Paper: arXiv 2604.02909

Authors: Ruichao Jiang, Long Wen

Abstract

We extend AMM trade functions to negative inputs via the \textit{concave continuation}, derived from the invariance of the local conservation law under allocation direction flips. This unifies routing and arbitrage into a single problem. We extend the one-hop transfer algorithm proposed in \cite{jiang} to this setting.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically elegant theoretical framework (‘concave continuation’) that unifies order routing and arbitrage in Automated Market Makers (AMMs). However, as a purely theoretical extension of existing DeFi mechanics, it lacks empirical backtesting, empirical validation, or real-world transaction data analysis.

Research Flowchart

  flowchart TD
    A[Research Goal: Unify AMM Routing & Arbitrage] --> B[Inputs: AMM Trade Functions & Asset Allocations]
    B --> C[Methodology: Derive Concave Continuation via Local Conservation Law]
    C --> D[Methodology: Extend One-Hop Transfer Algorithm to Negative Inputs]
    D --> E[Computational Optimization Across One-Hop AMM Paths]
    E --> F[Outcome: Single-Framework Solver for Joint AMM Routing & Arbitrage]

Cited References (9)

  1. Optimal Routing for Constant Function Market Makers (2022)
  2. CFMMRouter.jl (2023) — link
  3. Convex Network Flows (2024) — link
  4. An Efficient Algorithm for Optimal Routing Through Constant Function Market Makers — → 2302.04938
  5. Short Paper: Transfer Algorithm for On-Chain One-Hop Routing (2026)
  6. On the Convergence Rate of the One-Hop Transfer Algorithm (2026) — link
  7. Uniswap v2 Core (2020) — link
  8. Uniswap v3 Core (2021) — link
and 1 more
  1. Quantifying Sub-Optimality in Routing for Automated Market Makers (2026)

1 of 9 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.