ARXIV:2605.13137 · AI FOR SCIENTIFIC RESEARCH TOOLS · SUBMITTED 14 MAY · 20:10 UTC · FRESHNESS FRESH

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving

Guoxiong Gao · Zeming Sun · Jiedong Jiang · Yutong Wang · Jingda Xu · Peihao Wu · +2 at arXiv

LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

Ship in 2-4 weeks›Score4.0Evidence unverified

Opportunity summary

Pain LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

Evidence 0 refs | 0 sources | 0% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while…

METHOD

Full abstract

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while premise-selection systems predict useful lemmas one tactic step at a time. Neither recovers the full premise set an entire theorem requires. We present LeanSearch v2, a two-mode retrieval system for this task. Its standard mode applies a hierarchy-informalized Mathlib corpus with an embedding-reranker pipeline, achieving state-of-the-art single-query retrieval without domain-specific fine-tuning (nDCG@10 of 0.62 vs. 0.53 for the next-best system). Its reasoning mode builds on standard mode as its retrieval substrate, targeting global premise retrieval through iterative sketch-retrieve-reflect cycles. On a 69-query benchmark of research-level Mathlib theorems, reasoning mode recovers 46.1% of ground-truth premise groups within 10 retrieved candidates, outperforming strong reasoning retrieval systems (38.0%) and premise-selection baselines (9.3%) on the same benchmark. In a controlled downstream evaluation with a fixed prover loop, replacing alternative retrievers with LeanSearch v2 yields the highest proof success (20% vs. 16% for the next-best system and 4% without retrieval), confirming that retrieval quality propagates to proof generation. We have open-sourced all code, data, and benchmarks. Code and data: https://github.com/frenzymath/LeanSearch-v2 . The standard mode is publicly available with API access at https://leansearch.net/ .

RESULT

ScienceToStartup currently rates this 4.0/10 on the public viability pass. Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task…

WHY NOW

AI for Scientific Research Tools moved forward this cycle; last verified May 2026. Public score 4.0/10. Implementation evidence is present through a linked repository.

Continue into Read for claims, analysis, references, and neighboring papers.

Opportunity summary

Score4.0

PainLeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

Evidence0 refs | 0 sources | 0% coverage

Blockerno shell-level blocker reported

Analysis summary

LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Competitive landscape

LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

Segment

AI for Scientific Research Tools

Adoption evidence

Public code linked for build inspection

Commercial read

4.0/10 public viability

Direct

not classified

Adjacent

not classified

Substitute

not classified

Unknown

not classified

{ "contract_version": "paper-r2", "paper_id": "37144646-2020-4167-b6e5-2f66e7ab7f86", "arxiv_id": "2605.13137", "canonical_route": "/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "active_tab": "synced from current hash by the drawer client", "selected_artifact": "leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "endpoints": { "paper_pack": "/api/v1/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving/paper-pack", "build_passport": "/api/v1/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving/build-passport", "mcp_resource": "sciencetostartup://surfaces/paper-workspace" } }

{ "surface": "paper", "mode": "paper", "query": "LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving", "normalized_query": "2605.13137", "route": "/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "paper_ref": "leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "topic_slug": null, "benchmark_ref": null, "dataset_ref": null }

