Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement
Jui-Hui Chung, Ziyang Cai, Zihao Li, Qishuo Yin, Rohit Agarwal, Simon Park, Rodrigo Porto, Narutatsu Ri
Abstract
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.
AI Impact Assessments
(1 models)Scientific Impact Assessment: Goedel-Architect
1. Core Contribution
Goedel-Architect introduces a blueprint-based paradigm for formal theorem proving in Lean 4 that differs meaningfully from the dominant recursive decomposition approach. The key insight is to generate an entire dependency graph (a "blueprint") of definitions and lemmas upfront, then prove each node in parallel with access only to its declared dependencies, and iteratively refine the blueprint based on structured failure diagnostics. This contrasts with top-down recursive subgoal decomposition (as in Hilbert) which can loop on dead-end strategies because it commits incrementally without global visibility.
The pipeline has three stages: (1) blueprint generation producing a well-typed, acyclic dependency graph; (2) parallel theorem proving of individual nodes with tool-integrated reasoning (Lean compiler + Mathlib retrieval); and (3) blueprint refinement consuming structured per-node diagnostics (negated sub-lemmas, forfeit analyses) to revise the global strategy. An optional natural-language proof can seed the initial blueprint for harder problems.
2. Methodological Rigor
The experimental evaluation is strong in several dimensions:
However, there are methodological concerns:
3. Potential Impact
Practical democratization: Perhaps the most significant impact is making competitive formal theorem proving accessible to researchers without frontier model API budgets. At $0.44/problem on PutnamBench using open-weight models, this is genuinely transformative for the field's accessibility.
Architectural paradigm: The blueprint-as-dependency-graph approach offers a compelling alternative to recursive decomposition. The idea that global strategy revision (rather than local subgoal retry) is the right abstraction for hard theorem proving could influence how future systems are designed, both in formal math and potentially in other structured reasoning domains (program synthesis, planning).
Diagnostic channels: The negated sub-lemma and structured forfeit mechanisms are elegant engineering contributions. Converting failure into localized, actionable diagnostic signals (rather than just "retry") is a broadly applicable idea for agentic systems.
Benchmark advancement: 100% on MiniF2F-test (first reported) and 88.8% on PutnamBench with NL guidance are milestone numbers, though the latter uses natural-language proofs as input, which somewhat changes the problem definition.
4. Timeliness & Relevance
This work addresses a genuine bottleneck: the field has strong formal provers but they're either closed-source, prohibitively expensive, or weak on hard problems. The gap between frontier closed systems (Seed-Prover, AlphaProof) and what's available to the broader community has been widening. Goedel-Architect narrows this gap substantially with open weights and pipeline code.
The timing is also apt given the rapid development of mathematical AI capabilities and growing need for formal verification of AI-generated proofs. As LLMs generate increasingly sophisticated mathematical arguments, the ability to formally verify them cheaply becomes critical infrastructure.
5. Strengths & Limitations
Key Strengths:
Notable Limitations:
Overall Assessment
Goedel-Architect makes a strong engineering and systems contribution to formal theorem proving, establishing that thoughtful pipeline design with open-weight models can rival or exceed expensive frontier systems. The blueprint paradigm is a genuine conceptual contribution, and the cost efficiency results are striking. The work is timely and addresses real barriers to adoption. However, the paper would benefit from deeper analysis of when and why the approach fails, more rigorous ablation of natural-language guidance, and theoretical motivation for the blueprint over recursive approaches.
Generated Jun 5, 2026
Comparison History (23)
Paper 1 likely has higher impact: it introduces a distinct blueprint-based agentic paradigm for Lean proving, demonstrates very large performance gains on widely used benchmarks (MiniF2F, PutnamBench) plus strong results on contemporaneous contest sets, and claims substantial cost efficiency—supporting broad real-world adoption in formal verification and math automation. Methodology appears system-level and validated across multiple datasets. Paper 2 offers a useful interpretability/control lens for activation steering, but its contribution is primarily explanatory/diagnostic and likely narrower in immediate downstream application breadth and measurable step-change performance.
Goedel-Architect achieves extraordinary results in formal theorem proving: 100% on MiniF2F-test, 88.8% on PutnamBench, and strong IMO/Putnam/USAMO performance—representing a massive leap over prior state-of-the-art. The blueprint generation and refinement paradigm is a novel architectural contribution to automated reasoning. Its open-source nature and 500x cost reduction dramatically broaden accessibility. Paper 2 addresses a useful but narrower problem (skill construction from traces) with more incremental improvements (10.5% gain). Paper 1's impact spans AI, mathematics, and formal verification, making it significantly more consequential.
