AI サービスが一時的に利用できないため、復旧後に翻訳を補完します。
[Submitted on 14 Oct 2026] Title:IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation View a PDF of the paper titled IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation, by Gaolei He and 4 other authors View PDF HTML (experimental) Abstract:Formal inequality proving requires mathematical reasoning and exact computation, often connected through intermediate lemmas and goal reformulations. We introduce IneqAgent, an agentic framework combining LLM reasoning with symbolic computation for inequality proving in Lean4. Lemma-level Monte Carlo Tree Search coordinates lemma construction, goal reformulation, and symbolic backend selection. Complementary sum-of-squares, Bernstein, and successive difference-substitution backends produce exact certificates for local Lean proof generation. The agent integrates these proofs with LLM-generated steps and uses Lean feedback to construct complete proofs checked against the original theorem statements. On four benchmarks, IneqAgent with DeepSeek-V4-Flash solves 175 of 186 problems (94.09%), achieving the highest overall success rate among the evaluated methods. Across four backbones, it achieves higher success rates at low LLM inference cost thresholds than Direct Agent using the same backbone, with lower mean inference costs over each method's successful runs. We also obtain Lean-verified strengthenings of Dittert's conjecture in dimensions four and five, and certify the Holens--Djokovic $(4,4)$ inequality, implying Merris's conjecture in dimension four. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2610.20681 [cs.AI] (or arXiv:2610.20681v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2610.20681 arXiv-issued DOI via DataCite Submission history From: Gaolei He [view email] [v1] Wed, 14 Oct 2026 16:29:11 UTC (203 KB) Full-text links: Access Paper: View a PDF of the paper titled IneqAgent: Agentic Inequality Proving in Lean with Symbolic Computation, by Gaolei He and 4 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.AI new | recent | 2026-10 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)