM behavior
   
3. Does NOT account for:
   - Fee structures (different by DEX)
   - Token decimals
   - Actual liquidity state changes

**Impact**: CRITICAL - Slippage estimates are wildly inaccurate, leading to:
- Overestimation of profit margins
- Approval of trades that will result in losses
- Risk assessment is completely unreliable

**Math Error**: Should use proper AMM invariant formulas instead of linear approximation

---

### 3. GAS COST CALCULATION - ARBITRARY BUFFER

**Location**: `/home/administrator/projects/mev-beta/pkg/profitcalc/profit_calc.go:271-273`

**Issue**: Gas cost calculation adds arbitrary 20% buffer

```go
// PROBLEMATIC CODE (Line 271-273)
// Add 20% buffer for MEV competition
buffer := new(big.Int).Div(gasCostWei, big.NewInt(5)) // 20%
gasCostWei.Add(gasCostWei, buffer)
```

**Problems**:
1. 20% buffer is ARBITRARY and not based on:
   - Actual MEV competition on Arbitrum
   - Historical gas price volatility
   - Current network conditions
   
2. May be:
   - TOO HIGH: Underestimates profitability unnecessarily
   - TOO LOW: Insufficient for actual MEV competition

3. No dynamic adjustment based on:
   - Network congestion
   - Price impact size
   - Complexity of transaction

**Impact**: MEDIUM - Profit calculations are systematically offset

**Fix**: Calculate actual expected gas based on transaction complexity and network state

---

### 4. PRICE IMPACT CALCULATION - MISSING FEE DEDUCTION

**Location**: `/home/administrator/projects/mev-beta/pkg/math/exchange_math.go:114-147`

**Issue**: Price impact is calculated WITHOUT considering trading fees in initial step

```go
// PROBLEMATIC CODE (Line 128-146)
// Calculate amount out
amountOut, err := u.CalculateAmountOut(amountIn, reserveIn, reserveOut, 3000)
if err != nil {
    return 0, err
}

// New reserves after swap
newReserveIn := new(big.Int).Add(reserveIn, amountIn)  // ← WRONG: doesn't account for fee deduction
newReserveOut := new(big.Int).Sub(reserveOut, amountOut)

// Price after = newReserveOut / newReserveIn
priceAfter := new(big.Float).Quo(new(big.Float).SetInt(newReserveOut), new(big.Float).SetInt(newReserveIn))

// Price impact = (priceBefore - priceAfter) / priceBefore
impact := new(big.Float).Sub(priceBefore, priceAfter)
impact.Quo(impact, priceBefore)
```

**Problem**:
- `newReserveIn` is calculated as `reserveIn + amountIn`
- But in reality, the input amount is `amountInWithFee` after fee deduction
- This causes price impact to be UNDERESTIMATED
- The actual price movement is larger than calculated

**Impact**: CRITICAL - Price impact is underestimated by 0.3-2% depending on fee tier

**Fix**: Use `amountInWithFee` in reserve calculation instead of raw `amountIn`

---

### 5. DIVISION BY ZERO RISK - Multiple Locations

**Location 1**: `/home/administrator/projects/mev-beta/pkg/profitcalc/slippage_protection.go:56`

```go
// PROBLEMATIC CODE
tradeSizeRatio := new(big.Float).Quo(tradeAmount, poolLiquidity)
```

**Issue**: If `poolLiquidity` is zero or extremely small, division fails silently

**Location 2**: `/home/administrator/projects/mev-beta/pkg/math/decimal_handler.go:308-312`

```go
// PROBLEMATIC CODE (Line 308-312)
// Scale numerator to maintain precision
totalDecimals := numerator.Decimals + resultDecimals
scalingFactor := dc.getScalingFactor(totalDecimals - denominator.Decimals)

scaledNumerator := new(big.Int).Mul(numerator.Value, scalingFactor)
quotient := new(big.Int).Div(scaledNumerator, denominator.Value)  // ← No zero check
```

**Impact**: MEDIUM - Silent failures in calculations

---

### 6. OVERFLOW RISK IN MULTIPLICATION - arbitrage_calculator.go

**Location**: `/home/administrator/projects/mev-beta/pkg/math/arbitrage_calculator.go:278`

**Issue**: Large number multiplication without overflow checking

```go
// PROBLEMATIC CODE
product := new(big.Int).Mul(a.Value, b.Value)

// Adjust for decimal places
totalInputDecimals := a.Decimals + b.Decimals
```

**Problem**:
- While Go's `big.Int` can handle large numbers, the multiplication is done BEFORE overflow check
- For very large token amounts (18 decimals), multiplying two large numbers can be slow
- No explicit overflow detection before performing expensive multiplication

**Impact**: LOW - Go handles this, but inefficient

---

### 7. NEGATIVE VALUE HANDLING - decimal_handler.go

**Location**: `/home/administrator/projects/mev-beta/pkg/math/decimal_handler.go:54-58`

```go
// PROBLEMATIC CODE
if value != nil {
    // Check for reasonable bounds - max value should not exceed what can be represented
    // in financial calculations (roughly 2^256 / 10^18 for safety)
    maxValue := new(big.Int)
    maxValue.Exp(big.NewInt(10), big.NewInt(60), nil) // 10^60 max value for safety

    absValue := new(big.Int).Abs(value)  // ← Using Abs() is correct but...
```

