This is a combined digest of five papers from the late-Apr to mid-May 2026 window that share an AMM-mathematics / LP-economics theme. They are tangentially connected to MEV (LP economics, arbitrage stability, prediction-market microstructure, agentic DeFi infrastructure) and are grouped here for indexing economy.

1. From Impermanent Loss to Sustainable Gain (Melnikov et al.)

Citation: Melnikov, I., Vlasov, R., Gorgadze, V., Seoev, A., Yanovich, Y. arXiv:2604.28014v1 [cs.DC] (Apr 30, 2026). Skoltech / MIPT / IDEAS / MEV-X.

Core idea: Reframes the LP-vs-arbitrageur conflict as symbiotic within a specific price-deviation range. Builds on the Impermanent Gain (IG) concept: when DEX↔CEX price deviation is small enough, fees from arb trades exceed the resulting IL → net LP profit.

Contributions:

  • Joint profitability model for arb + LP on CFMMs (Uniswap V2, Balancer).
  • Closed-form analytical bounds for Uniswap V2 defining the price-ratio interval where arbitrage is profitable for both arbitrageur and LP — a “symbiotic equilibrium zone”.
  • Probabilistic risk framework: GBM model for external price → upper bound on expected blocks until IL.
  • Lower bound on the pool fee required to achieve a target probability of staying in the IG zone within a block.
  • Validation: deployed both baseline and private (whitelisted-arbitrageur) pools on-chain, demonstrated stable returns with reduced IL in the curated configuration.

Why MEV-relevant: explicit framing of arbitrageur-LP relationship as design parameter — connects to PropAMMs: Proportional AMMs and On-Chain Market Making (which goes the other direction: replace bonding curves entirely), and to Arbitrage: CEX-DEX and AMM Arb (CEX-DEX arb is the canonical IG-creating activity).

2. Characterizing Path-Independent Fees: Zero Impermanent Loss in CPMMs (Voronin et al.)

Citation: Voronin, A., Vlasov, R., Gorgadze, V., Seoev, A., Yanovich, Y. arXiv:2604.28017v1 [cs.DC] (Apr 30, 2026). Novosibirsk State / MIPT / IDEAS / MEV-X / Skoltech.

Core problem: When fees in a CPMM (Uniswap V2 / V4) are auto-reinvested into the pool, the final pool state after a trade can depend on how the trade is split into smaller transactions — path dependence. This breaks composability guarantees and creates strategic-fragmentation incentives.

Contributions:

  • Characterization theorem: the complete functional class of fee structures that ensure path independence is exactly those where the combined fee factor depends only on the current pool invariant k = xy.
  • For this class, derives a system of ODEs governing pool dynamics + a closed-form integral exchange formula.
  • Constructs a parametric family of fee functions that achieve zero IL for a given initial pool state.
  • Negative result: no single fee function can eliminate IL for all initial states simultaneously.
  • Analyzes implications for arbitrage windows and slippage; validated by controlled simulations.

Why MEV-relevant: path-dependence creates a category of fragmentation MEV (arbs splitting trades to reduce effective fees or exploit slippage patterns). The path-independence characterization gives protocol designers a principled fix that closes that vector.

3. Arbitrage Analysis in Polymarket NBA Markets (Cheng, Yang, Zou)

Citation: Cheng, G., Yang, J., Zou, H. arXiv:2605.00864v1 [q-fin.TR] (Apr 22 → May 5, 2026). UCLA.

Empirical scope: 75M+ limit-order-book snapshots, 173 NBA games on Polymarket. First systematic high-frequency arbitrage analysis of a major decentralized prediction market.

Headline numbers:

  • Single-market arbitrage: 7 executable in-game episodes, median duration 3.6 seconds → microstructurally efficient.
  • Combinatorial arbitrage: 290 active episodes, overwhelmingly concentrated in final minutes of live play. Median return: 101 bps.
  • Theoretical “Middle” jackpot: never empirically realized.
  • 76.9% of combinatorial opportunities constrained to average executable size of just 14.8 shares by shallow order-book depth → executable mispricings exist but are structurally bounded by liquidity, confining risk-free extraction strictly to retail scale.

NBA market significance: ~30% of Polymarket’s sports activity in 2025 → high-liquidity, structurally regular venue.

