Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Goedel-Architect is an agentic framework for formal theorem proving in Lean 4, centered on blueprint generation and refinement. It constructs a dependency graph of definitions and lemmas, which a Lean prover then attempts to close in parallel. Failed lemmas drive global blueprint refinement, a strategy that avoids inefficient recursive decomposition. Using the open-weight DeepSeek-V4-Flash (284B-A13B) backbone, Goedel-Architect achieves 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With optional natural-language proof guidance, it reaches 100% on MiniF2F-test and 88.8% on PutnamBench. It also solves 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This pipeline delivers leading performance for an open-source solution, costing up to 500 times less than comparable alternatives.

Key takeaway

For AI Scientists and ML Engineers developing formal verification systems, Goedel-Architect presents a compelling open-source solution. Its blueprint generation and refinement approach, powered by DeepSeek-V4-Flash, delivers leading performance on benchmarks like PutnamBench at significantly reduced costs. Consider integrating this pipeline for complex mathematical problems. You should especially leverage natural-language proof guidance to improve initial blueprint quality and overall solve rates.

Key insights

Goedel-Architect streamlines formal theorem proving via iterative blueprint generation and refinement, leveraging an open-weight LLM.

Principles

• Utilize a global dependency graph for parallel lemma proving.
• Iteratively refine blueprints based on specific prover failure diagnoses.
• Natural language proofs can structurally guide initial blueprint generation.

Method

Generate an initial dependency graph blueprint, then iteratively prove lemmas in parallel. Refine the global blueprint based on prover diagnoses (statement_wrong, proof_too_hard) until all nodes are solved.

In practice

• Integrate DeepSeek-V4-Flash for high-performance, low-cost formal proving.
• Seed initial blueprints with natural-language proofs for challenging problems.
• Analyze negated sub-lemmas or forfeited proofs for targeted blueprint revisions.

Topics

• Formal Theorem Proving
• Lean 4
• Agentic AI
• Blueprint Generation
• DeepSeek-V4-Flash
• Mathematical Reasoning

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.