{
 "generated": "2026-11-14",
 "stages": [
  "Registered",
  "Checks rerun",
  "Reading guide written",
  "Read independently",
  "Claim rule met"
 ],
 "claims": [
  {
   "repo": "DEBRIEF-math-erdos1061",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos1061",
   "label": "Erdős #1061",
   "title": "The claimed solution of Erdős Problem #1061 (solutions of sigma(a) + sigma(b) = sigma(a+b))",
   "area": "Number theory: arithmetic functions",
   "rests_on": "an arXiv paper only; no formal deduction",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 2,
   "first_ask": "No formal deduction exists for the claimed proof",
   "first_ask_what": "a Lean formalization of the main theorem, by the claimant or anyone else, with the statement written by a third party",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-24",
   "last_text": "24 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos1133",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos1133",
   "label": "Erdős #1133",
   "title": "The claimed solution of Erdős Problem #1133 (polynomials agreeing with bounded data at most nodes)",
   "area": "Analysis: polynomials",
   "rests_on": "a PDF write-up in a public repository; no formal deduction",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 2,
   "first_ask": "No formal deduction exists for the claimed proof",
   "first_ask_what": "a Lean formalization of the main theorem, by the claimant or anyone else, with the statement written by a third party",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-04-29",
   "last_text": "29 Apr 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos1177",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos1177",
   "label": "Erdős #1177",
   "title": "The claimed solution of Erdős Problem #1177 (three statements about triple systems avoiding a fixed finite one)",
   "area": "Set theory and hypergraphs: chromatic number",
   "rests_on": "an arXiv paper and a Lean development shared with the claim on problem 593",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 3,
   "first_ask": "The Lean development has not been built or kernel-checked by anyone outside the claimant",
   "first_ask_what": "a pre-registered rerun: fetch at the pinned commit, build, confirm no sorry or admit, print the axioms",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-23",
   "last_text": "23 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos306",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos306",
   "label": "Erdős #306",
   "title": "The claimed solution of Erdős Problem #306 (sums of unit fractions with semiprime denominators)",
   "area": "Number theory: unit fractions",
   "rests_on": "an arXiv paper and a Lean development, built on an earlier conditional Lean development by another author",
   "stage": 2,
   "stage_name": "Reading guide written",
   "needs_next": "two independent readers to sign the semantic read",
   "certified": 2,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 2,
   "first_ask": "Do the formal statements say what the problem asks?",
   "first_ask_what": "a machine comparison of the claimant's main theorem with the third-party formal statement in google-deepmind/formal-conjectures, then a human read of any difference",
   "people": [
    "Nervous Machine (Heidi Bennett; Claude Code as the operating agent)"
   ],
   "outside": [],
   "cycles": 2,
   "last": "2026-11-14",
   "last_text": "14 Nov 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos550",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos550",
   "label": "Erdős #550",
   "title": "The claimed solution of Erdős Problem #550 (Ramsey numbers of trees versus complete multipartite graphs)",
   "area": "Graph theory: Ramsey theory",
   "rests_on": "an arXiv paper and a Lean development",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 3,
   "first_ask": "The Lean development has not been built or kernel-checked by anyone outside the claimant",
   "first_ask_what": "a pre-registered rerun: fetch at the pinned commit, build, confirm no sorry or admit, print the axioms",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-22",
   "last_text": "22 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos593",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos593",
   "label": "Erdős #593",
   "title": "The claimed solutions of Erdős Problem #593 (finite triple systems forced by uncountable chromatic number)",
   "area": "Set theory and hypergraphs: chromatic number",
   "rests_on": "two independent arXiv or PDF write-ups and two Lean developments, one per claimant",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 4,
   "first_ask": "The Lean development has not been built or kernel-checked by anyone outside the claimant",
   "first_ask_what": "a pre-registered rerun: fetch at the pinned commit, build, confirm no sorry or admit, print the axioms",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-23",
   "last_text": "23 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos671",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos671",
   "label": "Erdős #671",
   "title": "The claimed solution of Erdős Problem #671 (Lagrange interpolation and the Lebesgue function)",
   "area": "Analysis: polynomial interpolation",
