{
  "P10794": {
    "problem_number": 10794,
    "slug": "unsolvedmath-0103-4-term-aps-in-fourier-uniform-sets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:17+00:00",
    "updated_at": "2026-08-18T02:55:17+00:00"
  },
  "P2624": {
    "problem_number": 2624,
    "slug": "b2-two-set-z100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:49+00:00",
    "updated_at": "2026-07-30T02:23:20+00:00"
  },
  "P2504": {
    "problem_number": 2504,
    "slug": "c7-fifth-power-independent-368",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:08+00:00",
    "updated_at": "2026-07-29T20:55:11+00:00"
  },
  "P2508": {
    "problem_number": 2508,
    "slug": "ramsey-55-43-graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:10+00:00",
    "updated_at": "2026-07-29T20:56:16+00:00"
  },
  "P12191": {
    "problem_number": 12191,
    "slug": "a-binary-lower-bound-for-addition-chain-length",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:22:39+00:00",
    "updated_at": "2026-09-01T19:22:44+00:00"
  },
  "P2616": {
    "problem_number": 2616,
    "slug": "q-analog-fano-plane",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:47+00:00",
    "updated_at": "2026-07-29T20:56:11+00:00"
  },
  "P12329": {
    "problem_number": 12329,
    "slug": "a-binary-floor-identity-for-a-congruence-filtered-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:39:26+00:00",
    "updated_at": "2026-09-01T19:39:31+00:00"
  },
  "P12369": {
    "problem_number": 12369,
    "slug": "a-binomial-sum-that-may-never-be-integral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:44:22+00:00",
    "updated_at": "2026-09-01T19:44:29+00:00"
  },
  "P12453": {
    "problem_number": 12453,
    "slug": "a-binomial-sum-supercongruence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:37:21+00:00",
    "updated_at": "2026-09-02T21:37:34+00:00"
  },
  "P2650": {
    "problem_number": 2650,
    "slug": "three-cubes-114-height-1e20",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:59+00:00",
    "updated_at": "2026-07-29T20:56:49+00:00"
  },
  "P3084": {
    "problem_number": 3084,
    "slug": "common-chromatic-subgraph-aleph-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:57+00:00",
    "updated_at": "2026-08-02T12:47:58+00:00"
  },
  "P12171": {
    "problem_number": 12171,
    "slug": "a-common-ideal-digital-mean-through-base-eight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:20:14+00:00",
    "updated_at": "2026-09-01T19:20:19+00:00"
  },
  "P11094": {
    "problem_number": 11094,
    "slug": "a-complete-classification-of-complex-hadamard-matrices-of-order-six",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T03:03:56+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P12413": {
    "problem_number": 12413,
    "slug": "a-congruence-ladder-modulo-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:33:15+00:00",
    "updated_at": "2026-09-02T21:33:27+00:00"
  },
  "P3334": {
    "problem_number": 3334,
    "slug": "erdos-problem-681",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:37+00:00",
    "updated_at": "2026-08-12T06:06:41+00:00"
  },
  "P8748": {
    "problem_number": 8748,
    "slug": "open-fc-5a1703384c1c9545ad12-erdos-681",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:03+00:00",
    "updated_at": "2026-08-17T19:20:15+00:00"
  },
  "P12311": {
    "problem_number": 12311,
    "slug": "a-continued-fraction-for-the-euler-number-generating-function",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:37:19+00:00",
    "updated_at": "2026-09-01T19:37:24+00:00"
  },
  "P12499": {
    "problem_number": 12499,
    "slug": "a-cotangent-floor-index-identity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:00+00:00",
    "updated_at": "2026-09-02T21:42:11+00:00"
  },
  "P11794": {
    "problem_number": 11794,
    "slug": "a-cubic-supercongruence-for-a-binomial-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:44:47+00:00",
    "updated_at": "2026-08-30T12:44:56+00:00"
  },
  "P11704": {
    "problem_number": 11704,
    "slug": "a-cubic-modulus-primality-criterion-from-binomial-3n-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:11+00:00",
    "updated_at": "2026-08-30T11:16:18+00:00"
  },
  "P3594": {
    "problem_number": 3594,
    "slug": "cyclic-resolvable-sqs16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:44+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12261": {
    "problem_number": 12261,
    "slug": "a-decimal-anagram-orbit-approaching-a-10-adic-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:31:14+00:00",
    "updated_at": "2026-09-01T19:31:20+00:00"
  },
  "P12507": {
    "problem_number": 12507,
    "slug": "a-delannoy-diagonal-from-a-symmetric-recurrence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:48+00:00",
    "updated_at": "2026-09-02T21:42:56+00:00"
  },
  "P8100": {
    "problem_number": 8100,
    "slug": "open-fc-02a25dcf74d817a58b99-erdos-158",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:41+00:00",
    "updated_at": "2026-08-17T18:34:41+00:00"
  },
  "P3468": {
    "problem_number": 3468,
    "slug": "kourovka-21-90-a-diameter-three-q-polynomial-distance-regular-graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:04+00:00",
    "updated_at": "2026-08-12T08:06:05+00:00"
  },
  "P11851": {
    "problem_number": 11851,
    "slug": "a-digit-template-for-the-least-prime-with-n-fours",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:00+00:00",
    "updated_at": "2026-08-30T16:15:06+00:00"
  },
  "P12319": {
    "problem_number": 12319,
    "slug": "a-digit-frequency-limit-in-the-look-and-say-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:38:14+00:00",
    "updated_at": "2026-09-01T19:38:20+00:00"
  },
  "P12211": {
    "problem_number": 12211,
    "slug": "a-divisibility-pattern-in-a-partial-theta-generating-function",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:25:04+00:00",
    "updated_at": "2026-09-01T19:25:10+00:00"
  },
  "P11714": {
    "problem_number": 11714,
    "slug": "a-divisor-function-family-of-zumkeller-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:00+00:00",
    "updated_at": "2026-08-30T11:17:06+00:00"
  },
  "P12203": {
    "problem_number": 12203,
    "slug": "a-divisor-propagation-formula-at-odd-prime-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:24:04+00:00",
    "updated_at": "2026-09-01T19:24:11+00:00"
  },
  "P12317": {
    "problem_number": 12317,
    "slug": "a-factorial-quotient-hidden-in-a-modular-square-root",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:38:00+00:00",
    "updated_at": "2026-09-01T19:38:06+00:00"
  },
  "P11915": {
    "problem_number": 11915,
    "slug": "a-factorial-with-exactly-nine-decimal-4s",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:22:43+00:00",
    "updated_at": "2026-08-30T16:22:50+00:00"
  },
  "P12425": {
    "problem_number": 12425,
    "slug": "a-fixed-point-of-the-primorial-log-derivative",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:34:27+00:00",
    "updated_at": "2026-09-02T21:34:39+00:00"
  },
  "P12765": {
    "problem_number": 12765,
    "slug": "a-fixed-row-asymptotic-for-complete-increasing-subsequences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:48:28+00:00",
    "updated_at": "2026-09-02T22:49:12+00:00"
  },
  "P3650": {
    "problem_number": 3650,
    "slug": "flag-complex-fourteen-beta-two-thirteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:03+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2908": {
    "problem_number": 2908,
    "slug": "exponential-square-free-group",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:46:30+00:00",
    "updated_at": "2026-08-01T23:25:19+00:00"
  },
  "P11680": {
    "problem_number": 11680,
    "slug": "a-gap-below-every-later-maximal-binary-determinant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:09:07+00:00",
    "updated_at": "2026-08-30T11:11:28+00:00"
  },
  "P12583": {
    "problem_number": 12583,
    "slug": "a-gaussian-prime-on-every-positive-vertical-line",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:52:24+00:00",
    "updated_at": "2026-09-02T21:52:51+00:00"
  },
  "P12435": {
    "problem_number": 12435,
    "slug": "a-gcd-sum-modulo-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:35:34+00:00",
    "updated_at": "2026-09-02T21:35:45+00:00"
  },
  "P12509": {
    "problem_number": 12509,
    "slug": "a-greedy-sequence-with-one-residue-class",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:55+00:00",
    "updated_at": "2026-09-02T21:43:07+00:00"
  },
  "P2520": {
    "problem_number": 2520,
    "slug": "hadamard-order-668",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:14+00:00",
    "updated_at": "2026-07-29T20:55:45+00:00"
  },
  "P12431": {
    "problem_number": 12431,
    "slug": "a-hankel-congruence-modulo-49",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:35:10+00:00",
    "updated_at": "2026-09-02T21:35:21+00:00"
  },
  "P12777": {
    "problem_number": 12777,
    "slug": "a-largest-prime-factor-recurrence-near-n-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:54:09+00:00",
    "updated_at": "2026-09-02T22:54:51+00:00"
  },
  "P11835": {
    "problem_number": 11835,
    "slug": "a-limit-across-square-blocks-of-prime-indices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:13:47+00:00",
    "updated_at": "2026-08-30T16:13:54+00:00"
  },
  "P12633": {
    "problem_number": 12633,
    "slug": "a-limit-ratio-for-prime-ladders-around-doubling",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:04:27+00:00",
    "updated_at": "2026-09-02T22:04:55+00:00"
  },
  "P12569": {
    "problem_number": 12569,
    "slug": "a-logarithmic-lower-bound-for-a-parity-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:49:56+00:00",
    "updated_at": "2026-09-02T21:50:03+00:00"
  },
  "P12079": {
    "problem_number": 12079,
    "slug": "a-missing-count-of-digit-3-in-factorials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:46+00:00",
    "updated_at": "2026-09-01T19:08:52+00:00"
  },
  "P12643": {
    "problem_number": 12643,
    "slug": "a-mobius-cube-root-divisor-sum-test",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:23+00:00",
    "updated_at": "2026-09-02T22:07:27+00:00"
  },
  "P11746": {
    "problem_number": 11746,
    "slug": "a-mod-16-pattern-at-indices-one-below-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:38:15+00:00",
    "updated_at": "2026-08-30T11:40:10+00:00"
  },
  "P11758": {
    "problem_number": 11758,
    "slug": "a-multiplicative-lower-bound-for-numbers-of-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:23:14+00:00",
    "updated_at": "2026-08-30T12:23:23+00:00"
  },
  "P12209": {
    "problem_number": 12209,
    "slug": "a-nested-sum-identity-for-unsigned-stirling-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:24:49+00:00",
    "updated_at": "2026-09-01T19:24:55+00:00"
  },
  "P11810": {
    "problem_number": 11810,
    "slug": "a-new-least-odd-prime-factor-of-a-central-binomial-coefficient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:47:10+00:00",
    "updated_at": "2026-08-30T12:48:50+00:00"
  },
  "P11698": {
    "problem_number": 11698,
    "slug": "a-non-overlap-victory-for-a-consecutive-prime-divisibility-run",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:44+00:00",
    "updated_at": "2026-08-30T11:15:51+00:00"
  },
  "P11784": {
    "problem_number": 11784,
    "slug": "a-nonzero-stabilized-residue-among-prime-divisors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:39:05+00:00",
    "updated_at": "2026-08-30T12:40:59+00:00"
  },
  "P11869": {
    "problem_number": 11869,
    "slug": "a-one-eigenspace-formula-for-the-ribbon-to-homogeneous-transition-matrix",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:19+00:00",
    "updated_at": "2026-08-30T16:16:24+00:00"
  },
  "P12407": {
    "problem_number": 12407,
    "slug": "a-p-adic-binomial-supercongruence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:32:45+00:00",
    "updated_at": "2026-09-02T21:32:53+00:00"
  },
  "P12347": {
    "problem_number": 12347,
    "slug": "a-paired-prime-product-across-the-two-classes-modulo-six",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:41:37+00:00",
    "updated_at": "2026-09-01T19:41:43+00:00"
  },
  "P12305": {
    "problem_number": 12305,
    "slug": "a-partition-inequality-for-reverse-alternating-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:36:36+00:00",
    "updated_at": "2026-09-01T19:36:41+00:00"
  },
  "P2556": {
    "problem_number": 2556,
    "slug": "knight-strip-domination-period-six",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:27+00:00",
    "updated_at": "2026-08-01T23:32:28+00:00"
  },
  "P2838": {
    "problem_number": 2838,
    "slug": "polynomial-bijection-q2-q",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:37:09+00:00",
    "updated_at": "2026-08-01T12:25:09+00:00"
  },
  "P11718": {
    "problem_number": 11718,
    "slug": "a-power-sum-characterization-of-prime-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:17+00:00",
    "updated_at": "2026-08-30T11:17:23+00:00"
  },
  "P12581": {
    "problem_number": 12581,
    "slug": "a-prime-between-p-and-p-sqrt-p",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:52:13+00:00",
    "updated_at": "2026-09-02T21:52:19+00:00"
  },
  "P12611": {
    "problem_number": 12611,
    "slug": "a-prime-in-every-quadratic-interval",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:57:15+00:00",
    "updated_at": "2026-09-02T21:57:25+00:00"
  },
  "P11670": {
    "problem_number": 11670,
    "slug": "a-prime-of-every-length-using-only-digits-1-and-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:17+00:00",
