{ "what": "Lane K of the openai/math audit: each Comparator challenge re-run on Linux with nanoda on, decided by the words of corpus/openai-math/preregistration.json (lanes.K). CERTIFIED here means the Lean theorem states exactly the challenge statement, uses only propext / Quot.sound / Classical.choice, and two independently written kernels accept the proof. It does not mean the paper's claim is proved: that is lane S.", "release": { "commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb", "challenges": 416 }, "decider": "Comparator (leanprover/comparator d03acab1 = tag v4.34.0, built with the release's toolchain v4.34.1), lean4export 076e8e57, landrun 811cfff5, nanoda_lib 3a240721 — on GitHub's Linux runners (.github/workflows/openai-math-kernel.yml), one job per challenge, the config and statement bytes sha256-checked against the census before the run", "declaredChanges": [ "enable_nanoda: true on every config — the independent Rust kernel replays every solution, where the release enabled it for 2 of 416 (412 false, 2 absent)", "for the 10 configs that declare definition_names: a SECOND run with definition_names emptied. Comparator compares a definition hole's name, universe levels, type and safety, never its body (Comparator/Compare.lean, definitionHoleMatches, at d03acab1); the second run compares those definitions as ordinary constants, body included, and so decides whether the theorem is proved about the definitions the challenge file displays", "nanoda's worker-thread stack (src/lib.rs STACK_SIZE, a hard-coded 16 MiB) raised to 1 GiB — the only byte of the independent kernel changed, its diff kept in the tools artifact (nanoda.patch); amendment 11", "for the re-runs of amendment 13 only: nanoda built with the patch posted in ammkrn/nanoda_lib#44 (2026-10-06; src/tc.rs only; copied byte for byte to corpus/openai-math/nanoda/issue44.patch, sha256 pinned in the workflow) — proof irrelevance three-valued and projections compared by lazy_delta_proj_reduction, both as Lean's reference kernel does them; every run records which nanoda build it used, and a row CERTIFIED by a patched nanoda says so" ], "trustBase": "the two kernels, lean4export, Comparator's comparison code, landrun's Landlock sandbox on the runner (recorded per job; Comparator calls landrun with --best-effort, so the job records the kernel's LSM list), the Mathlib cache fetched by lake exe cache get, and GitHub's runners. Comparator's README also asks for systemd-run with AF_UNIX restricted; GitHub's runners have no user systemd session, so that guard is NOT applied, and the page says so.", "notRunYet": [], "counts": { "decided": 416, "of": 416, "cancelledBeforeComparator": 0, "words": { "CERTIFIED": 398, "REFUSED": 18 }, "strict": { "SAME BODIES": 7, "BODIES DIFFER": 3 }, "transfer": { "TRANSFERS": 6, "NOT DEFINITIONAL": 2, "NOT DECIDED": 2 }, "displayed": { "PROVED": 9, "OPEN": 1 } }, "rows": [ { "challenge": "AbhyankarSathaye", "families": [ "049" ], "statementLines": 22, "nanodaInRelease": false, "definitionHoles": 0, "runs": [ { "run": 38017370880, "workflowSha": "f860b6ef280a08e07484de2252589b64fd5d8139", "at": "2026-10-10T03:12:38Z", "nanodaBuild": "stock", "exit": 0, "seconds": 44, "cacheSeconds": 166, "maxRssKB": 2276272, "kernels": [ "Lean default kernel accepts the solution", "nanoda kernel accepts the solution" ], "decided": { "word": "CERTIFIED", "why": "Comparator exit 0; nanoda and Lean's kernel both accept" }, "strict": null, "transfer": null } ], "word": "CERTIFIED", "why": "Comparator exit 0; 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