   "rests_on": "two written arguments and two Lean files, one pinned by hash and one a live-editor link",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 4,
   "first_ask": "The Lean development has not been built or kernel-checked by anyone outside the claimant",
   "first_ask_what": "a pre-registered rerun: fetch at the pinned commit, build, confirm no sorry or admit, print the axioms",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-22",
   "last_text": "22 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos731",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos731",
   "label": "Erdős #731",
   "title": "The claimed solution of Erdős Problem #731 (the least non-divisor of the central binomial coefficient)",
   "area": "Number theory: binomial coefficients",
   "rests_on": "an arXiv paper and a Lean development, under the claimant's own formalisation of the word 'reasonable'",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 4,
   "first_ask": "The Lean development has not been built or kernel-checked by anyone outside the claimant",
   "first_ask_what": "a pre-registered rerun: fetch at the pinned commit, build, confirm no sorry or admit, print the axioms",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-06-27",
   "last_text": "27 Jun 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos768",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos768",
   "label": "Erdős #768",
   "title": "The claimed solution of Erdős Problem #768 (density of integers with a witness divisor for every prime factor)",
   "area": "Number theory: multiplicative structure",
   "rests_on": "an arXiv paper and a Lean development that vendors two other Lean projects",
   "stage": 2,
   "stage_name": "Reading guide written",
   "needs_next": "two independent readers to sign the semantic read",
   "certified": 1,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 2,
   "first_ask": "Do the formal statements say what the problem asks?",
   "first_ask_what": "two independent mathematicians read the formal statement against the problem as posed and sign, or refuse",
   "people": [
    "Nervous Machine (Heidi Bennett; Claude Code as the operating agent)"
   ],
   "outside": [],
   "cycles": 2,
   "last": "2026-11-14",
   "last_text": "14 Nov 2026"
  },
  {
   "repo": "DEBRIEF-math-erdos856",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-erdos856",
   "label": "Erdős #856",
   "title": "The claimed solution of Erdős Problem #856 (sets with no k elements sharing a pairwise least common multiple)",
   "area": "Number theory: extremal problems",
   "rests_on": "an Overleaf read-only document; no fixed file and no formal deduction",
   "stage": 0,
   "stage_name": "Registered",
   "needs_next": "an independent rerun of whatever is machine-checkable",
   "certified": 0,
   "accepted": 0,
   "refuted": 0,
   "open_gaps": 3,
   "first_ask": "No formal deduction exists for the claimed proof",
   "first_ask_what": "a Lean formalization of the main theorem, by the claimant or anyone else, with the statement written by a third party",
   "people": [],
   "outside": [],
   "cycles": 0,
   "last": "2026-04-15",
   "last_text": "15 Apr 2026"
  },
  {
   "repo": "DEBRIEF-math-primegaps",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-primegaps",
   "label": "Prime gaps ≤ 186 (OpenAI)",
   "title": "The claim that primes come within 186 of each other infinitely often",
   "area": "Number theory: gaps between primes",
   "rests_on": "a Lean formalization with three stated assumptions, a numerical certificate (Python/FLINT) and a paper",
   "stage": 2,
   "stage_name": "Reading guide written",
   "needs_next": "two independent readers to sign the semantic read",
   "certified": 5,
   "accepted": 5,
   "refuted": 0,
   "open_gaps": 3,
   "first_ask": "Do the formal statements say what a mathematician means?",
   "first_ask_what": "a number theorist reads the definitional trace against the formal file and the paper and signs its checklist",
   "people": [
    "Nervous Machine (Heidi Bennett; Claude Code as the operating agent)",
    "Fredrik Prüzelius (with Claude Code)"
   ],
   "outside": [
    "Fredrik Prüzelius (with Claude Code)"
   ],
   "cycles": 4,
   "last": "2026-11-14",
   "last_text": "14 Nov 2026"
  },
  {
   "repo": "DEBRIEF-math-zhang240",
   "url": "https://github.com/Nervous-Machine/DEBRIEF-math-zhang240",
   "label": "Prime gaps ≤ 240 (Zhang)",
   "title": "The claim that primes come within 240 of each other infinitely often (Zhang)",
   "area": "Number theory: gaps between primes",
   "rests_on": "an exact arithmetic certificate (Python) and a paper",
   "stage": 1,
   "stage_name": "Checks rerun",
   "needs_next": "a reading guide that traces each formal statement to its definitions",
   "certified": 3,
   "accepted": 1,
   "refuted": 0,
   "open_gaps": 3,
   "first_ask": "The analytic argument has no formal deduction and no referee report",
   "first_ask_what": "a referee report or an independent expert read of the analytic sections",
   "people": [
    "Nervous Machine (Heidi Bennett; Claude Code as the operating agent)"
   ],
   "outside": [],
   "cycles": 1,
   "last": "2026-11-08",
   "last_text": "8 Nov 2026"
  }
 ]
}