Curve Finance Explained: Inside the StableSwap AMM and Its Invariant

Curve Finance uses a StableSwap AMM invariant designed specifically for stablecoin swaps, solving the high-slippage problem of traditional constant-product AMMs like Uniswap. The protocol introduces an amplification factor (A) that interpolates between constant-sum behavior (near equilibrium, low slippage) and constant-product behavior (under imbalance, LP protection). Since the invariant D cannot be solved analytically, Curve uses Newton-Raphson iteration with bounded loops (max 64) for gas-safe convergence. The post also covers token decimal normalization across ERC-20 tokens with different precisions, non-standard ERC-20 handling (e.g., USDT), and mainnet-fork testing strategies using Hardhat to validate real-world behavior.