LeanFlow Automates Mathematical Paper Formalization with LLM Agents

This paper introduces LeanFlow, an AI agent system powered by large language models (LLMs) specifically engineered to automate the formalization of mathematical papers. The system's primary function is to convert complex mathematical texts into executable Lean projects, a formal proof assistant. The research investigates how different runtime mechanisms influence the completion, auditability, and efficiency of this document-to-project formalization process. The study involved case studies on two previously unformalized mathematical papers, one in number theory and another in measure theory. Using models like Kimi2.6 and GPT5.5, the researchers performed ablations on the model, proof-workflow, and toolset, meticulously tracking task outcomes, API calls, and token usage. Results showed that with Kimi2.6, the full LeanFlow workflow successfully completed both document-level projects within a 2000-call budget, while variants without a queue hit the budget limit. With GPT5.5, all document-level variants completed, and the full workflow consistently demonstrated the lowest or tied-lowest input-token cost for both source papers. Complementary evaluations on benchmarks like the PFR slice of RLM25 and ICML 2026 AI for Math TCS challenge projects further validated LeanFlow's capabilities, achieving 75.7% BEq+ and solving all five challenge projects with GPT5.5.