{"type":"analysis","id":"analysis:research-the-kls500-lean-proof-targets-openai-s-full-kls-statement-but-only-its-author","slug":"research-the-kls500-lean-proof-targets-openai-s-full-kls-statement-but-only-its-author","title":"The KLS500 Lean proof targets OpenAI's full KLS statement, but only its author has reported building it, and it does not formalize the recur","description":"Hongru Zhao's Lean 4 repository ends in a theorem that proves OpenAI's pinned, dimension-free KLS statement with constant 500. The build and audit evidence is self-reported, external checkers were not run, and the formalization follows the Bizeul–Klartag–Lehec route rather than Song and Zhang's iterated recursion.","published_at":"2026-10-24T20:00:00.000Z","updated_at":"2026-10-24T20:00:00.000Z","record_date":"2026-10-24","topics":["openai","research"],"source_urls":["https://raw.githubusercontent.com/HongruZhao/KLS500/main/KLS500.lean","https://raw.githubusercontent.com/HongruZhao/KLS500/main/verification/actual-endpoint-types.txt","https://raw.githubusercontent.com/HongruZhao/KLS500/main/third_party/openai-model/UPSTREAM.json","https://raw.githubusercontent.com/openai/math/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Analysis/KLS/Model.lean","https://github.com/openai/math","https://raw.githubusercontent.com/HongruZhao/KLS500/main/verification/README.md","https://github.com/HongruZhao/KLS500/tree/main/verification","https://raw.githubusercontent.com/HongruZhao/KLS500/main/lean-toolchain","https://raw.githubusercontent.com/HongruZhao/KLS500/main/lake-manifest.json","https://raw.githubusercontent.com/HongruZhao/KLS500/main/verification/final-source-scan.json","https://zenodo.org/records/23229034","https://github.com/HongruZhao/KLS500","https://arxiv.org/abs/2610.05474","https://arxiv.org/abs/2610.01447","https://www.microsoft.com/en-us/research/blog/solving-a-31-year-old-grand-challenge-in-mathematics-the-kls-conjecture/","https://arxiv.org/abs/2610.07728v2"],"language":"en","routes":{"html":"https://newruntime.com/analysis/research-the-kls500-lean-proof-targets-openai-s-full-kls-statement-but-only-its-author/","markdown":"https://newruntime.com/analysis/research-the-kls500-lean-proof-targets-openai-s-full-kls-statement-but-only-its-author.md","json":"https://newruntime.com/analysis/research-the-kls500-lean-proof-targets-openai-s-full-kls-statement-but-only-its-author.json"},"author":{"role":"author","name":"Andrey Reshetnikov","profile":"https://newruntime.com/owner-profile.md","profile_json":"https://newruntime.com/owner-profile.json","same_as":["https://www.linkedin.com/in/reshetnikov1/","https://t.me/lapetuse"]},"editorial_provenance":{"desk":"authorial","target_ref":"deep_research:5879ec4a-19c4-415e-9037-f4d401b00968","authorial_article_id":"5879ec4a-19c4-415e-9037-f4d401b00968"},"next_reads":[{"type":"topic","path":"/topics/openai/","url":"https://newruntime.com/topics/openai/","title":"Openai","reason":"Explore the openai topic hub.","media_type":"text/html","markdown_url":"https://newruntime.com/topics/openai.md","json_url":"https://newruntime.com/topics/openai.json"},{"type":"topic","path":"/topics/research/","url":"https://newruntime.com/topics/research/","title":"Research","reason":"Explore the research topic hub.","media_type":"text/html","markdown_url":"https://newruntime.com/topics/research.md","json_url":"https://newruntime.com/topics/research.json"},{"type":"collection","path":"/analysis/","url":"https://newruntime.com/analysis/","title":"Analysis","reason":"Open the latest authorial analysis.","media_type":"text/html","json_url":"https://newruntime.com/analysis.json"},{"type":"collection","path":"/source-ledger.json","url":"https://newruntime.com/source-ledger.json","title":"Source Ledger","reason":"Inspect the public source evidence graph.","media_type":"application/json"}]}
