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ARXIV:2606.03303 · FORMAL MATHEMATICS LLMS · SUBMITTED 03 JUN · 20:41 UTC · FRESHNESS FRESH
ARXIV:2606.03303FORMAL MATHEMATICS LLMSSUBMITTED 03 JUN · 20:41 UTCFRESHNESS FRESHPo-Nien Kung · Linfeng Song · Dawsen Hwang · Jinsung Yoon · Chun-Liang Li · Simone Severini · +7 at arXiv
LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition.
Opportunity summary
Pain LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition. We present LEAP, an agentic framework that enables…
Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve…
ScienceToStartup currently rates this 8.0/10 on the public viability pass. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. Code availability is flagged…
Formal Mathematics LLMs moved forward this cycle; last verified June 2026. Public score 8.0/10. Production flags indicate code availability.
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LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition.
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10.48550/arXiv.2606.03303LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition.
Abstract
Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. LEAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement. By decomposing complex problems into smaller units, the system bridges formal proof construction with informal blueprints through continuous interaction with the Lean compiler. To provide a rigorous evaluation beyond increasingly saturated benchmarks, we introduce Lean-IMO-Bench, a benchmark of IMO-style problems formalized in Lean, with short statements yet highly non-routine and multi-step proofs across a wide range of difficulty levels. Empirically, on the latest 2025 Putnam Competition, an annual mathematics competition for undergraduate students in North America, LEAP solves all 12 problems, matching recent breakthroughs by frontier formal mathematical models. On Lean-IMO-Bench, LEAP boosts the one-shot formal solve rate of general-purpose LLMs from below 10% to 70%, notably surpassing the 48% benchmark set by a specialized, gold-medal-caliber IMO system. Furthermore, we demonstrate LEAP's research-level utility by autonomously formalizing complex proofs for open combinatorial challenges, including a verified proof for a key subproblem in Knuth's Hamiltonian decomposition of even-order Cayley graphs.
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Proof status
unverified0 refs; 3 sources; 50% coverage.
What was readable
Derived fallback: Estimated from adjacent evidence; not verified from source.
Viability
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Commercial
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Preparing verified analysis
Dimensions overall score 8.0
PROBLEM
LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition. We present LEAP, an agentic framework that enables general-purpose foundation models to...
METHOD
Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art per...
RESULT
ScienceToStartup currently rates this 8.0/10 on the public viability pass. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. Code availability is flagged in the produc...
WHY NOW
Formal Mathematics LLMs moved forward this cycle; last verified June 2026. Public score 8.0/10. Production flags indicate code availability.
{"file name": "input.pdf", "number of pages": 24, "author": "Po-Nien Kung; Linfeng Song; Dawsen Hwang; Jinsung Yoon; Chun-Liang Li; Simone Severini; Mirek Ol\u0161\u00e1k; Edward Lockhart; Quoc V Le; Burak Gokturk
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Concepts
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LEAP is an agentic framework that supercharges general LLMs to achieve state-of-the-art performance in formal mathematics theorem proving, solving all problems on the 2025 Putnam Competition.
Segment
Formal Mathematics LLMs
Adoption evidence
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Commercial read
8.0/10 public viability
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CITED BY
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Build Passport
Build passport pending - Proof Lab budget No verified cost estimate / $7.00 cap
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missing
reason
passport_row_missing
proof status
unverified
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confidence low
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Evidence coverage
OpportunityKernel evidence_receipt
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fresh
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Build readiness
BuildPassport EvidenceState
passport absent
fresh
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Artifact maturity
GitHub and Hugging Face maturity payloads
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fresh
Open source artifacts or mark the gap as missing. verified:false
Technical feasibility
partial
Current read
Runnable path is not fully verified.
Evidence
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Gaps
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Run minimal reproduction from the Build Passport prototype path.
Market urgency
missing
Current read
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Evidence
0 references, 3 sources, 50% evidence coverage.
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Buyer clarity
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Defensibility
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Integration burden
missing
Current read
No public implementation surface observed.
Evidence
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Write integration checklist from prototype path and target workflow.
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Classify regulatory flags before commercialization planning.
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People
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Prototype owner missing.
Build Passport does not name an implementer.
People
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Operator workflow not sourced.
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ARTIFACTS
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DEFENSIBILITY
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