Paper 1 presents a concrete, measurable breakthrough in AI for formal mathematics, achieving state-of-the-art performance on highly rigorous benchmarks like MiniF2F (up to 100%), IMO, and Putnam. Its empirical success, cost-efficiency, and open-source nature offer immediate, broad utility across AI and mathematics. Paper 2, while philosophically significant and timely, proposes a theoretical ethical framework that lacks the immediate, quantifiable scientific utility and technological applicability of Paper 1's algorithmic achievements.
Paper 2 achieves groundbreaking, state-of-the-art results in formal theorem proving, solving highly complex IMO and Putnam problems while reaching up to 100% on MiniF2F. Its blueprint generation and refinement approach represents a major leap in automated mathematical reasoning, a high-interest field, promising broader impact than Paper 1's tool planning improvements.
Paper 1 presents a highly innovative agentic framework for formal theorem proving that achieves striking state-of-the-art results on extremely challenging benchmarks (100% on MiniF2F, strong performance on IMO 2025). Advancing AI mathematical reasoning and formal verification is currently a frontier with massive implications for AGI development. While Paper 2 offers a solid optimization insight for imbalanced learning, Paper 1 represents a major, cost-effective leap in automated reasoning, yielding a much higher potential breadth of impact and timeliness in the current AI landscape.
Paper 2 presents a paradigm-shifting breakthrough in AI-driven formal theorem proving, achieving unprecedented results (100% on MiniF2F-test, state-of-the-art on IMO/Putnam) using a novel blueprint generation framework. While Paper 1 offers a valuable, practical DRL application for pharmaceutical supply chains, its methodological contribution is largely incremental. Paper 2's immense leaps in advanced mathematical reasoning capabilities and extreme cost-efficiency demonstrate significantly higher novelty, timeliness, and potential to broadly impact both the artificial intelligence and mathematics fields.
Paper 1 likely has higher scientific impact due to broader novelty and generality: it proposes a scalable task family (OPT*) to study optimization-like step-by-step reasoning across expanding search spaces without new labels, introduces training regimes (solver-guided online PO and solver-free offline RL), and offers theoretical framing relating performance to information gained per search budget. This can transfer to many real-world planning/optimization domains beyond math/proving. Paper 2 is highly timely and strong empirically, but is more domain-specific (Lean theorem proving) and primarily an engineering/system advance, limiting breadth despite impressive results.
Goedel-Architect achieves extraordinary results in formal theorem proving: 100% on MiniF2F-test, 88.8% on PutnamBench, and strong performance on IMO 2025 and Putnam 2025 — representing a massive leap in automated mathematical reasoning. The blueprint-based approach is highly novel, and achieving these results with open-weight models at 500x lower cost is transformative for the field. Paper 2 introduces a useful but incremental idea (consequence-aware compute allocation) with moderate improvements on software engineering benchmarks. Paper 1's breakthrough results will have far broader impact across AI, mathematics, and formal verification.
Goedel-Architect demonstrates groundbreaking results in formal theorem proving, achieving 100% on MiniF2F-test and near-perfect scores on PutnamBench, solving IMO/Putnam/USAMO competition problems—representing clear state-of-the-art with dramatic cost reductions (500x). The blueprint generation paradigm is a novel architectural contribution with broad implications for mathematical reasoning and formal verification. Paper 1 offers a useful conceptual bridge between traditional XAI and agentic systems but is more of a diagnostic/evaluation framework comparison with incremental insights, whereas Paper 2 pushes the frontier of AI capabilities in mathematics with immediately measurable, record-setting results.
Paper 2 has higher potential impact due to a more novel, broadly applicable methodology (agentic blueprint generation/refinement for Lean proving) and clear, state-of-the-art quantitative gains on widely recognized benchmarks (MiniF2F, PutnamBench, competition problems). Its applications span formal methods, mathematics, software verification, and AI tooling, making cross-field impact large and timely given rapid advances in LLM-based theorem proving. Paper 1 is solid and useful but is narrower (Japan-specific veterinary pharmacovigilance) and largely incremental in using standard unsupervised clustering with domain tailoring.
Goedel-Architect achieves extraordinary results in formal theorem proving: 100% on MiniF2F-test, 88.8% on PutnamBench, and strong performance on IMO 2025 and Putnam 2025—representing massive leaps over prior state-of-the-art. The blueprint generation and refinement paradigm is a novel architectural contribution with immediate practical applications in mathematics and formal verification. The 500x cost reduction and use of open-weight models further amplify impact. Paper 2 contributes a useful but niche dataset for human-AI collaboration research with more incremental impact on the field.