**Problem**:
- Code correctly checks `Abs(value)` for upper bound
- But `NewUniversalDecimal` doesn't properly handle NEGATIVE values
- Negative amounts should not be allowed in profit calculations
- No check for negative amounts in critical functions

**Impact**: MEDIUM - Could allow invalid negative profit amounts

---

### 8. UNISWAP V3 PRICE CALCULATION - PRECISION LOSS

**Location**: `/home/administrator/projects/mev-beta/pkg/uniswap/pricing.go:22-45`

**Issue**: SqrtPriceX96 to Price conversion loses precision

```go
// PROBLEMATIC CODE
// Convert to big.Float for precision
sqrtPrice := new(big.Float).SetPrec(256).SetInt(sqrtPriceX96)

// Calculate sqrtPrice^2
price := new(big.Float).SetPrec(256)
price.Mul(sqrtPrice, sqrtPrice)

// Divide by 2^192 using global cached constant
denominator := new(big.Float).SetPrec(256).SetInt(GetQ192())
price.Quo(price, denominator)
```

**Problem**:
- Precision of 256 bits = ~77 decimal digits
- Actual prices are often in 10-18 decimal range
- Converting from `big.Int` to `big.Float` and back loses lower bits
- SetFloat64(0.0) for invalid input silently returns 0

**Impact**: MEDIUM - Slight precision loss in V3 price calculations

---

### 9. PROFIT THRESHOLD COMPARISON - TYPE MISMATCH

**Location**: `/home/administrator/projects/mev-beta/pkg/profitcalc/profit_calc.go:214-216`

```go
// PROBLEMATIC CODE
if netProfit.Sign() > 0 {
    netProfitWei, _ := netProfit.Int(nil)  // ← Converts big.Float to big.Int
    if netProfitWei.Cmp(spc.minProfitThreshold) >= 0 {
```

**Problem**:
- `netProfit` is `*big.Float`
- Converting to `big.Int` truncates ALL decimal places
- For ETH with 18 decimals: 0.0001 ETH becomes 0 (100 wei becomes 0 in Int representation)
- This causes profits < 1 wei to be rejected as "below threshold"

**Impact**: CRITICAL - Legitimate small profit opportunities are rejected

**Example Bug**:
```
netProfit = 0.00005 ETH (50000 wei as float)
netProfitWei, _ := netProfit.Int(nil)  // Returns 0 (rounds down)
netProfitWei.Cmp(0.01 ETH) >= 0  // FALSE - rejects valid opportunity
```

---

### 10. MISSING ROUND-UP IN AMOUNT CALCULATIONS

**Location**: `/home/administrator/projects/mev-beta/pkg/math/exchange_math.go:107-109`

```go
// PROBLEMATIC CODE
// amountIn = numerator / denominator + 1 (round up)
amountIn := new(big.Int).Div(numerator, denominator)
amountIn.Add(amountIn, big.NewInt(1))
```

**Problem**:
- Comment says "round up" but this ALWAYS adds 1
- Should use proper banker's rounding or conditional rounding
- Adding 1 to every result causes slight overestimation

**Impact**: LOW-MEDIUM - Slight overestimation of required input amounts

---

## SUMMARY TABLE

| Issue | Severity | Type | Impact |
|-------|----------|------|--------|
| 1. Profit margin cap at 100% | HIGH | Logic Error | Rejects valid opportunities |
| 2. Slippage formula incorrect | CRITICAL | Math Error | Wildly inaccurate slippage |
| 3. Gas cost buffer arbitrary | MEDIUM | Configuration | Systematic bias in profits |
| 4. Price impact misses fees | CRITICAL | Calculation Error | Underestimates price movement |
| 5. Division by zero risk | MEDIUM | Input Validation | Silent failures |
| 6. Overflow in multiplication | LOW | Performance | Slow for large numbers |
| 7. Negative value handling | MEDIUM | Validation | Invalid states allowed |
| 8. V3 price precision loss | MEDIUM | Precision | Slight accuracy loss |
| 9. Float to Int conversion | CRITICAL | Type Error | Legitimate profits rejected |
| 10. Always round up by 1 | LOW | Rounding | Slight overestimation |

---

## RECOMMENDATIONS

### Immediate (Critical Priority)
1. **Fix profit margin check** - Remove 100% cap, allow any positive profit
2. **Fix slippage calculation** - Implement proper AMM invariant formulas
3. **Fix profit threshold comparison** - Properly compare float values without truncation
4. **Fix price impact** - Use fee-adjusted amounts in reserve calculations

### Short-term (High Priority)
5. Add division-by-zero checks everywhere
6. Implement proper rounding strategies
7. Add overflow detection before large multiplications
8. Test against known Arbitrum DEX prices

### Medium-term (Medium Priority)
9. Dynamic gas cost calculation based on network state
10. More accurate slippage models for each DEX type
11. Proper handling of negative values and edge cases

---

## TESTING RECOMMENDATIONS

Create test cases for:
- Arbitrage with >100% profit margins
- Small profit amounts (<0.001 ETH)
- Very large trade sizes (>50% of pool)
- Extreme price impacts (>10%)
- Zero and near-zero liquidity
- Fee-adjusted amount calculations

---

Generated: November 1, 2025