Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement
On the map: LLM agents and tool use → Educational agents and math problem solving
Abstract (arXiv)
We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies. This blueprint is 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 strategy contrasts with other mainstream approaches which 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 the harder problems, we additionally close the remaining two MiniF2F-test problems (reaching 100%), lift PutnamBench to 88.8% (597/672), and solve 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This represents state-of-the-art performance for an open-source pipeline at a price point up to 500x less than comparable open-source pipelines.
Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use. Builds on 20 of its 28 references that are in the map. First posted on arXiv 4 Jun 2026.
Builds on
20 of 28 references.
Closest ancestors · 2
Same direction, newest first
- 2026A Minimal Agent for Automated Theorem Proving27 Feb
- 2026Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics20 Jan
Other references · 18
- 2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,796
- 2021MiniF2F: a cross-system benchmark for formal Olympiad-level mathematicscited by 391
- 2022Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofscited by 291
- 2025DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decompositioncited by 287
- 2024DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Datacited by 234
- 2024DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Searchcited by 197
- 2025Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learningcited by 180
- 2024PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competitioncited by 165
- 2025Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correctioncited by 154
- 2025Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Provingcited by 133
- 2025Seed-Prover: Deep and Broad Reasoning for Automated Theorem Provingcited by 101
- 2024Lean-STaR: Learning to Interleave Thinking and Provingcited by 68
6 more
- 2025Hilbert: Recursively Building Formal Proofs with Informal Reasoningcited by 60
- 2024TheoremLlama: Transforming General-Purpose LLMs into Lean4 Expertscited by 59
- 2025Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experiencecited by 44
- 2024HunyuanProver: A Scalable Data Synthesis Framework and Guided Tree Search for Automated Theorem Provingcited by 33
- 2026LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learningcited by 7
- 2026LeanArchitect: Automating Blueprint Generation for Humans and AIcited by 6
Built on by
Citing papers per year: 2026: 9.
9 papers.
- 2026BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprintscited by 2
- 2026Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolutioncited by 1
- 2026Theoretical Foundations of max@k Reinforcement Learningcited by 0
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Sciencecited by 0
- 2026FORALL-LEAN-AGENT for Auditable Reasoning in Formal Mathematics and Software Verificationcited by 0
- 2026Cost-Efficient Theorem Proving via Agent Orchestration in Program Verificationcited by 0
- 2026LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphscited by 0
- 2026Humanize Olympiad Agents: A Multi-Session Workflow for Olympiad Problem Solving with Solve, Review, Wiki, Verifycited by 0
- 2026Do Theorem Provers Need Theorem-Proving Agents? mini-Lean-agent: A Coding-Agent Baseline for Leancited by 0
- 2026Do Theorem Provers Need Theorem-Proving Agents? mini-Lean-agent: A Coding-Agent Baseline for Lean12 Oct 2026
- 2026Humanize Olympiad Agents: A Multi-Session Workflow for Olympiad Problem Solving with Solve, Review, Wiki, Verify9 Oct 2026
- 2026LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs8 Oct 2026
- 2026Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification7 Oct 2026
- 2026FORALL-LEAN-AGENT for Auditable Reasoning in Formal Mathematics and Software Verification1 Oct 2026
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science28 Sep 2026
- 2026BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprints30 Jul 2026
- 2026Theoretical Foundations of max@k Reinforcement Learning20 Jul 2026
- 2026Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolution19 Jul 2026
Similar, not cited
Close in wording, no citation either way
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- 2026DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent
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- 2026MechMath: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving
- 2026LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks
- 2025Prover Agent: An Agent-Based Framework for Formal Mathematical Proofs