Saha, Rahul, Li, Alan, Xue, Anton, Chaudhuri, Swarat, Klivans, Adam, Kothari, Pravesh K., Meka, Raghu · Nov 7, 2026
Improving Analytic Constants via Interpretable AI-Guided Lean Proof Refinement
Markdown · JSON · Original source
The authors propose using AI to improve mathematical bounds by tightening parts of existing proofs rather than rebuilding whole arguments. They represent proofs as partially-formalized blueprints: dependency graphs connecting definitions, lemmas and theorems. An iteratively refines Lean code while preserving that structure, so local changes can propagate to a verified final bound and people can inspect how the changes affect the theorem. The authors report an explicit improvement to the bound on Grothendieck's constant over Krivine's 1977 bound, and a higher lower bound for Korenblum's constant than Wang's 2025 bound. Their abstract presents these results as evidence of the potential of partial formalization and iterative refinement for interpretable mathematical discovery. It does not give the detailed experiments or explain how broadly the method applies beyond these examples.
Headline and summary by Escape Meridian, prepared by Luna from the attributed source. A source check is not independent confirmation of the source’s claims.
Original source
cs.AI · Article
Source details
Original source date: Nov 7, 2026 (2026-11-07).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-10T18:33:29.946Z. First observed: 2026-11-10T08:36:24.321Z. Retrieved: 2026-11-10T18:32:51.147Z.
Referenced by
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Limits
The evidence is the paper's abstract; it does not provide the detailed experiments or their evaluation criteria. The abstract reports results for Grothendieck's constant and Korenblum's constant, but does not establish how broadly the approach applies beyond these examples.
Open question
What results beyond these two constants would show how broadly the authors' approach can be applied?
Source-stated
The authors propose refining intermediate steps in existing proofs to improve quantitative bounds, rather than reconstructing the entire proof.
existing proofs often contain slack in intermediate lemmas, which can be tightened without reconstructing the entire argument.
Source-stated
They encode proofs as partially-formalized Lean blueprints, dependency graphs that people can inspect, and have an AI agent refine Lean code while preserving the blueprint's structure.
we represent proofs as partially-formalized Lean blueprints: human-interpretable dependency graphs of definitions, lemmas, and theorems.
Source-stated
The authors report an improved upper bound on Grothendieck's constant relative to Krivine's 1977 bound.
an explicit numerical improvement over Krivine's 1977 bound.
Source-stated
The authors report a higher lower bound for Korenblum's constant than Wang's 2025 bound.
improving Wang's 2025 bound of $0.3554$.
Source-stated
The authors characterize their experiments as demonstrating potential, not as establishing the method's broad applicability.
Our experiments demonstrate the potential of both partial formalization and iterative agentic refinement for interpretable mathematical discovery.
Source and contributor context
Saha, Rahul, Li, Alan, Xue, Anton, Chaudhuri, Swarat, Klivans, Adam, Kothari, Pravesh K., Meka, Raghu · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
AI agent
An AI system that chooses and carries out actions toward a goal, often using software tools.
Agentic AI
AI systems that plan and carry out a series of steps toward a goal, often by using other software, rather than giving one answer.
Lean
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 1. Publication ID: 133ea172-b660-40e0-80e9-71d5375e7dfb.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-10T18:33:29.946Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: material_development.
Observation: 325041f81a266e183953855db5bc64f710bf92141c6c91a39a6588999e4ec522. Source text hash: ac8cd32af6b3e4638d97f846acb5f95efac9feba882eb245e0b6a7cc901ecf39.
Revision and source-check history
Version 1 · 2026-11-10T18:33:29.946Z
Improving Analytic Constants via Interpretable AI-Guided Lean Proof Refinement
The authors propose using AI to improve mathematical bounds by tightening parts of existing proofs rather than rebuilding whole arguments. They represent proofs as partially-formalized blueprints: dependency graphs connecting definitions, lemmas and theorems. An iteratively refines Lean code while preserving that structure, so local changes can propagate to a verified final bound and people can inspect how the changes affect the theorem. The authors report an explicit improvement to the bound on Grothendieck's constant over Krivine's 1977 bound, and a higher lower bound for Korenblum's constant than Wang's 2025 bound. Their abstract presents these results as evidence of the potential of partial formalization and iterative refinement for interpretable mathematical discovery. It does not give the detailed experiments or explain how broadly the method applies beyond these examples.
Original source
cs.AI · Article
Source details
Original source date: Nov 7, 2026 (2026-11-07).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-10T18:33:29.946Z. First observed: 2026-11-10T08:36:24.321Z. Retrieved: 2026-11-10T18:32:51.147Z.
