{
 "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. THIS LEDGER IS THE SECOND PIN, 7ef5c0cc5ca4b0e072b7a050fca09ab24bc6fa3a (pre-registration amendment 17): only the 20 challenges ADDED or CHANGED since fd4aeeb2 are members; the 399 unchanged ones are not re-run, and the audit pin's ledger, certs/openai-math-kernel.json, stands as it was.",
 "release": {
  "commit": "7ef5c0cc5ca4b0e072b7a050fca09ab24bc6fa3a",
  "challenges": 419,
  "previous": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "members": 20,
  "unchangedNotRun": 399,
  "amendment": 17
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 "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.",
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  "words": {
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  "strict": {
   "BODIES DIFFER": 1
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  "transfer": {
   "NOT DEFINITIONAL": 1
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  "displayed": {
   "OPEN": 1
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