LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization

Abstract:Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work. We present LeanMarathon, a multi-agent harness for reliable research-level Lean autoformalization. Its core abstraction is an evolving blueprint: a Lean file that serves simultaneously as formal proof skeleton, natural-language proof graph, and shared system of record. Four contract-scoped agents construct, audit, prove, and repair this blueprint. These agents are coordinated by a two-stage orchestrator that first stabilizes target fidelity through adversarial review and then discharges the proof directed acyclic graph (DAG) from its dynamic leaves upward in parallel CI-gated rounds. LeanMarathon turns one brittle multi-hour run into many local, recoverable, parallel transactions. We evaluate LeanMarathon on two recent research papers spanning four Erdős problems (#1051, #1196, #164, #1217). Across three autonomous runs, it formalizes all seven target theorems with no sorry, proving 258 lemmas and theorems. These results show that reliable AI co-mathematics requires not only stronger provers, but durable harnesses that preserve target fidelity across long mathematical developments. The code can be found at this https URL.

26 pages, 9 figures. Comments are welcome

Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2606.05400 [cs.AI]

(or arXiv:2606.05400v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2606.05400 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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