Concave Continuation: Linking Routing to Arbitrage

Battle Count: 73

Highly relevant for DeFi quantitative trading, MEV strategies, and algorithmic execution on DEXes. The unified routing-arbitrage framework is directly applicable to on-chain trading bots and liquidity aggregators. The on-chain implementation with reasonable gas costs makes it immediately deployable. However, relevance to traditional quantitative trading (equities, futures) is limited as the framework is specific to AMM-based DEXes.

The algorithm is conceptually simple (iterative price equalization with halving rule) and the paper demonstrates it can run fully on-chain with native Uniswap V3 APIs (quoteExactOutputSingle, sqrtPriceX96After). The mathematical framework (concave continuation) requires understanding of convex analysis and AMM mechanics. The extended halving rule adds modest complexity over the original transfer algorithm. No external solver (like CVXPY) is needed.

The paper provides complete algorithm pseudocode (Algorithms 1-4), mathematical definitions, and three experiments (Python, Julia, Solidity on Base mainnet). However, no explicit code repository is linked. The on-chain experiment references a specific block number (43,550,927) on Base mainnet, enabling partial reproduction. The mathematical framework is self-contained.