{ "@context": "https://schema.org", "@graph": [ { "@type": "WebPage", "@id": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving#webpage", "url": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "name": "LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving", "description": "LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.", "isPartOf": { "@id": "https://sciencetostartup.com/#website" } }, { "@type": "ScholarlyArticle", "@id": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving#scholarlyArticle", "headline": "LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving", "description": "LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.", "url": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving", "sameAs": "https://arxiv.org/abs/2605.13137", "identifier": { "@type": "PropertyValue", "propertyID": "arXiv", "value": "2605.13137" }, "isAccessibleForFree": true, "isPartOf": { "@id": "https://sciencetostartup.com/#website" }, "datePublished": "2026-05-13T08:04:57.000Z", "author": [ { "@type": "Person", "name": "Guoxiong Gao", "affiliation": { "@type": "Organization", "name": "Peking University" } }, { "@type": "Person", "name": "Zeming Sun", "affiliation": { "@type": "Organization", "name": "Peking University, Kyoto University" } }, { "@type": "Person", "name": "Jiedong Jiang", "affiliation": { "@type": "Organization", "name": "Westlake University" } }, { "@type": "Person", "name": "Yutong Wang", "affiliation": { "@type": "Organization", "name": "IQuest Research" } }, { "@type": "Person", "name": "Jingda Xu", "affiliation": { "@type": "Organization", "name": "IQuest Research" } }, { "@type": "Person", "name": "Peihao Wu", "affiliation": { "@type": "Organization", "name": "IQuest Research" } }, { "@type": "Person", "name": "Bryan Dai", "affiliation": { "@type": "Organization", "name": "IQuest Research" } }, { "@type": "Person", "name": "Bin Dong", "affiliation": { "@type": "Organization", "name": "Peking University" } } ], "codeRepository": "https://github.com/frenzymath/LeanSearch-v2", "additionalProperty": [ { "@type": "PropertyValue", "propertyID": "viabilityScore", "value": 4 }, { "@type": "PropertyValue", "propertyID": "researchDomain", "value": "AI for Scientific Research Tools" }, { "@type": "PropertyValue", "propertyID": "commercialReadiness", "value": "code, repo url" } ] }, { "@type": "SoftwareSourceCode", "@id": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving#software", "name": "LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving - Source Code", "description": "LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.", "codeRepository": "https://github.com/frenzymath/LeanSearch-v2", "url": "https://github.com/frenzymath/LeanSearch-v2" }, { "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://sciencetostartup.com" }, { "@type": "ListItem", "position": 2, "name": "AI for Scientific Research Tools", "item": "https://sciencetostartup.com/topics" }, { "@type": "ListItem", "position": 3, "name": "LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem P", "item": "https://sciencetostartup.com/paper/leansearch-v2-global-premise-retrieval-for-lean-4-theorem-proving" } ] }, { "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "What is the startup potential of \"LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem P\"?", "acceptedAnswer": { "@type": "Answer", "text": "LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results." } }, { "@type": "Question", "name": "What products could be built from this research?", "acceptedAnswer": { "@type": "Answer", "text": "To productize this, develop a software plug-in that integrates with the Lean 4 environment, offering users a more efficient theorem proving process by using the advanced retrieval capabilities of LeanSearch v2." } }, { "@type": "Question", "name": "What are the practical use cases?", "acceptedAnswer": { "@type": "Answer", "text": "A commercial application could be a premium plugin for Lean 4 users that offers enhanced premise retrieval to save time and effort in theorem proving, particularly useful for professional mathematicians and educators." } }, { "@type": "Question", "name": "What industries could this research disrupt?", "acceptedAnswer": { "@type": "Answer", "text": "This technology could replace or augment existing theorem-proving tools by providing a faster, more accurate retrieval system for premises in Lean 4, reducing dependency on less efficient manual search methods." } } ] } ] }

Competitive landscape

LeanSearch v2 optimizes global premise retrieval for Lean 4 theorem proving by significantly enhancing retrieval performance with state-of-the-art results.

Segment

AI for Scientific Research Tools

Adoption evidence

Public code linked for build inspection

Commercial read

4.0/10 public viability

Direct

not classified

Adjacent

not classified

Substitute

not classified

Unknown

not classified

LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving

LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving

Claim map

Constellation map

Competitive landscape

Buzz

PDF

REFERENCES

Related Papers

Subscribe to the weekly brief

Build artifacts

Brief

Experiment plan

Validation checklist

Scientific founder

Translational engineer

Domain operator

GTM lead

Regulatory/clinical advisor

Timeline

Claim map

Constellation map

Competitive landscape

Buzz

PDF

REFERENCES

Related Papers

Subscribe to the weekly brief

Build artifacts

Brief

Experiment plan

Validation checklist

Scientific founder

Translational engineer

Domain operator

GTM lead

Regulatory/clinical advisor

Timeline