{
 "what": "The AlphaProof Nexus audit, kernel lane: each Erdős proof of google-deepmind/alphaproof-nexus-results @ 0647711a checked by Comparator v4.27.0 against formal-conjectures' own statement at the commit the repository builds against (7862bf6a), with nanoda on (.github/workflows/apn-kernel.yml). CERTIFIED here means the proof proves exactly that statement, uses only propext / Quot.sound / Classical.choice, and two independently written kernels accept it. Whether the statement is the problem Erdős posed is the reading lane's question.",
 "generated": "2026-10-20T11:47:25Z",
 "workflow": ".github/workflows/apn-kernel.yml",
 "rule": "tools/comparator-verdict.js",
 "deciders": {
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  "workflow": "3e6d6a40c40abd0233126d74f173fd5ce95891ebf5d8451f061b32be5f1b4bbe"
 },
 "counts": {
  "CERTIFIED": 10
 },
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     "cacheSeconds": 82,
     "maxRssKB": 6612728,
     "kernels": [
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     ],
     "decided": {
      "word": "CERTIFIED",
      "why": "Comparator exit 0; nanoda and Lean's kernel both accept"
     }
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   "word": "CERTIFIED",
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   "stage": null
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     ],
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     }
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   "word": "CERTIFIED",
   "why": "Comparator exit 0; nanoda and Lean's kernel both accept",
   "stage": null
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   "word": "CERTIFIED",
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     "decided": {
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     }
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   "why": "Comparator exit 0; nanoda and Lean's kernel both accept",
   "stage": null
  },
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     }
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   "word": "CERTIFIED",
   "why": "Comparator exit 0; nanoda and Lean's kernel both accept",
   "stage": null
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     "decided": {
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      "stage": "export or replay",
      "why": "/home/runner/.elan/toolchains/leanprover--lean4---v4.27.0/lib/lean | /home/runner/.elan/toolchains/leanprover--lean4---v4.27.0/lib/lean | Command exited with non-zero status 1"
     }
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     "at": "2026-10-20T11:16:43Z",
     "exit": 1,
     "seconds": 89,
     "cacheSeconds": 83,
     "maxRssKB": 7203492,
     "kernels": [],
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     ],
     "decided": {
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      "why": "uncaught exception: Version invalid: '{\"meta\":{\"exporter\":{\"name\":\"lean4export\",\"version\":\"3.1.0\"},\"format\":{\"version\":\"3.1.0\"},\"lean\":{\"githash\":\"db93fe1608548721853390a10cd40580fe7d22ae\",\"version\":\"4.27.0\"}}}' | Command exited with non-zero status 1"
     }
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     }
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   ],
   "word": "CERTIFIED",
   "why": "Comparator exit 0; nanoda and Lean's kernel both accept",
   "stage": null
  },
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     "kernels": [
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   ],
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   "why": "Comparator exit 0; nanoda and Lean's kernel both accept",
   "stage": null
  }
 ],
 "redControls": [
  {
   "item": "erdos_846.red.statement",
   "what": "our challenge weakened (ε > 0 to ε ≥ 0): the solution no longer proves the challenge statement",
   "run": 39416708323,
   "word": "REFUTED?",
   "why": "uncaught exception: Challenge and solution theorem statement do not match: 'Erdos846.target_theorem_0'",
   "fired": true
  },
  {
   "item": "erdos_846.red.sorry",
   "what": "their solution with the main proof replaced by sorry: it rests on sorryAx, not permitted",
   "run": 39416708323,
   "word": "REFUTED?",
   "why": "uncaught exception: Illegal axiom detected: 'sorryAx'",
   "fired": true
  }
 ]
}