AI that proves theorems from a "blueprint" — "Goedel-Architect" for formal theorem proving in Lean 4

This work (Goedel-Architect) has AI plan a "blueprint" before formally proving a theorem.

Goedel-Architect is an agentic framework for formal theorem proving in the Lean 4 proof assistant, centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem.

First, it generates a blueprint of formally stated definitions and lemmas, along with declared dependencies (optionally guided by a natural-language proof). Then a tool-equipped Lean prover component closes each open lemma node in parallel using relevant dependencies. Failed lemmas, in turn, drive refinement of the global blueprint. This contrasts with mainstream approaches that use recursive lemma decomposition and can inefficiently loop on dead-end strategies.

Using the open-weight DeepSeek-V4-Flash (284B-A13B) as the backbone, Goedel-Architect attains 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With an optional natural-language proof seeding the initial blueprint on harder problems, it closes the remaining two MiniF2F-test problems (100%), lifts PutnamBench to 88.8% (597/672), and solves 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026 — state-of-the-art for an open-source pipeline at up to 500x lower cost than comparable ones.