Why MEV-relevant: prediction markets are an emerging MEV venue; the result that combinatorial mispricings exist but are liquidity-bounded informs the Paper: Blockspace Under Pressure — Spam MEV on High-Throughput Blockchains / Arbitrage: CEX-DEX and AMM Arb literature on what fraction of theoretical MEV is actually capturable. Also validates the “10-day, 252-commit, 52% win-rate prediction-market bot” anecdote on a more rigorous empirical footing.

4. Arbitrage and the Stability of AMM Price Tracking (Li, Dahmani, Cai)

Citation: Li, P., Dahmani, N., Cai, W. arXiv:2605.06060v1 [cs.CE] (May 7, 2026).

Core question: When does AMM-vs-reference price tracking remain stable under realistic blockchain execution constraints (fees, discrete blocks, ordering, delays, tx failure)?

Contributions:

  • Block-scale stochastic closed-loop model: tracking error as the state, arbitrage as the corrective input, blockchain execution inside the loop.
  • Reduces the execution layer to a single per-block summary: total successful correction confirmed in each block.
  • Under a block-level correction condition, proves geometric ergodicity of the tracking error.
  • Explicit one-step bounds connecting tracking quality to liquidity and execution quality.
  • For CPMMs: how fees, fixed execution costs, and local liquidity map into the no-trade band and the optimal corrective trade.
  • Empirical proxies for theorem quantities from realized block data → reduced simulation framework.

Why MEV-relevant: formalizes the causal link between MEV-extraction quality and oracle/AMM trust. In environments where arb extraction is degraded (failed tx, censoring), tracking error grows → AMM prices become less reliable as oracles for downstream protocols (lending collateral marks, derivatives settlement). Connects directly to PropAMMs: Proportional AMMs and On-Chain Market Making design and Bridge Finality Risks and Pre-Finality Actions.

5. State Twins: An Off-Chain Substrate for Agentic Reasoning over DeFi (Moore)

Citation: Moore, I. C. arXiv:2605.11522v1 [cs.DC] (May 12, 2026). DeFiMind.

Core problem: Agentic DeFi stacks today couple reasoning to chain time — every “what-if?” query incurs a new RPC read or a real transaction. Counterfactual queries, multi-scenario evaluation, “thinking before acting” are not first-class operations in this reactive architecture.

Contributions:

  • Formalizes each AMM family (Uniswap V2/V3, Balancer, Stableswap) as a discrete-time controlled dynamical system.
  • The State Twin: typed, in-memory, replayable replica of an on-chain AMM pool that preserves the protocol’s exact mathematics while admitting forking, replay, branching, counterfactual rollout.
  • Proves a quantitative fidelity bound on twin↔chain divergence.
  • Open architecture (DeFiPy v2): Python toolkit + reference Model Context Protocol (MCP) server exposing typed analytical primitives as LLM tools.
  • Same primitive serves a notebook quant, a backtest, and an LLM agent without modification.
  • Worked example: single live RPC seed → N independent in-memory twins under distinct price-shock scenarios, sub-second wall-clock.

Why MEV-relevant: agentic MEV is a coming category (cf Paper: Timing Games — Probabilistic Backrunning and Spam (Flashbots/Offchain Labs) note that >50% of OpenTTT PoT records were generated by AI agents via MCP calls). State Twins is the substrate that makes counterfactual MEV-strategy reasoning tractable for agents — searchers / market makers can run fork-and-evaluate in sub-second wall-clock time, which fundamentally changes the latency landscape.

Cross-Cluster Themes

  1. AMM-LP economics matures into a real research field — closed-form bounds (papers 1, 2), stability theorems (paper 4), agentic substrates (paper 5).
  2. MEV-X and MIPT/Skoltech as a publishing cluster — papers 1, 2, plus the standalone “Origins of MEV” paper share authors. Russian academic-blockchain pipeline producing significant volume.
  3. “Arb is required for stability” thread — paper 4 makes the CFMM stability claim conditional on arb working; paper 1 makes the LP profitability claim conditional on arb being symbiotic; together they form an emerging consensus that arb is load-bearing infrastructure, not just rent-extraction.
  4. Agentic-everything — paper 5 plus the Untapped Gardens “autonomous agent economies” thesis (Institutional DeFi as a Systems Problem) plus the OpenTTT >50%-of-records-from-AI-agents observation (Paper: Timing Games — Probabilistic Backrunning and Spam (Flashbots/Offchain Labs)) → the AI-agent share of on-chain compute and MEV is becoming a research category in its own right.

See Also