    "updated_at": "2026-08-30T16:34:02+00:00"
  },
  "P12081": {
    "problem_number": 12081,
    "slug": "a-prime-permutation-from-odd-digit-sums-of-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:57+00:00",
    "updated_at": "2026-09-01T19:09:03+00:00"
  },
  "P11766": {
    "problem_number": 11766,
    "slug": "a-prime-plus-two-shifted-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:24:05+00:00",
    "updated_at": "2026-08-30T12:24:16+00:00"
  },
  "P12231": {
    "problem_number": 12231,
    "slug": "a-prime-power-congruence-for-tribonacci-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:27:31+00:00",
    "updated_at": "2026-09-01T19:27:37+00:00"
  },
  "P11891": {
    "problem_number": 11891,
    "slug": "a-prime-power-supercongruence-for-products-of-apery-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:29+00:00",
    "updated_at": "2026-08-30T16:20:35+00:00"
  },
  "P11849": {
    "problem_number": 11849,
    "slug": "a-prime-square-congruence-for-a-triple-factorial-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:52+00:00",
    "updated_at": "2026-08-30T16:14:57+00:00"
  },
  "P12437": {
    "problem_number": 12437,
    "slug": "a-primorial-minus-one-window",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:35:39+00:00",
    "updated_at": "2026-09-02T21:35:53+00:00"
  },
  "P11660": {
    "problem_number": 11660,
    "slug": "a-product-with-exactly-four-s-prime-factorizations",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:03:49+00:00",
    "updated_at": "2026-08-30T11:03:59+00:00"
  },
  "P2614": {
    "problem_number": 2614,
    "slug": "projective-plane-order-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:46+00:00",
    "updated_at": "2026-07-29T20:56:05+00:00"
  },
  "P12617": {
    "problem_number": 12617,
    "slug": "a-proposed-formula-for-the-least-inverse-totient-of-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:58:21+00:00",
    "updated_at": "2026-09-02T21:58:27+00:00"
  },
  "P2876": {
    "problem_number": 2876,
    "slug": "euclidean-three-space-rainbow-free-rhombus-colouring",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:42:14+00:00",
    "updated_at": "2026-08-01T12:07:41+00:00"
  },
  "P12127": {
    "problem_number": 12127,
    "slug": "a-ramanujan-prime-bound-in-the-residue-class-1-modulo-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:14:46+00:00",
    "updated_at": "2026-09-01T19:14:51+00:00"
  },
  "P12313": {
    "problem_number": 12313,
    "slug": "a-ratio-limit-for-binary-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:37:33+00:00",
    "updated_at": "2026-09-01T19:37:38+00:00"
  },
  "P12321": {
    "problem_number": 12321,
    "slug": "a-rational-family-of-accelerated-series-for-zeta-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:38:29+00:00",
    "updated_at": "2026-09-01T19:38:34+00:00"
  },
  "P12299": {
    "problem_number": 12299,
    "slug": "a-rational-generating-function-for-the-hal-tiling",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:35:55+00:00",
    "updated_at": "2026-09-01T19:36:00+00:00"
  },
  "P12533": {
    "problem_number": 12533,
    "slug": "a-recurrence-test-for-x-2-55y-2-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:45:21+00:00",
    "updated_at": "2026-09-02T21:45:32+00:00"
  },
  "P12619": {
    "problem_number": 12619,
    "slug": "a-restricted-recursion-for-minimum-prime-factor-sum-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:58:30+00:00",
    "updated_at": "2026-09-02T21:59:00+00:00"
  },
  "P2914": {
    "problem_number": 2914,
    "slug": "coalescence-stochastic-dominance-counterexample",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:47:19+00:00",
    "updated_at": "2026-08-01T11:34:23+00:00"
  },
  "P12403": {
    "problem_number": 12403,
    "slug": "a-root-of-unity-permanent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:32:21+00:00",
    "updated_at": "2026-09-02T21:32:29+00:00"
  },
  "P11792": {
    "problem_number": 11792,
    "slug": "a-safe-prime-in-every-doubled-interval",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:44:37+00:00",
    "updated_at": "2026-08-30T12:44:45+00:00"
  },
  "P12045": {
    "problem_number": 12045,
    "slug": "a-seven-n-bound-for-2-ramanujan-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:56:26+00:00",
    "updated_at": "2026-09-01T18:56:37+00:00"
  },
  "P12161": {
    "problem_number": 12161,
    "slug": "a-shifted-gilbreath-difference-triangle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:19:00+00:00",
    "updated_at": "2026-09-01T19:19:06+00:00"
  },
  "P12629": {
    "problem_number": 12629,
    "slug": "a-shifted-pascal-array-formula-for-the-vertical-sum-triangle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:00:48+00:00",
    "updated_at": "2026-09-02T22:01:23+00:00"
  },
  "P11752": {
    "problem_number": 11752,
    "slug": "a-smaller-prime-generating-two-prime-fields",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:22:44+00:00",
    "updated_at": "2026-08-30T12:22:52+00:00"
  },
  "P12751": {
    "problem_number": 12751,
    "slug": "a-sole-divisibility-exception-in-a056921",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:41:14+00:00",
    "updated_at": "2026-09-02T22:41:44+00:00"
  },
  "P11899": {
    "problem_number": 11899,
    "slug": "a-sqrt-2-2-displacement-bijection-for-rotated-triangular-lattices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:21:09+00:00",
    "updated_at": "2026-08-30T16:21:15+00:00"
  },
  "P12519": {
    "problem_number": 12519,
    "slug": "a-square-criterion-for-primes-of-the-form-k-2-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:43:59+00:00",
    "updated_at": "2026-09-02T21:44:10+00:00"
  },
  "P12309": {
    "problem_number": 12309,
    "slug": "a-strengthened-prime-power-congruence-for-a-binomial-cube-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:37:04+00:00",
    "updated_at": "2026-09-01T19:37:10+00:00"
  },
  "P11967": {
    "problem_number": 11967,
    "slug": "a-strengthened-supercongruence-for-averaged-apery-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:59:06+00:00",
    "updated_at": "2026-08-31T03:59:21+00:00"
  },
  "P12273": {
    "problem_number": 12273,
    "slug": "a-strong-asymptotic-for-n-queens-configurations",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:32:43+00:00",
    "updated_at": "2026-09-01T19:32:48+00:00"
  },
  "P12603": {
    "problem_number": 12603,
    "slug": "a-subsequence-question-for-multiply-perfect-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:55:46+00:00",
    "updated_at": "2026-09-02T21:55:53+00:00"
  },
  "P2854": {
    "problem_number": 2854,
    "slug": "support-three-zero-divisor-f2-group-ring",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:39:15+00:00",
    "updated_at": "2026-08-01T12:32:06+00:00"
  },
  "P2860": {
    "problem_number": 2860,
    "slug": "tarski-monster-exponent-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:40:03+00:00",
    "updated_at": "2026-08-01T23:49:48+00:00"
  },
  "P11738": {
    "problem_number": 11738,
    "slug": "a-ten-step-bound-for-convergent-digit-product-cube-trajectories",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:30:36+00:00",
    "updated_at": "2026-08-30T11:31:50+00:00"
  },
  "P12409": {
    "problem_number": 12409,
    "slug": "a-ternary-radius-one-covering",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:32:52+00:00",
    "updated_at": "2026-09-02T21:33:03+00:00"
  },
  "P12315": {
    "problem_number": 12315,
    "slug": "a-theta-coefficient-series-for-the-square-root-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:37:47+00:00",
    "updated_at": "2026-09-01T19:37:52+00:00"
  },
  "P11694": {
    "problem_number": 11694,
    "slug": "a-third-binary-concatenating-three-factor-representation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:26+00:00",
    "updated_at": "2026-08-30T11:15:33+00:00"
  },
  "P11959": {
    "problem_number": 11959,
    "slug": "a-third-noninitial-prime-in-the-fresh-remainder-gcd-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:53:29+00:00",
    "updated_at": "2026-08-31T03:53:32+00:00"
  },
  "P12183": {
    "problem_number": 12183,
    "slug": "a-triangular-square-and-pentagonal-representation-for-every-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:21:41+00:00",
    "updated_at": "2026-09-01T19:21:46+00:00"
  },
  "P2840": {
    "problem_number": 2840,
    "slug": "polynomial-image-z2-nonnegative-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:37:24+00:00",
    "updated_at": "2026-08-01T12:25:35+00:00"
  },
  "P12263": {
    "problem_number": 12263,
    "slug": "a-unique-equality-after-shifting-prime-factors-downward",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:31:30+00:00",
    "updated_at": "2026-09-01T19:31:36+00:00"
  },
  "P11788": {
    "problem_number": 11788,
    "slug": "a-universal-weighted-sum-of-five-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:44:17+00:00",
    "updated_at": "2026-08-30T12:44:25+00:00"
  },
  "P9710": {
    "problem_number": 9710,
    "slug": "open-fc-9a305855d834e1e28224-erdos-950-variants-weaker-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:00+00:00",
    "updated_at": "2026-08-17T20:02:01+00:00"
  },
  "P8956": {
    "problem_number": 8956,
    "slug": "open-fc-fd4fcfbe83d0bf1935c8-erdos-325-variants-weaker",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:18+00:00",
    "updated_at": "2026-08-17T19:41:19+00:00"
  },
  "P12295": {
    "problem_number": 12295,
    "slug": "a-wolstenholme-type-supercongruence-for-squared-binomial-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:35:27+00:00",
    "updated_at": "2026-09-01T19:35:32+00:00"
  },
  "P12471": {
    "problem_number": 12471,
    "slug": "a-zumkeller-partition-of-312",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:39:12+00:00",
    "updated_at": "2026-09-02T21:39:24+00:00"
  },
  "P8980": {
    "problem_number": 8980,
    "slug": "open-fc-6a5c0ec55564c6a440ec-erdos-32-variants-log-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:15+00:00",
    "updated_at": "2026-08-17T19:44:16+00:00"
  },
  "P8352": {
    "problem_number": 8352,
    "slug": "open-fc-22e177275f5293790e16-erdos-32",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:15+00:00",
    "updated_at": "2026-08-17T18:40:16+00:00"
  },
  "P2984": {
    "problem_number": 2984,
    "slug": "erdos-problem-32",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:52+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8280": {
    "problem_number": 8280,
    "slug": "open-fc-1b974656a30c0dbd3a43-complete-for-alpha-in-ioo-one-to-goldenratio",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:13+00:00",
    "updated_at": "2026-08-17T18:38:15+00:00"
  },
  "P2826": {
    "problem_number": 2826,
    "slug": "additive-cube-four-term-progression-alphabet",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:01+00:00",
    "updated_at": "2026-07-30T02:22:48+00:00"
  },
  "P11748": {
    "problem_number": 11748,
    "slug": "adjacent-terms-in-the-paired-run-squarefree-composite-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:22:23+00:00",
    "updated_at": "2026-08-30T12:22:31+00:00"
  },
  "P9004": {
    "problem_number": 9004,
    "slug": "open-fc-7efa5fcb3740793460a8-green-94",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:45+00:00",
    "updated_at": "2026-08-17T19:44:46+00:00"
  },
  "P12631": {
    "problem_number": 12631,
    "slug": "affine-generation-of-cantor-deletion-numerators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:02:26+00:00",
    "updated_at": "2026-09-02T22:03:00+00:00"
  },
  "P8770": {
    "problem_number": 8770,
    "slug": "open-fc-63de4509fe85b9d79132-agrawal-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:15:14+00:00",
    "updated_at": "2026-08-17T19:15:28+00:00"
  },
  "P8804": {
    "problem_number": 8804,
    "slug": "open-fc-899631ab2c36684b6da5-algebraicindependent-e-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:22:36+00:00",
    "updated_at": "2026-08-17T19:22:45+00:00"
  },
  "P11166": {
    "problem_number": 11166,
    "slug": "algebraicity-of-thue-morse-product-q",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:20:41+00:00",
    "updated_at": "2026-08-29T18:48:32+00:00"
  },
  "P9368": {
    "problem_number": 9368,
    "slug": "open-fc-f0782d0781084821f0b4-lam-litt-variants-integrality-implies-algebraicity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:13+00:00",
    "updated_at": "2026-08-17T19:51:13+00:00"
  },
  "P11686": {
    "problem_number": 11686,
    "slug": "aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:12:59+00:00",
    "updated_at": "2026-08-31T03:54:17+00:00"
  },
  "P3124": {
    "problem_number": 3124,
    "slug": "normalized-prime-gap-limit-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:06+00:00",
    "updated_at": "2026-08-02T12:53:35+00:00"
  },
  "P10806": {
    "problem_number": 10806,
    "slug": "unsolvedmath-0144-almost-invariant-sets-under-affine-maps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:20+00:00",
    "updated_at": "2026-08-18T02:55:21+00:00"
  },
  "P3478": {
    "problem_number": 3478,
    "slug": "kourovka-21-101-almost-simple-automorphism-groups-of-regular-maps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:28+00:00",
    "updated_at": "2026-08-12T08:06:36+00:00"
  },
  "P3472": {
    "problem_number": 3472,
    "slug": "kourovka-21-95-almost-simple-groups-recognizable-by-prime-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:09+00:00",
    "updated_at": "2026-08-12T08:06:13+00:00"
  },
  "P10788": {
    "problem_number": 10788,
    "slug": "unsolvedmath-0097-almost-sum-free-sets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:15+00:00",
    "updated_at": "2026-08-18T02:55:15+00:00"
  },
  "P8650": {
    "problem_number": 8650,
    "slug": "open-fc-8cf20e965e7efff4a9b0-erdos-522",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:22+00:00",
    "updated_at": "2026-08-17T18:59:32+00:00"
  },
  "P8152": {
    "problem_number": 8152,
    "slug": "open-fc-0826fac6caece8bcfbff-erdos-522-variants-zero-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:22+00:00",
    "updated_at": "2026-08-17T18:35:22+00:00"
  },
  "P8184": {
    "problem_number": 8184,
    "slug": "open-fc-0b8ec36aa8a624e21bef-erdos-400-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:36+00:00",
    "updated_at": "2026-08-17T18:36:37+00:00"
  },
  "P12353": {
    "problem_number": 12353,
    "slug": "almost-prime-middles-of-twin-prime-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:42:22+00:00",
    "updated_at": "2026-09-01T19:42:29+00:00"
  },
  "P12035": {
    "problem_number": 12035,
    "slug": "alternating-derangement-ratios-bracketing-e",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:54:26+00:00",
    "updated_at": "2026-09-01T18:54:37+00:00"
  },
  "P3456": {
    "problem_number": 3456,
    "slug": "kourovka-21-72-amenable-torsion-free-and-prime-exponent-tarski-monsters",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:36+00:00",
    "updated_at": "2026-08-12T08:05:38+00:00"
  },
  "P12327": {
    "problem_number": 12327,
    "slug": "an-abel-value-for-the-m-bius-weighted-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:39:12+00:00",
    "updated_at": "2026-09-01T19:39:17+00:00"
  },
  "P8292": {
    "problem_number": 8292,
    "slug": "open-fc-1c88aa9ae4f4a284f97a-isaccumulationpoint-three-halves-pow",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:28+00:00",
    "updated_at": "2026-08-17T18:38:36+00:00"
  },
  "P2620": {
    "problem_number": 2620,
    "slug": "apn-permutation-f256",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:48+00:00",
    "updated_at": "2026-07-29T20:55:04+00:00"
  },
  "P11841": {
    "problem_number": 11841,
    "slug": "an-arithmetic-derivative-goldbach-problem-for-three-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:20+00:00",
    "updated_at": "2026-08-30T16:14:25+00:00"
  },
  "P11092": {
    "problem_number": 11092,
    "slug": "an-asymptotic-solution-to-the-erd-s-four-edge-intersection-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T01:03:50+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P11903": {
    "problem_number": 11903,
    "slug": "an-exact-linear-recurrence-for-the-pisot-sequence-t-5-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:21:29+00:00",
    "updated_at": "2026-08-30T16:21:34+00:00"
  },
  "P3086": {
    "problem_number": 3086,
    "slug": "constructive-exponential-ramsey-lower-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:57+00:00",
    "updated_at": "2026-08-02T12:48:03+00:00"
  },
  "P11606": {
    "problem_number": 11606,
    "slug": "an-explicit-generating-function-for-solid-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:37:57+00:00",
    "updated_at": "2026-08-30T04:38:05+00:00"
  },
  "P2618": {
    "problem_number": 2618,
    "slug": "extremal-type-ii-code-72",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:47+00:00",
    "updated_at": "2026-07-29T20:55:39+00:00"
  },
  "P2526": {
    "problem_number": 2526,
    "slug": "ideal-pte-size-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:16+00:00",
    "updated_at": "2026-08-01T23:30:34+00:00"
  },
  "P2926": {
    "problem_number": 2926,
    "slug": "all-operators-norm-attaining-banach-space",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:48:55+00:00",
    "updated_at": "2026-08-01T11:30:52+00:00"
  },
  "P11742": {
    "problem_number": 11742,
    "slug": "an-integrality-product-built-from-consecutive-prime-gaps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:33:31+00:00",
    "updated_at": "2026-08-30T11:35:37+00:00"
  },
  "P12423": {
    "problem_number": 12423,
    "slug": "an-irreducible-ap-ry-polynomial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:34:21+00:00",
    "updated_at": "2026-09-02T21:34:28+00:00"
  },
  "P2868": {
    "problem_number": 2868,
    "slug": "o-minimal-super-iterated-exponential",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:41:09+00:00",
    "updated_at": "2026-08-01T12:21:43+00:00"
  },
  "P48": {
    "problem_number": 48,
    "slug": "andrews-curtis-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T11:31:15+00:00"
  },
  "P8504": {
    "problem_number": 8504,
    "slug": "open-fc-58d606ac4af305b0a96a-andrica-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:13+00:00",
    "updated_at": "2026-08-17T18:53:18+00:00"
  },
  "P11855": {
    "problem_number": 11855,
    "slug": "another-equal-pair-in-the-tuple-factorial-smarandache-function",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:18+00:00",
    "updated_at": "2026-08-30T16:15:23+00:00"
  },
  "P11720": {
    "problem_number": 11720,
    "slug": "antichain-sums-of-shifted-5-smooth-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:25+00:00",
    "updated_at": "2026-08-30T11:17:32+00:00"
  },
  "P9658": {
    "problem_number": 9658,
    "slug": "open-fc-586cfdb006bd0060a750-beaver-math-olympiad-problem-2-antihydra-variants-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:43+00:00",
    "updated_at": "2026-08-17T20:00:44+00:00"
  },
  "P12133": {
    "problem_number": 12133,
    "slug": "arbitrarily-long-constant-runs-in-a-prime-interval-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:15:31+00:00",
    "updated_at": "2026-09-01T19:15:37+00:00"
  },
  "P11376": {
    "problem_number": 11376,
    "slug": "arbitrarily-long-one-runs-in-last-half-word",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:42:05+00:00",
    "updated_at": "2026-08-29T18:52:00+00:00"
  },
  "P11186": {
    "problem_number": 11186,
    "slug": "red-black-rooted-tree-count-prime-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:46:34+00:00",
    "updated_at": "2026-08-29T18:48:49+00:00"
  },
  "P11388": {
    "problem_number": 11388,
    "slug": "prime-squarefree-parts-fibonacci-square-indices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:45:24+00:00",
    "updated_at": "2026-08-29T18:52:13+00:00"
  },
  "P11390": {
    "problem_number": 11390,
    "slug": "cyclotomic-values-at-two-squarefree-exceptions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:45:48+00:00",
    "updated_at": "2026-08-29T18:52:16+00:00"
  },
  "P11426": {
    "problem_number": 11426,
    "slug": "factorial-divisor-count-exceptions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:55:09+00:00",
    "updated_at": "2026-08-29T18:52:49+00:00"
  },
  "P12729": {
    "problem_number": 12729,
    "slug": "are-all-a068779-terms-after-a-4-multiples-of-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:33:22+00:00",
    "updated_at": "2026-09-02T22:44:59+00:00"
  },
  "P12355": {
    "problem_number": 12355,
    "slug": "are-all-almost-perfect-numbers-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:42:38+00:00",
    "updated_at": "2026-09-01T19:42:44+00:00"
  },
  "P12677": {
    "problem_number": 12677,
    "slug": "are-all-bernoulli-gcd-indices-congruent-to-7-modulo-21",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:11:16+00:00",
    "updated_at": "2026-09-02T22:11:20+00:00"
  },
  "P11290": {
    "problem_number": 11290,
    "slug": "catalan-square-coefficient-polynomials-irreducible",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:21:50+00:00",
    "updated_at": "2026-08-29T18:50:36+00:00"
  },
  "P11500": {
    "problem_number": 11500,
    "slug": "lucas-product-coefficient-range",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:30:12+00:00",
    "updated_at": "2026-08-29T18:53:56+00:00"
  },
  "P11508": {
    "problem_number": 11508,
    "slug": "cyclic-class-group-maxima-modulo-24",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:36:28+00:00",
    "updated_at": "2026-08-29T18:54:02+00:00"
  },
  "P12193": {
    "problem_number": 12193,
    "slug": "are-all-large-absolute-primes-decimal-repunits",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:22:53+00:00",
    "updated_at": "2026-09-01T19:22:58+00:00"
  },
  "P11907": {
    "problem_number": 11907,
    "slug": "are-all-multiply-perfect-numbers-practical",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:21:49+00:00",
    "updated_at": "2026-08-30T16:21:56+00:00"
  },
  "P12761": {
    "problem_number": 12761,
    "slug": "are-all-normalized-domb-hankel-determinants-positive-and-odd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:46:56+00:00",
    "updated_at": "2026-09-02T22:47:24+00:00"
  },
  "P11905": {
    "problem_number": 11905,
    "slug": "are-all-powers-of-two-after-2-168-decimal-pandigital",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:21:39+00:00",
    "updated_at": "2026-08-30T16:21:45+00:00"
  },
  "P12755": {
    "problem_number": 12755,
    "slug": "are-all-solutions-of-the-neighboring-divisor-sum-balance-odd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:43:54+00:00",
    "updated_at": "2026-09-02T22:44:25+00:00"
  },
  "P11420": {
    "problem_number": 11420,
    "slug": "eventual-pandigitality-of-powers-of-eleven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:53:54+00:00",
    "updated_at": "2026-08-29T18:52:44+00:00"
  },
  "P12783": {
    "problem_number": 12783,
    "slug": "are-all-unitary-weird-numbers-divisible-by-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T23:05:43+00:00",
    "updated_at": "2026-09-02T23:06:12+00:00"
  },
  "P11348": {
    "problem_number": 11348,
    "slug": "consecutive-prime-gpf-recurrence-preperiods-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:32:48+00:00",
    "updated_at": "2026-08-29T18:51:39+00:00"
  },
  "P11438": {
    "problem_number": 11438,
    "slug": "cyclic-difference-basis-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:59:31+00:00",
    "updated_at": "2026-08-29T18:52:57+00:00"
  },
  "P12613": {
    "problem_number": 12613,
    "slug": "are-disjoint-composite-runs-always-preceded-by-a-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:57:18+00:00",
    "updated_at": "2026-09-02T21:57:56+00:00"
  },
  "P11378": {
    "problem_number": 11378,
    "slug": "integer-complexity-downward-jumps-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:42:30+00:00",
    "updated_at": "2026-08-29T18:52:02+00:00"
  },
  "P11402": {
    "problem_number": 11402,
    "slug": "factorial-odd-even-divisor-sums-finite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:49:08+00:00",
    "updated_at": "2026-08-29T18:52:32+00:00"
  },
  "P11398": {
    "problem_number": 11398,
    "slug": "fermat-congruence-maximal-lift-heights-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:48:16+00:00",
    "updated_at": "2026-08-29T18:52:27+00:00"
  },
  "P11322": {
    "problem_number": 11322,
    "slug": "maximal-linked-prime-chain-lengths-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:22:28+00:00",
    "updated_at": "2026-08-29T18:51:12+00:00"
  },
  "P12003": {
    "problem_number": 12003,
    "slug": "are-nine-indices-the-complete-bernoulli-denominator-equality-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:34:24+00:00",
    "updated_at": "2026-09-01T18:35:53+00:00"
  },
  "P11490": {
    "problem_number": 11490,
    "slug": "finiteness-of-highly-composite-refactorable-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:24:55+00:00",
    "updated_at": "2026-08-29T18:53:49+00:00"
  },
  "P11190": {
    "problem_number": 11190,
    "slug": "apery-like-binomial-polynomial-irreducibility",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:47:25+00:00",
    "updated_at": "2026-08-29T18:48:53+00:00"
  },
  "P11418": {
    "problem_number": 11418,
    "slug": "cube-root-two-continued-fraction-partial-quotients-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:53:31+00:00",
    "updated_at": "2026-08-29T18:52:43+00:00"
  },
  "P11336": {
    "problem_number": 11336,
    "slug": "unbounded-partial-quotients-cube-root-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:27:21+00:00",
    "updated_at": "2026-08-29T18:51:28+00:00"
  },
  "P11422": {
    "problem_number": 11422,
    "slug": "coupled-nested-rs-global-definition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:54:18+00:00",
    "updated_at": "2026-08-29T18:52:47+00:00"
  },
  "P12665": {
    "problem_number": 12665,
    "slug": "are-the-gcd-values-at-powers-of-two-always-1-except-at-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:09:50+00:00",
    "updated_at": "2026-09-02T22:09:55+00:00"
  },
  "P11484": {
    "problem_number": 11484,
    "slug": "clique-divergence-of-the-snub-disphenoid",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:21:20+00:00",
    "updated_at": "2026-08-29T18:53:45+00:00"
  },
  "P12759": {
    "problem_number": 12759,
    "slug": "are-the-limit-superior-and-inferior-of-a-n-n-equal-to-1-and-0-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:46:11+00:00",
    "updated_at": "2026-09-02T22:46:48+00:00"
  },
  "P11194": {
    "problem_number": 11194,
    "slug": "triperfect-number-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:48:11+00:00",
    "updated_at": "2026-08-29T18:48:57+00:00"
  },
  "P11210": {
    "problem_number": 11210,
    "slug": "consecutive-prime-product-residue-prime-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:51:53+00:00",
    "updated_at": "2026-08-29T18:49:12+00:00"
  },
  "P11450": {
    "problem_number": 11450,
    "slug": "arbitrarily-long-zero-runs-of-the-mertens-function",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:03:44+00:00",
    "updated_at": "2026-08-29T18:53:13+00:00"
  },
  "P12769": {
    "problem_number": 12769,
    "slug": "are-there-finitely-many-exponents-dividing-the-digit-sum-of-6-k",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:50:45+00:00",
    "updated_at": "2026-09-02T22:51:23+00:00"
  },
  "P12019": {
    "problem_number": 12019,
    "slug": "are-there-finitely-many-integers-of-abundancy-13-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:51:14+00:00",
    "updated_at": "2026-09-01T18:51:25+00:00"
  },
  "P11236": {
    "problem_number": 11236,
    "slug": "unitary-divisor-sum-iterate-multiplier-three-finiteness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:01:20+00:00",
    "updated_at": "2026-08-29T18:49:40+00:00"
  },
  "P11446": {
    "problem_number": 11446,
    "slug": "infinitely-many-adjacent-equal-divisor-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:02:56+00:00",
    "updated_at": "2026-08-29T18:53:07+00:00"
  },
  "P11558": {
    "problem_number": 11558,
    "slug": "infinitude-of-binary-and-balanced-ternary-palindromes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:04:59+00:00",
    "updated_at": "2026-08-29T18:54:39+00:00"
  },
  "P11170": {
    "problem_number": 11170,
    "slug": "oeis-a085104-infinitely-many-brazilian-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:22:01+00:00",
    "updated_at": "2026-08-29T18:48:40+00:00"
  },
  "P12663": {
    "problem_number": 12663,
    "slug": "are-there-infinitely-many-gap-two-neighbors-in-the-a066728-fiber-at-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:09:41+00:00",
    "updated_at": "2026-09-02T22:09:46+00:00"
  },
  "P11480": {
    "problem_number": 11480,
    "slug": "mem0-infinitely-many-immortal-nim-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:18:36+00:00",
    "updated_at": "2026-08-29T18:53:41+00:00"
  },
  "P11524": {
    "problem_number": 11524,
    "slug": "infinitely-many-integer-complexity-multiplicative-drops",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:45:50+00:00",
    "updated_at": "2026-08-29T18:54:15+00:00"
  },
  "P11346": {
    "problem_number": 11346,
    "slug": "infinitely-many-ramanujan-tau-one-mod-p-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:31:30+00:00",
    "updated_at": "2026-08-29T18:51:38+00:00"
  },
  "P11546": {
    "problem_number": 11546,
    "slug": "infinitely-many-quartic-only-unit-indecomposables",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:59:44+00:00",
    "updated_at": "2026-08-29T18:54:31+00:00"
  },
  "P11498": {
    "problem_number": 11498,
    "slug": "finite-squarefree-neighbor-moduli",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:28:35+00:00",
    "updated_at": "2026-08-29T18:53:54+00:00"
  },
  "P11252": {
    "problem_number": 11252,
    "slug": "prime-free-gaps-between-composite-prime-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:05:33+00:00",
    "updated_at": "2026-08-29T18:49:57+00:00"
  },
  "P12223": {
    "problem_number": 12223,
    "slug": "arithmetic-derivatives-modulo-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:26:31+00:00",
    "updated_at": "2026-09-01T19:26:37+00:00"
  },
  "P8820": {
    "problem_number": 8820,
    "slug": "open-fc-9748f1251a2cd15c9866-artin-primitive-roots-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:23+00:00",
    "updated_at": "2026-08-17T19:24:30+00:00"
  },
  "P18": {
    "problem_number": 18,
    "slug": "artins-primitive-root-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:31:37+00:00"
  },
  "P2828": {
    "problem_number": 2828,
    "slug": "first-order-spectra-complement-closure",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:02+00:00",
    "updated_at": "2026-07-30T00:55:00+00:00"
  },
  "P8876": {
    "problem_number": 8876,
    "slug": "open-fc-c32eb1c039c17d3489e9-erdos-726",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:08+00:00",
    "updated_at": "2026-08-17T19:36:09+00:00"
  },
  "P8338": {
    "problem_number": 8338,
    "slug": "open-fc-21df1c18a0a921fd707f-erdos-357-variants-monotone-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:03+00:00",
    "updated_at": "2026-08-17T18:40:04+00:00"
  },
  "P8300": {
    "problem_number": 8300,
    "slug": "open-fc-1e4edd65085d9e5eba31-erdos-1054-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:51+00:00",
    "updated_at": "2026-08-17T18:38:56+00:00"
  },
  "P8110": {
    "problem_number": 8110,
    "slug": "open-fc-02ff093eec583c06b5a5-erdos-507-equivalent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:44+00:00",
    "updated_at": "2026-08-17T18:34:44+00:00"
  },
  "P3190": {
    "problem_number": 3190,
    "slug": "erdos-problem-1137",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:50:26+00:00",
    "updated_at": "2026-08-12T05:50:39+00:00"
  },
  "P9816": {
    "problem_number": 9816,
    "slug": "open-fc-ece9979e1979933027f7-twentyone-le-rank-height-count-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:56+00:00",
    "updated_at": "2026-08-17T20:02:56+00:00"
  },
  "P8262": {
    "problem_number": 8262,
    "slug": "open-fc-182cfe633493d9c9d039-error-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:52+00:00",
    "updated_at": "2026-08-17T18:37:54+00:00"
  },
  "P8220": {
    "problem_number": 8220,
    "slug": "open-fc-11d9e33d666ff6e62d4f-numtransversalszn",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:16+00:00",
    "updated_at": "2026-08-17T18:37:19+00:00"
  },
  "P9594": {
    "problem_number": 9594,
    "slug": "open-fc-e2b70fe9645f95a6afed-erdos-770-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:27+00:00",
    "updated_at": "2026-08-17T19:56:29+00:00"
  },
  "P9250": {
    "problem_number": 9250,
    "slug": "open-fc-9625b06121a7fe8b7361-erdos-390",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:24+00:00",
    "updated_at": "2026-08-17T19:50:24+00:00"
  },
  "P3298": {
    "problem_number": 3298,
    "slug": "erdos-problem-170",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:24+00:00",
    "updated_at": "2026-08-12T06:03:26+00:00"
  },
  "P8620": {
    "problem_number": 8620,
    "slug": "open-fc-4007d216e8329c03aa3a-erdos170",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:14+00:00",
    "updated_at": "2026-08-17T19:10:17+00:00"
  },
  "P9232": {
    "problem_number": 9232,
    "slug": "open-fc-8113e4f708c7daa12136-erdos-912-variants-tao",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:06+00:00",
    "updated_at": "2026-08-17T19:50:09+00:00"
  },
  "P8356": {
    "problem_number": 8356,
    "slug": "open-fc-231fe048d8bfc961273d-erdos-912",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:18+00:00",
    "updated_at": "2026-08-17T18:40:19+00:00"
  },
  "P3304": {
    "problem_number": 3304,
    "slug": "erdos-problem-975",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:41+00:00",
    "updated_at": "2026-08-12T06:03:42+00:00"
  },
  "P9874": {
    "problem_number": 9874,
    "slug": "open-fc-5cf43027d0ddbb9c2959-erdos-975",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:10+00:00",
    "updated_at": "2026-08-17T20:04:10+00:00"
  },
  "P8340": {
    "problem_number": 8340,
    "slug": "open-fc-222a4f9bd71aaf400a7b-rank-height-count-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:05+00:00",
    "updated_at": "2026-08-17T18:40:07+00:00"
  },
  "P9288": {
    "problem_number": 9288,
    "slug": "open-fc-b1a80ef78d5a7b102579-green-39-variant-theta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:38+00:00",
    "updated_at": "2026-08-17T19:50:38+00:00"
  },
  "P9330": {
    "problem_number": 9330,
    "slug": "open-fc-d12d6df6f41c70c493b7-green-39-variant-101",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:56+00:00",
    "updated_at": "2026-08-17T19:50:56+00:00"
  },
  "P8522": {
    "problem_number": 8522,
    "slug": "open-fc-61b832d3db3cfafcab78-erdos-859",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:09+00:00",
    "updated_at": "2026-08-17T18:54:10+00:00"
  },
  "P3192": {
    "problem_number": 3192,
    "slug": "erdos-problem-456",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:50:41+00:00",
    "updated_at": "2026-08-12T05:50:52+00:00"
  },
  "P9198": {
    "problem_number": 9198,
    "slug": "open-fc-4ef5c2d68c9e901dda68-erdos-456-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:13+00:00",
    "updated_at": "2026-08-17T19:49:13+00:00"
  },
  "P3340": {
    "problem_number": 3340,
    "slug": "erdos-problem-1061",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:54+00:00",
    "updated_at": "2026-08-12T06:07:10+00:00"
  },
  "P9084": {
    "problem_number": 9084,
    "slug": "open-fc-b94d49572087065128d4-half-rank-zero-and-half-rank-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:12+00:00",
    "updated_at": "2026-08-17T19:47:14+00:00"
  },
  "P9228": {
    "problem_number": 9228,
    "slug": "open-fc-7f36b9c5930935bd52a5-erdos-1002",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:58+00:00",
    "updated_at": "2026-08-17T19:50:00+00:00"
  },
  "P8106": {
    "problem_number": 8106,
    "slug": "open-fc-02ee456433625c557d3a-erdos-789-variants-cube-root-linearithmic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:42+00:00",
    "updated_at": "2026-08-17T18:34:43+00:00"
  },
  "P9094": {
    "problem_number": 9094,
    "slug": "open-fc-c24331e9351320491781-erdos-950-variants-sum-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:26+00:00",
    "updated_at": "2026-08-17T19:47:28+00:00"
  },
  "P8948": {
    "problem_number": 8948,
    "slug": "open-fc-f6aaa6f6e8de1af55e60-first-hardy-littlewood-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:13+00:00",
    "updated_at": "2026-08-17T19:41:15+00:00"
  },
  "P3048": {
    "problem_number": 3048,
    "slug": "erdos-problem-142",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:20+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8206": {
    "problem_number": 8206,
    "slug": "open-fc-0e6ed7ca217436e103f1-erdos-142-variants-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:05+00:00",
    "updated_at": "2026-08-17T18:37:07+00:00"
  },
  "P8420": {
    "problem_number": 8420,
    "slug": "open-fc-2c702381777a97a85e78-erdos-857",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:49+00:00",
    "updated_at": "2026-08-17T19:05:04+00:00"
  },
  "P10010": {
    "problem_number": 10010,
    "slug": "open-fc-c3bdd5f615cacc4d6dd4-erdos-416-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:23+00:00",
    "updated_at": "2026-08-17T20:05:23+00:00"
  },
  "P12235": {
    "problem_number": 12235,
    "slug": "asymptotic-growth-of-a-double-euler-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:28:00+00:00",
    "updated_at": "2026-09-01T19:28:06+00:00"
  },
  "P8330": {
    "problem_number": 8330,
    "slug": "open-fc-20bf04e3817d061f28ce-erdos-950-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:49+00:00",
    "updated_at": "2026-08-17T18:39:57+00:00"
  },
  "P8274": {
    "problem_number": 8274,
    "slug": "open-fc-1a2540b413ca12fcecbc-erdos-138-variants-quotient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:06+00:00",
    "updated_at": "2026-08-17T18:38:09+00:00"
  },
  "P3044": {
    "problem_number": 3044,
    "slug": "erdos-problem-138",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:16+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P3246": {
    "problem_number": 3246,
    "slug": "erdos-problem-1106",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:57:38+00:00",
    "updated_at": "2026-08-12T05:57:43+00:00"
  },
  "P3274": {
    "problem_number": 3274,
    "slug": "erdos-problem-562",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:00:07+00:00",
    "updated_at": "2026-08-12T06:00:09+00:00"
  },
  "P9112": {
    "problem_number": 9112,
    "slug": "open-fc-ce827a0d84547b6e1581-erdos-562",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:40+00:00",
    "updated_at": "2026-08-17T19:47:40+00:00"
  },
  "P8378": {
    "problem_number": 8378,
    "slug": "open-fc-25d735a3cfcd79e9f8f3-erdos-200",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:45+00:00",
    "updated_at": "2026-08-17T18:48:47+00:00"
  },
  "P3346": {
    "problem_number": 3346,
    "slug": "erdos-problem-272",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:07:51+00:00",
    "updated_at": "2026-08-12T06:07:59+00:00"
  },
  "P8278": {
    "problem_number": 8278,
    "slug": "open-fc-1b5f8e837e9dfdb6c879-erdos-272",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:11+00:00",
    "updated_at": "2026-08-17T18:38:13+00:00"
  },
  "P3244": {
    "problem_number": 3244,
    "slug": "erdos-problem-241",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:57:22+00:00",
    "updated_at": "2026-08-12T05:57:31+00:00"
  },
  "P8656": {
    "problem_number": 8656,
    "slug": "open-fc-4f3c9478a207d73c4484-erdos-241",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:51+00:00",
    "updated_at": "2026-08-17T19:00:02+00:00"
  },
  "P10024": {
    "problem_number": 10024,
    "slug": "open-fc-cdebbea89b768f267457-erdos-153",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:30+00:00",
    "updated_at": "2026-08-17T20:05:31+00:00"
  },
  "P3054": {
    "problem_number": 3054,
    "slug": "erdos-problem-153",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:26+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8568": {
    "problem_number": 8568,
    "slug": "open-fc-7a6d775041d1bbc4ab27-green-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:55:10+00:00",
    "updated_at": "2026-08-17T18:55:18+00:00"
  },
  "P8652": {
    "problem_number": 8652,
    "slug": "open-fc-4c41633c21cba2adecd8-green-40-variants-arbitrary-subsets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:33+00:00",
    "updated_at": "2026-08-17T18:59:45+00:00"
  },
  "P8390": {
    "problem_number": 8390,
    "slug": "open-fc-27a6fba43c3a2d5ca605-erdos-295",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:07+00:00",
    "updated_at": "2026-08-17T18:49:09+00:00"
  },
  "P8548": {
    "problem_number": 8548,
    "slug": "open-fc-6e5a7b06825e8849c95b-erdos-1054-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:33+00:00",
    "updated_at": "2026-08-17T18:54:35+00:00"
  },
  "P3026": {
    "problem_number": 3026,
    "slug": "erdos-problem-98",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:55+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9798": {
    "problem_number": 9798,
    "slug": "open-fc-e04ed4cb68e5c978b799-erdos-98",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:45+00:00",
    "updated_at": "2026-08-17T20:02:45+00:00"
  },
  "P9898": {
    "problem_number": 9898,
    "slug": "open-fc-6e7f648ca40864be6e9b-erdos-889-variants-general",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:22+00:00",
    "updated_at": "2026-08-17T20:04:22+00:00"
  },
  "P9674": {
    "problem_number": 9674,
    "slug": "open-fc-700055b3480c2e8cc33c-erdos-539",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:06+00:00",
    "updated_at": "2026-08-17T20:01:08+00:00"
  },
  "P9876": {
    "problem_number": 9876,
    "slug": "open-fc-5e20c7d663bc31d49ecb-erdos-359-variants-isgoodfor-1-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:11+00:00",
    "updated_at": "2026-08-17T20:04:11+00:00"
  },
  "P8702": {
    "problem_number": 8702,
    "slug": "open-fc-3bf8315b8d04eda542c7-erdos-385-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:52+00:00",
    "updated_at": "2026-08-17T19:09:58+00:00"
  },
  "P3352": {
    "problem_number": 3352,
    "slug": "erdos-problem-600",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:08:28+00:00",
    "updated_at": "2026-08-12T06:08:32+00:00"
  },
  "P8796": {
    "problem_number": 8796,
    "slug": "open-fc-8233df64c46ca1934729-erdos-600-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:21:36+00:00",
    "updated_at": "2026-08-17T19:21:44+00:00"
  },
  "P9754": {
    "problem_number": 9754,
    "slug": "open-fc-bbff26cb51cdb4541b35-erdos-142",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:23+00:00",
    "updated_at": "2026-08-17T20:02:23+00:00"
  },
  "P8772": {
    "problem_number": 8772,
    "slug": "open-fc-7d5d15ace5bbe2bd887a-erdos-853-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:15:18+00:00",
    "updated_at": "2026-08-17T19:21:18+00:00"
  },
  "P9170": {
    "problem_number": 9170,
    "slug": "open-fc-fa2316543dffc72bbf15-a-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:55+00:00",
    "updated_at": "2026-08-17T19:47:55+00:00"
  },
  "P8622": {
    "problem_number": 8622,
    "slug": "open-fc-87cfd9187ac77a2a5f9e-erdos-359-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:22+00:00",
    "updated_at": "2026-08-17T18:58:34+00:00"
  },
  "P8138": {
    "problem_number": 8138,
    "slug": "open-fc-05b8aa8457d91622d1af-erdos-357-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:02+00:00",
    "updated_at": "2026-08-17T18:35:04+00:00"
  },
  "P3188": {
    "problem_number": 3188,
    "slug": "erdos-problem-357",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:50:15+00:00",
    "updated_at": "2026-08-12T05:50:22+00:00"
  },
  "P9106": {
    "problem_number": 9106,
    "slug": "open-fc-c8171079704d4623adc3-erdos-789",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:37+00:00",
    "updated_at": "2026-08-17T19:47:37+00:00"
  },
  "P3214": {
    "problem_number": 3214,
    "slug": "erdos-problem-789",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:53:04+00:00",
    "updated_at": "2026-08-12T05:53:08+00:00"
  },
  "P9972": {
    "problem_number": 9972,
    "slug": "open-fc-a5a0657cc5a1f83f2dac-erdos-82",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:04+00:00",
    "updated_at": "2026-08-17T20:05:04+00:00"
  },
  "P3016": {
    "problem_number": 3016,
    "slug": "erdos-problem-82",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:42+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P12389": {
    "problem_number": 12389,
    "slug": "asymptotic-growth-of-the-mian-chowla-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:30:51+00:00",
    "updated_at": "2026-09-02T21:31:04+00:00"
  },
  "P9348": {
    "problem_number": 9348,
    "slug": "open-fc-e1d92535f239e50ce8a7-green-37-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:04+00:00",
    "updated_at": "2026-08-17T19:51:04+00:00"
  },
  "P9104": {
    "problem_number": 9104,
    "slug": "open-fc-c74e9b41e89a76681440-erdos-624",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:36+00:00",
    "updated_at": "2026-08-17T19:47:36+00:00"
  },
  "P9724": {
    "problem_number": 9724,
    "slug": "open-fc-a2f3098c82dcfae7022e-erdos-18b",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:05+00:00",
    "updated_at": "2026-08-17T20:02:05+00:00"
  },
  "P9350": {
    "problem_number": 9350,
    "slug": "open-fc-e29ff775eb760c4c4cb1-erdos-456-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:04+00:00",
    "updated_at": "2026-08-17T19:51:04+00:00"
  },
  "P9958": {
    "problem_number": 9958,
    "slug": "open-fc-9afb4fe3ba0113882465-erdos-156",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:54+00:00",
    "updated_at": "2026-08-17T20:04:55+00:00"
  },
  "P9096": {
    "problem_number": 9096,
    "slug": "open-fc-c33c70393444fc5bcf6a-green-40-variants-all-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:29+00:00",
    "updated_at": "2026-08-17T19:47:30+00:00"
  },
  "P8268": {
    "problem_number": 8268,
    "slug": "open-fc-19b09dd75e7f13bfe410-erdos-409-parts-i-islittleo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:02+00:00",
    "updated_at": "2026-08-17T18:38:03+00:00"
  },
  "P8808": {
    "problem_number": 8808,
    "slug": "open-fc-910439e827d6ddf3c1ba-erdos-138-variants-dvd-two-pow",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:23:11+00:00",
    "updated_at": "2026-08-17T19:23:20+00:00"
  },
  "P8860": {
    "problem_number": 8860,
    "slug": "open-fc-b62062dec231cbc07abc-erdos-357-parts-ii-bigtheta-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:14+00:00",
    "updated_at": "2026-08-17T19:35:19+00:00"
  },
  "P8878": {
    "problem_number": 8878,
    "slug": "open-fc-c4166924755d331d388c-erdos-357-variants-monotone-parts-ii-bigtheta-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:11+00:00",
    "updated_at": "2026-08-17T19:36:14+00:00"
  },
  "P8558": {
    "problem_number": 8558,
    "slug": "open-fc-7378bc511725cab34403-erdos-319-variants-istheta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:47+00:00",
    "updated_at": "2026-08-17T18:54:49+00:00"
  },
  "P9556": {
    "problem_number": 9556,
    "slug": "open-fc-c44898d0971a719994bb-growthratezn",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:14+00:00",
    "updated_at": "2026-08-17T19:55:16+00:00"
  },
  "P8874": {
    "problem_number": 8874,
    "slug": "open-fc-c17ff7f6738ee1f0afba-voronovskaja-theorem-bezier-bernstein-operators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:07+00:00",
    "updated_at": "2026-08-17T19:36:08+00:00"
  },
  "P8608": {
    "problem_number": 8608,
    "slug": "open-fc-835e1922e6082fc96800-erdos-812-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:28+00:00",
    "updated_at": "2026-08-17T20:01:46+00:00"
  },
  "P8562": {
    "problem_number": 8562,
    "slug": "open-fc-75fa172fe6b35e376018-erdos-323-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:52+00:00",
    "updated_at": "2026-08-17T18:54:53+00:00"
  },
  "P8414": {
    "problem_number": 8414,
    "slug": "open-fc-2b90c53cae83b2ed479a-erdos-325",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:26+00:00",
    "updated_at": "2026-08-17T18:50:31+00:00"
  },
  "P3282": {
    "problem_number": 3282,
    "slug": "erdos-problem-325",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:44+00:00",
    "updated_at": "2026-08-12T06:02:47+00:00"
  },
  "P8264": {
    "problem_number": 8264,
    "slug": "open-fc-18a8aa6e7d4a325f425c-erdos-507-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:54+00:00",
    "updated_at": "2026-08-17T18:37:59+00:00"
  },
  "P9226": {
    "problem_number": 9226,
    "slug": "open-fc-7b53cff84b80709a9664-erdos-688-parts-i-lower-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:52+00:00",
    "updated_at": "2026-08-17T19:49:56+00:00"
  },
  "P8116": {
    "problem_number": 8116,
    "slug": "open-fc-03f2864ca31d2661abc1-erdos-357-variants-monotone-parts-ii-littleo-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:45+00:00",
    "updated_at": "2026-08-17T18:34:46+00:00"
  },
  "P9362": {
    "problem_number": 9362,
    "slug": "open-fc-eb7a14044a6e5dda4078-erdos-872-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:10+00:00",
    "updated_at": "2026-08-17T19:51:10+00:00"
  },
  "P8092": {
    "problem_number": 8092,
    "slug": "open-fc-01a1c8cda18d4dc87c3d-erdos-653",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:39+00:00",
    "updated_at": "2026-08-17T18:34:39+00:00"
  },
  "P8196": {
    "problem_number": 8196,
    "slug": "open-fc-0ceb5e87bd5aae6f1310-erdos-291-variants-shiu-heuristic-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:52+00:00",
    "updated_at": "2026-08-17T18:36:54+00:00"
  },
  "P9280": {
    "problem_number": 9280,
    "slug": "open-fc-ab71220b2e3a39fc1a55-erdos-539-variants-sq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:35+00:00",
    "updated_at": "2026-08-17T19:50:36+00:00"
  },
  "P9074": {
    "problem_number": 9074,
    "slug": "open-fc-b0e9214138b5af67f53d-erdos-340-variants-istheta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:55+00:00",
    "updated_at": "2026-08-17T19:46:57+00:00"
  },
  "P9938": {
    "problem_number": 9938,
    "slug": "open-fc-8d193b9fd3c9379f35e9-erdos-409-variants-sigma-istheta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:43+00:00",
    "updated_at": "2026-08-17T20:04:43+00:00"
  },
  "P9146": {
    "problem_number": 9146,
    "slug": "open-fc-e9e11a9768ad9b482075-green-37-theta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:49+00:00",
    "updated_at": "2026-08-17T19:47:49+00:00"
  },
  "P9038": {
    "problem_number": 9038,
    "slug": "open-fc-976ebff404f47aec9fbf-erdos-789-variants-sq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:51+00:00",
    "updated_at": "2026-08-17T19:45:53+00:00"
  },
  "P9906": {
    "problem_number": 9906,
    "slug": "open-fc-74c74c9ecb3e30f63ef0-erdos-409-parts-i-istheta",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:26+00:00",
    "updated_at": "2026-08-17T20:04:26+00:00"
  },
  "P8686": {
    "problem_number": 8686,
    "slug": "open-fc-36638916b5f69784bc04-erdos-600-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:49+00:00",
    "updated_at": "2026-08-17T19:04:51+00:00"
  },
  "P8746": {
    "problem_number": 8746,
    "slug": "open-fc-55371376167d40e9276a-erdos-416-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:52+00:00",
    "updated_at": "2026-08-17T19:13:12+00:00"
  },
  "P9294": {
    "problem_number": 9294,
    "slug": "open-fc-b66da91bcd3830949f03-erdos-241-variants-generalization",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:41+00:00",
    "updated_at": "2026-08-17T19:50:41+00:00"
  },
  "P9970": {
    "problem_number": 9970,
    "slug": "open-fc-a2fb314ac50b4e8fe5e4-green-37-littleo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:02+00:00",
    "updated_at": "2026-08-17T20:05:03+00:00"
  },
  "P9592": {
    "problem_number": 9592,
    "slug": "open-fc-e202f09f157a775ac3f1-erdos-400-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:22+00:00",
    "updated_at": "2026-08-17T19:56:24+00:00"
  },
  "P9890": {
    "problem_number": 9890,
    "slug": "open-fc-690182d879646127946f-erdos-1054-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:17+00:00",
    "updated_at": "2026-08-17T20:04:18+00:00"
  },
  "P9670": {
    "problem_number": 9670,
    "slug": "open-fc-69d8b78f1b781661237d-green-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:01+00:00",
    "updated_at": "2026-08-17T20:01:02+00:00"
  },
  "P9770": {
    "problem_number": 9770,
    "slug": "open-fc-c6ef7b84fa4e4a316ec9-erdos-208-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:28+00:00",
    "updated_at": "2026-08-17T20:02:29+00:00"
  },
  "P10048": {
    "problem_number": 10048,
    "slug": "open-fc-e22faafe1a039bcd1290-erdos-101",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:48+00:00",
    "updated_at": "2026-08-17T20:05:49+00:00"
  },
  "P3032": {
    "problem_number": 3032,
    "slug": "erdos-problem-101",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:03+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9150": {
    "problem_number": 9150,
    "slug": "open-fc-ed8590f9abf25ac27e30-green-37-bigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:49+00:00",
    "updated_at": "2026-08-17T19:47:50+00:00"
  },
  "P9474": {
    "problem_number": 9474,
    "slug": "open-fc-85939ff2e9becd5683fb-erdos-142-variants-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:02+00:00",
    "updated_at": "2026-08-17T19:54:03+00:00"
  },
  "P9864": {
    "problem_number": 9864,
    "slug": "open-fc-54ff4f6acfbf618209e6-erdos-323-variants-k-gt-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:04+00:00",