Limits
The evidence is the paper's abstract; it does not provide the detailed experiments or their evaluation criteria. The abstract reports results for Grothendieck's constant and Korenblum's constant, but does not establish how broadly the approach applies beyond these examples.
Open question
What results beyond these two constants would show how broadly the authors' approach can be applied?
Source-stated
The authors propose refining intermediate steps in existing proofs to improve quantitative bounds, rather than reconstructing the entire proof.
existing proofs often contain slack in intermediate lemmas, which can be tightened without reconstructing the entire argument.
Source-stated
They encode proofs as partially-formalized Lean blueprints, dependency graphs that people can inspect, and have an AI agent refine Lean code while preserving the blueprint's structure.
we represent proofs as partially-formalized Lean blueprints: human-interpretable dependency graphs of definitions, lemmas, and theorems.
Source-stated
The authors report an improved upper bound on Grothendieck's constant relative to Krivine's 1977 bound.
an explicit numerical improvement over Krivine's 1977 bound.
Source-stated
The authors report a higher lower bound for Korenblum's constant than Wang's 2025 bound.
improving Wang's 2025 bound of $0.3554$.
Source-stated
The authors characterize their experiments as demonstrating potential, not as establishing the method's broad applicability.
Our experiments demonstrate the potential of both partial formalization and iterative agentic refinement for interpretable mathematical discovery.
Source and contributor context
Saha, Rahul, Li, Alan, Xue, Anton, Chaudhuri, Swarat, Klivans, Adam, Kothari, Pravesh K., Meka, Raghu · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
AI agent
An AI system that chooses and carries out actions toward a goal, often using software tools.
Agentic AI
AI systems that plan and carry out a series of steps toward a goal, often by using other software, rather than giving one answer.
Lean
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 1. Publication ID: 133ea172-b660-40e0-80e9-71d5375e7dfb.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-10T18:33:29.946Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: material_development.
Observation: 325041f81a266e183953855db5bc64f710bf92141c6c91a39a6588999e4ec522. Source text hash: ac8cd32af6b3e4638d97f846acb5f95efac9feba882eb245e0b6a7cc901ecf39.
uncertain · 2026-11-10T18:33:29.946Z · anthropic/claude-opus-5.5
Publication: 133ea172-b660-40e0-80e9-71d5375e7dfb
attribution — pass: The reading consistently attributes the method and results to the paper's authors, Saha, Li, Xue, Chaudhuri, Klivans, Kothari and Meka, using phrases such as 'The authors report.' It presents the bounds as their claims, not as independently established facts.
Authors:Rahul Saha, Alan Li, Anton Xue, Swarat Chaudhuri, Adam Klivans, Pravesh K. Kothari, Raghu Meka
summary — uncertain: The summary is faithful, but a general reader may not follow it. 'Lean' is never identified as computer proof-checking software, so 'verified final bound' loses its meaning. 'Bound' and 'analytic constant' are also unexplained. It also omits the paper's motivating stake: AI-generated proofs can be hard to understand and verify. Smallest repairs: add the motivating sentence, add a Lean tooltip or a brief gloss, and note the Grothendieck improvement's stated size (10^-17) so readers can judge its scale.
yet their reasoning and generated proofs can be difficult to understand and verify
date — pass: The originalPublished date, 2026-11-07, matches the v1 arXiv submission date. The feed date of Nov 10 is later and correctly not used.
[Submitted on 7 Nov 2026]
support — pass: Each claim matches the abstract: tightening slack in intermediate lemmas, Lean blueprints as dependency graphs, an agent refining the code while preserving that structure, the improvement over Krivine's 1977 bound, and the improvement over Wang's 2025 bound. The 'potential' framing is preserved. The limitations and the question follow from the abstract-only evidence without inventing benefits or costs.
allowing local improvements to automatically propagate to a verified final bound
media — pass: The selected media is the verified direct link to the original arXiv abstract page, which is the most direct way to access the source.
Challenge or correct this reading
Send a correction or an opposing source with this reading’s URL. Disagreement and uncertainty can remain unresolved.
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Explore LeanAn AI system that chooses and carries out actions toward a goal, often using software tools.
Definition referenceAI systems that plan and carry out a series of steps toward a goal, often by using other software, rather than giving one answer.
Definition referencearXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivLean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Explore LeanAn AI system that chooses and carries out actions toward a goal, often using software tools.
Definition referenceAI systems that plan and carry out a series of steps toward a goal, often by using other software, rather than giving one answer.
Definition referencearXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXiv