Paper: arXiv 2507.10149

Authors: Abhimanyu Nag, Madhur Prabhakar, Tanuj Behl

Abstract

We propose a mathematically rigorous framework for identifying and completing Coincidence of Wants (CoW) cycles in decentralized exchange (DEX) aggregators. Unlike existing auction based systems such as CoWSwap, our approach introduces an asset matrix formulation that not only verifies feasibility using oracle prices and formal conservation laws but also completes partial CoW cycles of swap orders that are discovered using graph traversal and are settled using imbalance correction. We define bridging orders and show that the resulting execution is slippage free and capital preserving for LPs. Applied to real world Arbitrum swap data, our algorithm demonstrates efficient discovery of CoW cycles and supports the insertion of synthetic orders for atomic cycle closure. This work can be thought of as the detailing of a potential delta-neutral strategy by liquidity providing market makers: a structured CoW cycle execution.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a dense, graph-theoretic and linear-algebraic framework with formal definitions, matrix formulations, and proofs, indicating high mathematical complexity. It is applied to real-world Arbitrum swap data with algorithmic simulations and discusses implementation for synthetic order insertion, demonstrating significant empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal"] --> B["Methodology"]
  B --> C["Data/Inputs"]
  C --> D["Computation"]
  D --> E["Outcomes"]
  
  A["Research Goal<br>Identify CoW cycles<br>for slippage-free execution"]
  
  B["Methodology<br>1. Asset Matrix Formulation<br>2. Graph Traversal<br>3. Imbalance Correction<br>4. Bridging Orders"]
  
  C["Data/Inputs<br>Oracle Prices<br>Conservation Laws<br>Real World Swap Data<br>(Arbitrum)"]
  
  D["Computation<br>Feasibility Verification<br>Partial Cycle Completion<br>Synthetic Order Insertion"]
  
  E["Outcomes<br>Slippage-Free Execution<br>Capital Preservation for LPs<br>Delta-Neutral Strategy Framework"]

Cited References (17)

  1. Decentralized exchange (2017)
  2. Automated market makers and decentralized exchanges: a DeFi primer (2022)
  3. An analysis of intent-based markets (2024) — link
  4. Maximal Extractable Value (MEV) (2023)
  5. A coincidence of wants: The novel and neoclassical economics (2014)
  6. Decentralized finance (2020)
  7. The costs of swapping on decentralized exchanges (2024)
  8. A theory of atomic transactions (1988)
and 9 more
  1. Competitive solvers in action: strategic optimization across CoWs and multi-chain AMMs (2025)
  2. SoK: Decentralized Finance (DeFi)–Fundamentals, Taxonomy and Risks (2024) — link
  3. Arbitrum nitro: A second-generation optimistic rollup (2022)
  4. Uniswap v3 core (2021)
  5. Balancer (2023)
  6. Analysis and Evaluation of the CoW Protocol for MEV Mitigation on the Ethereum Blockchain (2023) — link
  7. Maximal Extractable Value in Batch Auctions (2025)
  8. Impermanent loss and slippage in Automated Market Makers (AMMs) with constant-product formula (2022)
  9. Efficient algorithms for shortest paths in sparse networks (1977)

0 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.