    "updated_at": "2026-08-17T20:04:05+00:00"
  },
  "P9444": {
    "problem_number": 9444,
    "slug": "open-fc-6f71c2fe326c7f392bc9-erdos-319-variants-islittleo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:29+00:00",
    "updated_at": "2026-08-17T19:53:31+00:00"
  },
  "P9902": {
    "problem_number": 9902,
    "slug": "open-fc-7262bd89867902010287-erdos-359-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:24+00:00",
    "updated_at": "2026-08-17T20:04:25+00:00"
  },
  "P8870": {
    "problem_number": 8870,
    "slug": "open-fc-be0c94c966e83dde8cbb-erdos-357-parts-ii-littleo-version-symm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:55+00:00",
    "updated_at": "2026-08-17T19:36:00+00:00"
  },
  "P8310": {
    "problem_number": 8310,
    "slug": "open-fc-1ee6fbd04822d8008058-erdos-962",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:18+00:00",
    "updated_at": "2026-08-17T18:39:34+00:00"
  },
  "P9116": {
    "problem_number": 9116,
    "slug": "open-fc-d0fa21c7b17850dee63d-upper-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:40+00:00",
    "updated_at": "2026-08-17T19:47:40+00:00"
  },
  "P3296": {
    "problem_number": 3296,
    "slug": "erdos-problem-304",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:21+00:00",
    "updated_at": "2026-08-12T06:03:23+00:00"
  },
  "P9812": {
    "problem_number": 9812,
    "slug": "open-fc-e916e8b0176a5e05de6c-erdos-357-variants-monotone-parts-ii-littleo-version-symm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:53+00:00",
    "updated_at": "2026-08-17T20:02:53+00:00"
  },
  "P9836": {
    "problem_number": 9836,
    "slug": "open-fc-f94f4b6a37bf24e97116-erdos-319-variants-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:02+00:00",
    "updated_at": "2026-08-17T20:03:03+00:00"
  },
  "P9416": {
    "problem_number": 9416,
    "slug": "open-fc-5b6eca62b2602a5e026d-erdos-890-parts-b",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:31+00:00",
    "updated_at": "2026-08-17T19:52:34+00:00"
  },
  "P9188": {
    "problem_number": 9188,
    "slug": "open-fc-4019ca7675dcbf8efbc7-erdos-409-variants-sigma-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:04+00:00",
    "updated_at": "2026-08-17T19:49:06+00:00"
  },
  "P9208": {
    "problem_number": 9208,
    "slug": "open-fc-5e6c153a36646627ae62-erdos-409-parts-i-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:22+00:00",
    "updated_at": "2026-08-17T19:49:25+00:00"
  },
  "P9714": {
    "problem_number": 9714,
    "slug": "open-fc-9c6f61d9592ac89421d5-erdos-688-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:02+00:00",
    "updated_at": "2026-08-17T20:02:02+00:00"
  },
  "P12307": {
    "problem_number": 12307,
    "slug": "asymptotics-of-a-nested-radical-limit-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:36:50+00:00",
    "updated_at": "2026-09-01T19:36:55+00:00"
  },
  "P12637": {
    "problem_number": 12637,
    "slug": "asymptotics-of-prime-centers-of-twin-prime-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:06:52+00:00",
    "updated_at": "2026-09-02T22:06:57+00:00"
  },
  "P11921": {
    "problem_number": 11921,
    "slug": "at-least-four-primes-between-every-two-consecutive-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:23:22+00:00",
    "updated_at": "2026-08-30T16:23:29+00:00"
  },
  "P11684": {
    "problem_number": 11684,
    "slug": "attaining-the-diameter-four-bipartite-moore-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:11:29+00:00",
    "updated_at": "2026-08-30T11:12:53+00:00"
  },
  "P3542": {
    "problem_number": 3542,
    "slug": "kourovka-21-143-automaticity-of-thompson-s-group-f",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:13:08+00:00",
    "updated_at": "2026-08-12T08:13:17+00:00"
  },
  "P12443": {
    "problem_number": 12443,
    "slug": "automorphic-lifts-modulo-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:36:23+00:00",
    "updated_at": "2026-09-02T21:36:36+00:00"
  },
  "P3436": {
    "problem_number": 3436,
    "slug": "kourovka-21-49-automorphism-groups-of-acylindrically-hyperbolic-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:02:05+00:00",
    "updated_at": "2026-08-12T08:02:22+00:00"
  },
  "P3448": {
    "problem_number": 3448,
    "slug": "kourovka-21-65-automorphisms-with-small-centralizers-in-soluble-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:04:20+00:00",
    "updated_at": "2026-08-12T08:04:26+00:00"
  },
  "P12165": {
    "problem_number": 12165,
    "slug": "average-distance-from-a-prime-to-twice-a-power-times-a-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:19:29+00:00",
    "updated_at": "2026-09-01T19:19:35+00:00"
  },
  "P12645": {
    "problem_number": 12645,
    "slug": "average-order-of-the-closest-divisor-gap",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:32+00:00",
    "updated_at": "2026-09-02T22:07:36+00:00"
  },
  "P9322": {
    "problem_number": 9322,
    "slug": "open-fc-ca192bc03fb7bdd33645-babai-seress-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:53+00:00",
    "updated_at": "2026-08-17T19:50:53+00:00"
  },
  "P3122": {
    "problem_number": 3122,
    "slug": "navier-stokes-half-space-backward-self-similar",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:05+00:00",
    "updated_at": "2026-08-02T12:53:21+00:00"
  },
  "P11800": {
    "problem_number": 11800,
    "slug": "balance-of-prime-counts-in-consecutive-square-intervals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:45:20+00:00",
    "updated_at": "2026-08-30T12:45:29+00:00"
  },
  "P3264": {
    "problem_number": 3264,
    "slug": "erdos-problem-617",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:59:42+00:00",
    "updated_at": "2026-08-12T05:59:44+00:00"
  },
  "P9426": {
    "problem_number": 9426,
    "slug": "open-fc-62c9d8ce25d23afdbd57-erdos-617",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:45+00:00",
    "updated_at": "2026-08-17T19:52:46+00:00"
  },
  "P3666": {
    "problem_number": 3666,
    "slug": "triangular-ising-seven-balanced-ground-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:16+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12241": {
    "problem_number": 12241,
    "slug": "balanced-parity-partitions-into-distinct-parts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:28:45+00:00",
    "updated_at": "2026-09-01T19:28:50+00:00"
  },
  "P3070": {
    "problem_number": 3070,
    "slug": "barnette-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:54+00:00",
    "updated_at": "2026-08-02T12:47:24+00:00"
  },
  "P12399": {
    "problem_number": 12399,
    "slug": "barycentric-subdivision-residues",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:31:57+00:00",
    "updated_at": "2026-09-02T21:32:05+00:00"
  },
  "P9504": {
    "problem_number": 9504,
    "slug": "open-fc-9c14f36eb19618ad032d-islychrel10-196",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:30+00:00",
    "updated_at": "2026-08-17T19:54:30+00:00"
  },
  "P9940": {
    "problem_number": 9940,
    "slug": "open-fc-8eb4e5414843be4530d3-collatzlike",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:44+00:00",
    "updated_at": "2026-08-17T20:04:45+00:00"
  },
  "P12439": {
    "problem_number": 12439,
    "slug": "bateman-horn-growth-for-primes-one-above-a-fourth-power",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:35:59+00:00",
    "updated_at": "2026-09-02T21:36:09+00:00"
  },
  "P12047": {
    "problem_number": 12047,
    "slug": "bateman-horn-growth-for-primes-one-above-a-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:56:49+00:00",
    "updated_at": "2026-09-01T18:56:59+00:00"
  },
  "P20": {
    "problem_number": 20,
    "slug": "beal-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:31:59+00:00"
  },
  "P8426": {
    "problem_number": 8426,
    "slug": "open-fc-2ea9013c5f9ee3147ae7-beaver-math-olympiad-problem-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:02+00:00",
    "updated_at": "2026-08-17T18:52:02+00:00"
  },
  "P12561": {
    "problem_number": 12561,
    "slug": "bends-in-soddy-s-sphere-packing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:49:00+00:00",
    "updated_at": "2026-09-02T21:49:06+00:00"
  },
  "P47": {
    "problem_number": 47,
    "slug": "berge-fulkerson-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T11:32:23+00:00"
  },
  "P11112": {
    "problem_number": 11112,
    "slug": "berkovich-uncu-fiber-equivalence-from-four-bijections",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T08:29:15+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P12189": {
    "problem_number": 12189,
    "slug": "bernoulli-denominators-in-an-odd-stirling-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:22:25+00:00",
    "updated_at": "2026-09-01T19:22:30+00:00"
  },
  "P3678": {
    "problem_number": 3678,
    "slug": "dyadic-absolute-value-degree-ten-approximation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:39+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3618": {
    "problem_number": 3618,
    "slug": "cyclic-nine-groebner-peak-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9850": {
    "problem_number": 9850,
    "slug": "open-fc-44e94c5fc827cac5bda9-erdos-160-better-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:56+00:00",
    "updated_at": "2026-08-17T20:03:56+00:00"
  },
  "P3758": {
    "problem_number": 3758,
    "slug": "clebsch-biclique-partition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:32+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9642": {
    "problem_number": 9642,
    "slug": "open-fc-3f8cf306001f365589ea-mathoverflow-21003",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:19+00:00",
    "updated_at": "2026-08-17T20:00:21+00:00"
  },
  "P12415": {
    "problem_number": 12415,
    "slug": "binary-weight-and-2-adic-valuation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:33:32+00:00",
    "updated_at": "2026-09-02T21:33:44+00:00"
  },
  "P12459": {
    "problem_number": 12459,
    "slug": "binary-zeros-and-a-negative-continued-fraction",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:38:02+00:00",
    "updated_at": "2026-09-02T21:38:09+00:00"
  },
  "P16": {
    "problem_number": 16,
    "slug": "birch-and-swinnerton-dyer-rank-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:33:11+00:00"
  },
  "P3072": {
    "problem_number": 3072,
    "slug": "birkhoff-billiard-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:54+00:00",
    "updated_at": "2026-08-02T12:47:29+00:00"
  },
  "P3074": {
    "problem_number": 3074,
    "slug": "bochner-riesz-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:55+00:00",
    "updated_at": "2026-08-02T12:47:33+00:00"
  },
  "P3076": {
    "problem_number": 3076,
    "slug": "borsuk-conjecture-in-four-dimensions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:55+00:00",
    "updated_at": "2026-08-02T12:47:38+00:00"
  },
  "P3498": {
    "problem_number": 3498,
    "slug": "kourovka-21-116-bounded-acyclicity-of-branch-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:08:17+00:00",
    "updated_at": "2026-08-12T08:08:24+00:00"
  },
  "P9472": {
    "problem_number": 9472,
    "slug": "open-fc-845d2f59f98d318bb072-problem-4-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:02+00:00",
    "updated_at": "2026-08-17T19:54:02+00:00"
  },
  "P9088": {
    "problem_number": 9088,
    "slug": "open-fc-bcb09feaaabaf731098f-erdos-887-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:18+00:00",
    "updated_at": "2026-08-17T19:47:19+00:00"
  },
  "P12025": {
    "problem_number": 12025,
    "slug": "bounded-exponents-without-repeated-adjacent-digits",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:52:20+00:00",
    "updated_at": "2026-09-01T18:52:29+00:00"
  },
  "P8946": {
    "problem_number": 8946,
    "slug": "open-fc-f565c24acb92b7d1c515-erdos-952",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:10+00:00",
    "updated_at": "2026-08-17T19:41:12+00:00"
  },
  "P12229": {
    "problem_number": 12229,
    "slug": "bounded-runs-of-three-symbols",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:27:17+00:00",
    "updated_at": "2026-09-01T19:27:22+00:00"
  },
  "P8926": {
    "problem_number": 8926,
    "slug": "open-fc-e8143826b2570ad9f06b-erdos-886",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:41+00:00",
    "updated_at": "2026-08-17T19:40:42+00:00"
  },
  "P11174": {
    "problem_number": 11174,
    "slug": "bounded-smallest-odd-prime-factor-central-binomial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:28:27+00:00",
    "updated_at": "2026-08-29T18:48:34+00:00"
  },
  "P9926": {
    "problem_number": 9926,
    "slug": "open-fc-83716e95209a3960c4ae-erdos-829",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:36+00:00",
    "updated_at": "2026-08-17T20:04:36+00:00"
  },
  "P8324": {
    "problem_number": 8324,
    "slug": "open-fc-2005be83f7078a25f5b2-erdos-377",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:39+00:00",
    "updated_at": "2026-08-17T18:39:46+00:00"
  },
  "P12233": {
    "problem_number": 12233,
    "slug": "bounds-and-mean-growth-of-a-quasi-logarithm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:27:46+00:00",
    "updated_at": "2026-09-01T19:27:51+00:00"
  },
  "P10766": {
    "problem_number": 10766,
    "slug": "unsolvedmath-1098-bounds-for-homogeneous-polynomial-zeros",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:08+00:00",
    "updated_at": "2026-08-18T02:55:08+00:00"
  },
  "P9678": {
    "problem_number": 9678,
    "slug": "open-fc-762f6bcbf8e6af61e42d-green-22",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:13+00:00",
    "updated_at": "2026-08-17T20:01:14+00:00"
  },
  "P3470": {
    "problem_number": 3470,
    "slug": "kourovka-21-92-brauer-character-counts-and-group-structure",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:07+00:00",
    "updated_at": "2026-08-12T08:06:08+00:00"
  },
  "P9800": {
    "problem_number": 9800,
    "slug": "open-fc-e163c9feabcf7ce72146-navier-stokes-breakdown-periodic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:46+00:00",
    "updated_at": "2026-08-17T20:02:47+00:00"
  },
  "P9260": {
    "problem_number": 9260,
    "slug": "open-fc-9bfae25faa72125d6901-navier-stokes-breakdown-r3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:28+00:00",
    "updated_at": "2026-08-17T19:50:29+00:00"
  },
  "P9846": {
    "problem_number": 9846,
    "slug": "open-fc-3f9b23002bf4f5e3d30c-brennan-universalspectrumbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:54+00:00",
    "updated_at": "2026-08-17T20:03:54+00:00"
  },
  "P9736": {
    "problem_number": 9736,
    "slug": "open-fc-acc24073e380c1e50376-brennan-universalspectrum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:10+00:00",
    "updated_at": "2026-08-17T20:02:11+00:00"
  },
  "P9148": {
    "problem_number": 9148,
    "slug": "open-fc-eb6381a40757d81928d9-brocard-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:49+00:00",
    "updated_at": "2026-08-17T19:47:49+00:00"
  },
  "P3166": {
    "problem_number": 3166,
    "slug": "erdos-problem-398",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:47:06+00:00",
    "updated_at": "2026-08-12T05:47:25+00:00"
  },
  "P8988": {
    "problem_number": 8988,
    "slug": "open-fc-7158e3ae9a7429c0b724-erdos-398",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:25+00:00",
    "updated_at": "2026-08-17T19:44:26+00:00"
  },
  "P21": {
    "problem_number": 21,
    "slug": "bunyakovsky-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:33:33+00:00"
  },
  "P9492": {
    "problem_number": 9492,
    "slug": "open-fc-9500acd3a0541a2bfc80-buchi-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:25+00:00",
    "updated_at": "2026-08-17T19:54:25+00:00"
  },
  "P8792": {
    "problem_number": 8792,
    "slug": "open-fc-75cc93c5cf6446624989-buchi-problem-m5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:21:08+00:00",
    "updated_at": "2026-08-17T19:21:13+00:00"
  },
  "P3082": {
    "problem_number": 3082,
    "slug": "cabling-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:56+00:00",
    "updated_at": "2026-08-02T12:47:53+00:00"
  },
  "P11548": {
    "problem_number": 11548,
    "slug": "minimum-squarefree-semiprime-egyptian-fraction-length",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:01:04+00:00",
    "updated_at": "2026-08-29T18:54:32+00:00"
  },
  "P11332": {
    "problem_number": 11332,
    "slug": "primitive-root-two-exceptional-prime-square-lift",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:25:23+00:00",
    "updated_at": "2026-08-29T18:51:24+00:00"
  },
  "P11296": {
    "problem_number": 11296,
    "slug": "binomial-first-crossing-equality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:23:02+00:00",
    "updated_at": "2026-08-29T18:50:42+00:00"
  },
  "P11316": {
    "problem_number": 11316,
    "slug": "double-powertrain-value-fourteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:18:27+00:00",
    "updated_at": "2026-08-29T18:51:05+00:00"
  },
  "P11871": {
    "problem_number": 11871,
    "slug": "can-a-factorial-contain-exactly-84-digit-1s",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:26+00:00",
    "updated_at": "2026-08-30T16:16:30+00:00"
  },
  "P11276": {
    "problem_number": 11276,
    "slug": "fixed-coefficient-consecutive-prime-divisibility-finiteness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:14:22+00:00",
    "updated_at": "2026-08-29T18:50:22+00:00"
  },
  "P11354": {
    "problem_number": 11354,
    "slug": "even-record-index-for-quadratic-surd-periods",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:34:53+00:00",
    "updated_at": "2026-08-29T18:51:43+00:00"
  },
  "P12251": {
    "problem_number": 12251,
    "slug": "can-a-perfect-power-sit-between-two-neighboring-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:29:59+00:00",
    "updated_at": "2026-09-01T19:30:05+00:00"
  },
  "P12225": {
    "problem_number": 12225,
    "slug": "can-a-powerful-number-share-sigma-s-top-prime-power",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:26:47+00:00",
    "updated_at": "2026-09-01T19:26:53+00:00"
  },
  "P11444": {
    "problem_number": 11444,
    "slug": "mersenne-number-base-3-pseudoprime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:01:38+00:00",
    "updated_at": "2026-08-29T18:53:05+00:00"
  },
  "P11394": {
    "problem_number": 11394,
    "slug": "existence-minimal-six-summand-sixth-power",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:46:36+00:00",
    "updated_at": "2026-08-29T18:52:21+00:00"
  },
  "P11302": {
    "problem_number": 11302,
    "slug": "sorted-digit-tribonacci-unbounded-orbit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:10:03+00:00",
    "updated_at": "2026-08-29T18:50:50+00:00"
  },
  "P11552": {
    "problem_number": 11552,
    "slug": "repeated-counts-for-equal-level-rooted-trees",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:02:47+00:00",
    "updated_at": "2026-08-29T18:54:35+00:00"
  },
  "P11436": {
    "problem_number": 11436,
    "slug": "twenty-three-primes-in-a-hundred-step-interval",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:59:07+00:00",
    "updated_at": "2026-08-29T18:52:56+00:00"
  },
  "P11464": {
    "problem_number": 11464,
    "slug": "square-overlap-left-right-role-disjointness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:10:18+00:00",
    "updated_at": "2026-08-29T18:53:30+00:00"
  },
  "P11540": {
    "problem_number": 11540,
    "slug": "composite-circular-sorting-upper-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:55:27+00:00",
    "updated_at": "2026-08-29T18:54:26+00:00"
  },
  "P11532": {
    "problem_number": 11532,
    "slug": "commutative-witness-for-symmetric-ternary-superposition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:50:21+00:00",
    "updated_at": "2026-08-29T18:54:20+00:00"
  },
  "P12741": {
    "problem_number": 12741,
    "slug": "can-every-nontrivial-term-shed-a-prime-factor-and-stay-in-a045576",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:38:04+00:00",
    "updated_at": "2026-09-02T22:38:31+00:00"
  },
  "P11340": {
    "problem_number": 11340,
    "slug": "every-qualifying-8-by-8-consecutive-prime-magic-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:29:20+00:00",
    "updated_at": "2026-08-29T18:51:32+00:00"
  },
  "P11342": {
    "problem_number": 11342,
    "slug": "every-qualifying-9-by-9-consecutive-prime-magic-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:29:47+00:00",
    "updated_at": "2026-08-29T18:51:35+00:00"
  },
  "P11408": {
    "problem_number": 11408,
    "slug": "six-positive-sixth-powers-equal-one-sixth-power",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:50:30+00:00",
    "updated_at": "2026-08-29T18:52:36+00:00"
  },
  "P12679": {
    "problem_number": 12679,
    "slug": "can-only-inner-digits-1-2-and-8-yield-prime-9-sandwiches",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:11:25+00:00",
    "updated_at": "2026-09-02T22:11:32+00:00"
  },
  "P11246": {
    "problem_number": 11246,
    "slug": "odd-solutions-totient-four-n-plus-one-divisor-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:03:19+00:00",
    "updated_at": "2026-08-29T18:49:50+00:00"
  },
  "P11248": {
    "problem_number": 11248,
    "slug": "odd-solutions-totient-four-n-minus-one-divisor-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:03:44+00:00",
    "updated_at": "2026-08-29T18:49:53+00:00"
  },
  "P12179": {
    "problem_number": 12179,
    "slug": "can-powers-of-three-have-abnormally-few-p-2q-representations",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:21:11+00:00",
    "updated_at": "2026-09-01T19:21:17+00:00"
  },
  "P11544": {
    "problem_number": 11544,
    "slug": "primitive-descartes-radius-chains-arbitrarily-long",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:58:24+00:00",
    "updated_at": "2026-08-29T18:54:29+00:00"
  },
  "P11428": {
    "problem_number": 11428,
    "slug": "twenty-seven-queen-graph-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:56:28+00:00",
    "updated_at": "2026-08-29T18:52:50+00:00"
  },
  "P11406": {
    "problem_number": 11406,
    "slug": "boomerang-fraction-nine-elevenths-return",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:50:05+00:00",
    "updated_at": "2026-08-29T18:52:35+00:00"
  },
  "P11520": {
    "problem_number": 11520,
    "slug": "stack-complete-collapse-after-twelve",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:43:47+00:00",
    "updated_at": "2026-08-29T18:54:11+00:00"
  },
  "P11324": {
    "problem_number": 11324,
    "slug": "divisor-totient-average-infinite-orbit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:23:47+00:00",
    "updated_at": "2026-08-29T18:51:15+00:00"
  },
  "P11344": {
    "problem_number": 11344,
    "slug": "prime-magic-square-order-10-constant-11426",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:30:12+00:00",
    "updated_at": "2026-08-29T18:51:36+00:00"
  },
  "P11364": {
    "problem_number": 11364,
    "slug": "infinite-greedy-three-sequence-difference-partition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:38:50+00:00",
    "updated_at": "2026-08-29T18:51:52+00:00"
  },
  "P11230": {
    "problem_number": 11230,
    "slug": "greedy-prime-bit-flip-sequence-infinitude",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:59:03+00:00",
    "updated_at": "2026-08-29T18:49:33+00:00"
  },
  "P11372": {
    "problem_number": 11372,
    "slug": "pythagorean-greedy-walk-never-gets-stuck",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:40:23+00:00",
    "updated_at": "2026-08-29T18:51:58+00:00"
  },
  "P11861": {
    "problem_number": 11861,
    "slug": "can-the-self-indexed-counting-recurrence-stay-constant-four-times",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:43+00:00",
    "updated_at": "2026-08-30T16:15:49+00:00"
  },
  "P11172": {
    "problem_number": 11172,
    "slug": "oeis-a057096-pythagorean-triple-product-collision",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:23:41+00:00",
    "updated_at": "2026-08-29T18:48:38+00:00"
  },
  "P3108": {
    "problem_number": 3108,
    "slug": "general-relay-channel-capacity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:02+00:00",
    "updated_at": "2026-08-02T12:51:09+00:00"
  },
  "P9638": {
    "problem_number": 9638,
    "slug": "open-fc-3707687007962822546e-green-85",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:13+00:00",
    "updated_at": "2026-08-17T20:00:15+00:00"
  },
  "P10040": {
    "problem_number": 10040,
    "slug": "open-fc-dc68228b30c37092845a-countablymonolithicspace-card-lt",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:37+00:00",
    "updated_at": "2026-08-17T20:05:38+00:00"
  },
  "P11176": {
    "problem_number": 11176,
    "slug": "factorial-tetrahedral-number-intersection-cardinality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:30:44+00:00",
    "updated_at": "2026-08-29T18:48:41+00:00"
  },
  "P10062": {
    "problem_number": 10062,
    "slug": "open-fc-ed407cc947ecf49ca45f-union-closed-variants-cardinality-even-of-union-closed-tight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:03+00:00",
    "updated_at": "2026-08-17T20:06:03+00:00"
  },
  "P3506": {
    "problem_number": 3506,
    "slug": "kourovka-21-122-cardinality-of-verbal-subgroups-in-profinite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:09:55+00:00",
    "updated_at": "2026-08-12T08:10:03+00:00"
  },
  "P9608": {
    "problem_number": 9608,
    "slug": "open-fc-edc5e4ded4b43095c04a-charmichaeltotient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:57+00:00",
    "updated_at": "2026-08-17T19:56:59+00:00"
  },
  "P12057": {
    "problem_number": 12057,
    "slug": "catalan-residues-at-mersenne-indices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:58:50+00:00",
    "updated_at": "2026-09-01T18:59:00+00:00"
  },
  "P9956": {
    "problem_number": 9956,
    "slug": "open-fc-9a41290ce7ba0c9a335d-catalans-mersenne-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:54+00:00",
    "updated_at": "2026-08-17T20:04:54+00:00"
  },
  "P12043": {
    "problem_number": 12043,
    "slug": "catalan-square-supercongruences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:56:04+00:00",
    "updated_at": "2026-09-01T18:56:14+00:00"
  },
  "P8258": {
    "problem_number": 8258,
    "slug": "open-fc-1810de8d663d5ef445bb-latintableauconjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:49+00:00",
    "updated_at": "2026-08-17T18:37:51+00:00"
  },
  "P3672": {
    "problem_number": 3672,
    "slug": "cesaro-hundred-l4-norm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:21+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3488": {
    "problem_number": 3488,
    "slug": "kourovka-21-108-character-codegrees-of-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:07:03+00:00",
    "updated_at": "2026-08-12T08:07:10+00:00"
  },
  "P3528": {
    "problem_number": 3528,
    "slug": "kourovka-21-135-character-degrees-and-trivial-solvable-radicals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:10+00:00",
    "updated_at": "2026-08-12T08:12:17+00:00"
  },
  "P3440": {
    "problem_number": 3440,
