Verifier-in-the-loop systems can produce large Lean artifacts from mathematical documents. It is unclear which runtime mechanisms affect completion, auditability, and efficiency when a whole paper is formalized into a buildable project.

LeanFlow runs a deterministic source preflight and builds a blueprint mapping source spans to planned Lean declarations. A statement/source gate checks faithfulness before proof search. A programmatic workflow manager then assigns one proof obligation at a time, keeps failed-attempt memory, and accepts an edit only after Lean/Lake verification and a hygiene scan for sorry and axioms. LeanProbe supplies low-latency cached checks, and ablations remove the queue and swap the full toolset for CLI-only access, using Kimi-K2.6 and GPT-5.5.

With Kimi-K2.6, the full workflow completed both previously unformalized papers (a number-theory paper on Pythagorean polynomials and a measure-theory paper on Cramer–Wold) within the 2000-call budget, while no-queue variants exhausted the budget. With GPT-5.5, all document-level variants completed, and the full workflow had the lowest or tied-lowest input-token cost. LeanFlow reached 75.7% BEq+ on the PFR slice of RLM25 and solved all five ICML 2026 AI for Math TCS challenge projects.