Paper 2 demonstrates state-of-the-art performance in automated formal theorem proving, a highly significant and challenging area in AI. Achieving near-perfect scores on rigorous benchmarks like MiniF2F and solving IMO problems represents a major methodological breakthrough with profound implications for both mathematics and advanced AI reasoning. While Paper 1 offers a practical and useful approach to infrastructure inspection, its scope, novelty, and potential breadth of impact are significantly narrower compared to the AI advancements presented in Paper 2.
Paper 2 likely has higher impact due to a more novel, generally applicable agentic paradigm (global blueprint generation/refinement) and exceptionally strong, state-of-the-art results across multiple challenging benchmarks (MiniF2F, PutnamBench, IMO/Putnam/USAMO) with large cost advantages. Its applications span automated reasoning, math, verification, and software/hardware assurance, giving broader cross-field relevance. Paper 1 is timely and practically important for networking reliability, but the contribution appears more incremental (benchmarking/tool-augmentation with modest gains) and narrower in scope.
Paper 1 demonstrates a breakthrough in AI-driven formal theorem proving, a fundamental and highly competitive area of AI research. Achieving 100% on MiniF2F and solving recent IMO problems at vastly reduced compute costs signals state-of-the-art innovation with broad implications for mathematical reasoning and AGI. In contrast, while Paper 2 explores interesting concepts in Graph RAG, its empirical evaluation is severely limited by a trivially small dataset (46 nodes, 23 queries). Therefore, Paper 1 exhibits vastly superior methodological rigor, scale, and potential impact on the broader AI community.
Paper 2 addresses a fundamental challenge in latent reasoning and test-time compute, which are highly relevant to current LLM advancements. By introducing a reconstruction-based fidelity check, it offers an elegant, self-supervised method applicable across broad domains (Math, QA, Code). While Paper 1 achieves impressive SOTA results in formal theorem proving, Paper 2's methodological innovation in latent space anchoring promises wider and more foundational impact across the field of AI.
Paper 1 likely has higher impact: it introduces a novel blueprint-based, parallelizable agentic framework for Lean theorem proving, demonstrates large state-of-the-art gains on widely recognized benchmarks (MiniF2F, PutnamBench) and recent competition-style problems, and emphasizes strong cost/performance—suggesting broad practical uptake in formal methods and AI-assisted mathematics. Its applications span automated reasoning, verification, and ML-for-math, with timely relevance given rapid progress in LLM-based provers. Paper 2 is a solid algorithmic contribution but appears narrower in scope and impact.
Goedel-Architect demonstrates concrete, verifiable state-of-the-art results on established benchmarks (100% MiniF2F-test, 88.8% PutnamBench, strong IMO/Putnam/USAMO results) with practical advantages (500x cost reduction, open-source). It advances formal theorem proving with a novel blueprint-based architecture that is immediately impactful. Paper 1 makes extraordinarily bold claims ('universally superior physical substrate') but operates on toy problems (5-qubit, Z_11, S_4) with limited NISQ validation, and its claims of superiority over classical networks are not convincingly demonstrated at meaningful scale.
Paper 2 has higher potential scientific impact: it introduces a broadly applicable abstraction (typed federated artifacts) that enables new guarantees and operations (field-wise DP, schema-aware merging, cross-architecture transfer) in federated settings where sharing weights/data is infeasible. This has clear real-world relevance for privacy-preserving, multi-organization LLM tooling and can influence federated learning, systems, security/privacy, and interoperability standards. Paper 1 is strong and timely with impressive benchmark gains, but is more domain-specific (Lean theorem proving) and appears primarily as an engineering/algorithmic pipeline improvement with narrower cross-field spillover.
Paper 2 likely has higher scientific impact: it introduces a novel agentic blueprint/refinement paradigm for Lean theorem proving, achieves striking state-of-the-art results across multiple established benchmarks (MiniF2F, PutnamBench) and recent contest sets, and emphasizes efficiency/cost reductions that can broaden adoption. Its methodological contribution (global dependency-graph planning + parallel lemma closure + iterative refinement) is broadly applicable to formal methods, AI reasoning, and verification. Paper 1 is valuable and timely for clinical ML robustness, but its impact is more domain-specific and incremental relative to fast-moving retrieval/representation work.
Goedel-Architect achieves groundbreaking results in formal theorem proving—100% on MiniF2F-test, 88.8% on PutnamBench, and strong performance on IMO/Putnam/USAMO competitions—representing a major leap in automated mathematics. The blueprint generation paradigm is a novel architectural contribution with broad implications for AI-driven mathematical reasoning. While TAPO addresses a genuine and well-characterized problem (credit misassignment in GRPO for tool-augmented agents), its contributions are more incremental and narrower in scope. Goedel-Architect's results are likely to catalyze significant follow-up work across formal verification, mathematical AI, and education.