    "slug": "kourovka-21-59-character-degree-multisets-of-almost-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:03:04+00:00",
    "updated_at": "2026-08-12T08:03:23+00:00"
  },
  "P9068": {
    "problem_number": 9068,
    "slug": "open-fc-ac762ce272649ce9f8cb-erdos-596",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:44+00:00",
    "updated_at": "2026-08-17T19:46:46+00:00"
  },
  "P3284": {
    "problem_number": 3284,
    "slug": "erdos-problem-596",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:49+00:00",
    "updated_at": "2026-08-12T06:02:53+00:00"
  },
  "P3372": {
    "problem_number": 3372,
    "slug": "kourovka-21-9-characteristic-intersections-in-free-pro-p-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:45:27+00:00",
    "updated_at": "2026-08-12T07:46:41+00:00"
  },
  "P3438": {
    "problem_number": 3438,
    "slug": "kourovka-21-50-characteristic-subgroups-of-finite-3-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:02:33+00:00",
    "updated_at": "2026-08-12T08:02:49+00:00"
  },
  "P8596": {
    "problem_number": 8596,
    "slug": "open-fc-355de8b39d83130c4bdf-erdos-700-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:44+00:00",
    "updated_at": "2026-08-17T18:56:50+00:00"
  },
  "P3292": {
    "problem_number": 3292,
    "slug": "erdos-problem-700",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:11+00:00",
    "updated_at": "2026-08-12T06:03:14+00:00"
  },
  "P9528": {
    "problem_number": 9528,
    "slug": "open-fc-ad34ec9d56b9b33d7c5c-issumofthreecubes-iff-mod-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:39+00:00",
    "updated_at": "2026-08-17T19:54:39+00:00"
  },
  "P8142": {
    "problem_number": 8142,
    "slug": "open-fc-06a51d87f833716e685f-erdos-593",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:07+00:00",
    "updated_at": "2026-08-17T18:35:07+00:00"
  },
  "P8724": {
    "problem_number": 8724,
    "slug": "open-fc-3e4a0fc35cb26773c793-molsexistenceproblem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:04+00:00",
    "updated_at": "2026-08-17T19:11:17+00:00"
  },
  "P9944": {
    "problem_number": 9944,
    "slug": "open-fc-91f4b9dc82fcde7839d5-erdos-349",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:47+00:00",
    "updated_at": "2026-08-17T20:04:48+00:00"
  },
  "P8964": {
    "problem_number": 8964,
    "slug": "open-fc-538583ad8138f1dbaff9-comesfromprimequadruple-of-a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:43:52+00:00",
    "updated_at": "2026-08-17T19:43:54+00:00"
  },
  "P8144": {
    "problem_number": 8144,
    "slug": "open-fc-06dbcd4389b24dd84f0f-erdos-282-variants-general",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:08+00:00",
    "updated_at": "2026-08-17T18:35:15+00:00"
  },
  "P12083": {
    "problem_number": 12083,
    "slug": "chen-prime-behavior-inside-a225868",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:09:09+00:00",
    "updated_at": "2026-09-01T19:09:15+00:00"
  },
  "P3390": {
    "problem_number": 3390,
    "slug": "kourovka-21-23-chordality-of-enhanced-power-graphs-of-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:09+00:00",
    "updated_at": "2026-08-12T07:56:11+00:00"
  },
  "P9620": {
    "problem_number": 9620,
    "slug": "open-fc-f4c06cfacd8659e6e59a-erdos-510",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:18+00:00",
    "updated_at": "2026-08-17T19:57:20+00:00"
  },
  "P9384": {
    "problem_number": 9384,
    "slug": "open-fc-fa73ffdd8ca16975f4be-johnson-chromaticnumber",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:20+00:00",
    "updated_at": "2026-08-17T19:51:20+00:00"
  },
  "P5740": {
    "problem_number": 5740,
    "slug": "circulant-1009-1-2-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:52:11+00:00",
    "updated_at": "2026-08-16T08:52:22+00:00"
  },
  "P5742": {
    "problem_number": 5742,
    "slug": "circulant-1013-1-3-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:52:28+00:00",
    "updated_at": "2026-08-16T08:52:36+00:00"
  },
  "P5744": {
    "problem_number": 5744,
    "slug": "circulant-1019-1-4-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:52:40+00:00",
    "updated_at": "2026-08-16T08:52:54+00:00"
  },
  "P5746": {
    "problem_number": 5746,
    "slug": "circulant-1021-1-5-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:53:02+00:00",
    "updated_at": "2026-08-16T08:53:11+00:00"
  },
  "P5748": {
    "problem_number": 5748,
    "slug": "circulant-1031-1-6-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:53:20+00:00",
    "updated_at": "2026-08-16T08:53:32+00:00"
  },
  "P5750": {
    "problem_number": 5750,
    "slug": "circulant-1033-1-7-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:53:43+00:00",
    "updated_at": "2026-08-16T08:53:52+00:00"
  },
  "P5752": {
    "problem_number": 5752,
    "slug": "circulant-1039-1-8-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:54:03+00:00",
    "updated_at": "2026-08-16T08:54:15+00:00"
  },
  "P5754": {
    "problem_number": 5754,
    "slug": "circulant-1049-1-9-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:54:23+00:00",
    "updated_at": "2026-08-16T08:54:34+00:00"
  },
  "P5756": {
    "problem_number": 5756,
    "slug": "circulant-1051-1-10-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:54:42+00:00",
    "updated_at": "2026-08-16T08:54:55+00:00"
  },
  "P5758": {
    "problem_number": 5758,
    "slug": "circulant-1061-1-11-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:55:02+00:00",
    "updated_at": "2026-08-16T08:55:13+00:00"
  },
  "P5760": {
    "problem_number": 5760,
    "slug": "circulant-1063-1-12-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:55:24+00:00",
    "updated_at": "2026-08-16T08:55:40+00:00"
  },
  "P5762": {
    "problem_number": 5762,
    "slug": "circulant-1069-1-2-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:55:48+00:00",
    "updated_at": "2026-08-16T08:55:57+00:00"
  },
  "P5764": {
    "problem_number": 5764,
    "slug": "circulant-1087-1-3-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:56:07+00:00",
    "updated_at": "2026-08-16T08:56:22+00:00"
  },
  "P5766": {
    "problem_number": 5766,
    "slug": "circulant-1091-1-4-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:56:30+00:00",
    "updated_at": "2026-08-16T08:56:46+00:00"
  },
  "P5768": {
    "problem_number": 5768,
    "slug": "circulant-1093-1-5-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:56:57+00:00",
    "updated_at": "2026-08-16T08:57:10+00:00"
  },
  "P5770": {
    "problem_number": 5770,
    "slug": "circulant-1097-1-6-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:57:15+00:00",
    "updated_at": "2026-08-16T08:57:28+00:00"
  },
  "P5772": {
    "problem_number": 5772,
    "slug": "circulant-1103-1-7-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:57:36+00:00",
    "updated_at": "2026-08-16T08:57:46+00:00"
  },
  "P5774": {
    "problem_number": 5774,
    "slug": "circulant-1109-1-8-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:57:55+00:00",
    "updated_at": "2026-08-16T08:58:05+00:00"
  },
  "P5776": {
    "problem_number": 5776,
    "slug": "circulant-1117-1-9-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:58:11+00:00",
    "updated_at": "2026-08-16T08:58:20+00:00"
  },
  "P5778": {
    "problem_number": 5778,
    "slug": "circulant-1123-1-10-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:58:26+00:00",
    "updated_at": "2026-08-16T08:58:34+00:00"
  },
  "P5780": {
    "problem_number": 5780,
    "slug": "circulant-1129-1-11-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:58:36+00:00",
    "updated_at": "2026-08-16T08:58:47+00:00"
  },
  "P5782": {
    "problem_number": 5782,
    "slug": "circulant-1151-1-12-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:58:54+00:00",
    "updated_at": "2026-08-16T08:58:56+00:00"
  },
  "P5784": {
    "problem_number": 5784,
    "slug": "circulant-1153-1-2-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:00+00:00",
    "updated_at": "2026-08-16T08:59:17+00:00"
  },
  "P5786": {
    "problem_number": 5786,
    "slug": "circulant-1163-1-3-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:25+00:00",
    "updated_at": "2026-08-16T08:59:29+00:00"
  },
  "P5788": {
    "problem_number": 5788,
    "slug": "circulant-1171-1-4-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:30+00:00",
    "updated_at": "2026-08-16T08:59:30+00:00"
  },
  "P5790": {
    "problem_number": 5790,
    "slug": "circulant-1181-1-5-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:31+00:00",
    "updated_at": "2026-08-16T08:59:37+00:00"
  },
  "P5792": {
    "problem_number": 5792,
    "slug": "circulant-1187-1-6-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:44+00:00",
    "updated_at": "2026-08-16T08:59:47+00:00"
  },
  "P5794": {
    "problem_number": 5794,
    "slug": "circulant-1193-1-7-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:48+00:00",
    "updated_at": "2026-08-16T08:59:56+00:00"
  },
  "P5796": {
    "problem_number": 5796,
    "slug": "circulant-1201-1-8-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:59:58+00:00",
    "updated_at": "2026-08-16T09:00:03+00:00"
  },
  "P5798": {
    "problem_number": 5798,
    "slug": "circulant-1213-1-9-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:06+00:00",
    "updated_at": "2026-08-16T09:00:07+00:00"
  },
  "P5800": {
    "problem_number": 5800,
    "slug": "circulant-1217-1-10-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:10+00:00",
    "updated_at": "2026-08-16T09:00:16+00:00"
  },
  "P5802": {
    "problem_number": 5802,
    "slug": "circulant-1223-1-11-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:20+00:00",
    "updated_at": "2026-08-16T09:00:22+00:00"
  },
  "P5804": {
    "problem_number": 5804,
    "slug": "circulant-1229-1-12-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:22+00:00",
    "updated_at": "2026-08-16T09:00:28+00:00"
  },
  "P5806": {
    "problem_number": 5806,
    "slug": "circulant-1231-1-2-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:33+00:00",
    "updated_at": "2026-08-16T09:00:42+00:00"
  },
  "P5808": {
    "problem_number": 5808,
    "slug": "circulant-1237-1-3-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:48+00:00",
    "updated_at": "2026-08-16T09:00:52+00:00"
  },
  "P5810": {
    "problem_number": 5810,
    "slug": "circulant-1249-1-4-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:00:54+00:00",
    "updated_at": "2026-08-16T09:01:05+00:00"
  },
  "P5812": {
    "problem_number": 5812,
    "slug": "circulant-1259-1-5-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:01:07+00:00",
    "updated_at": "2026-08-16T09:01:20+00:00"
  },
  "P5814": {
    "problem_number": 5814,
    "slug": "circulant-1277-1-6-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:01:22+00:00",
    "updated_at": "2026-08-16T09:01:33+00:00"
  },
  "P5816": {
    "problem_number": 5816,
    "slug": "circulant-1279-1-7-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:01:38+00:00",
    "updated_at": "2026-08-16T09:01:42+00:00"
  },
  "P5818": {
    "problem_number": 5818,
    "slug": "circulant-1283-1-8-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:01:47+00:00",
    "updated_at": "2026-08-16T09:01:52+00:00"
  },
  "P5820": {
    "problem_number": 5820,
    "slug": "circulant-1289-1-9-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:01:57+00:00",
    "updated_at": "2026-08-16T09:02:00+00:00"
  },
  "P5822": {
    "problem_number": 5822,
    "slug": "circulant-1291-1-10-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:05+00:00",
    "updated_at": "2026-08-16T09:02:11+00:00"
  },
  "P5824": {
    "problem_number": 5824,
    "slug": "circulant-1297-1-11-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:17+00:00",
    "updated_at": "2026-08-16T09:02:19+00:00"
  },
  "P5826": {
    "problem_number": 5826,
    "slug": "circulant-1301-1-12-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:20+00:00",
    "updated_at": "2026-08-16T09:02:31+00:00"
  },
  "P5828": {
    "problem_number": 5828,
    "slug": "circulant-1303-1-2-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:32+00:00",
    "updated_at": "2026-08-16T09:02:34+00:00"
  },
  "P5830": {
    "problem_number": 5830,
    "slug": "circulant-1307-1-3-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:38+00:00",
    "updated_at": "2026-08-16T09:02:41+00:00"
  },
  "P5832": {
    "problem_number": 5832,
    "slug": "circulant-1319-1-4-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:42+00:00",
    "updated_at": "2026-08-16T09:02:45+00:00"
  },
  "P5834": {
    "problem_number": 5834,
    "slug": "circulant-1321-1-5-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:46+00:00",
    "updated_at": "2026-08-16T09:02:51+00:00"
  },
  "P5836": {
    "problem_number": 5836,
    "slug": "circulant-1327-1-6-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:51+00:00",
    "updated_at": "2026-08-16T09:02:56+00:00"
  },
  "P5838": {
    "problem_number": 5838,
    "slug": "circulant-1361-1-7-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:02:58+00:00",
    "updated_at": "2026-08-16T09:02:59+00:00"
  },
  "P5840": {
    "problem_number": 5840,
    "slug": "circulant-1367-1-8-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:01+00:00",
    "updated_at": "2026-08-16T09:03:06+00:00"
  },
  "P5842": {
    "problem_number": 5842,
    "slug": "circulant-1373-1-9-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:08+00:00",
    "updated_at": "2026-08-16T09:03:12+00:00"
  },
  "P5844": {
    "problem_number": 5844,
    "slug": "circulant-1381-1-10-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:16+00:00",
    "updated_at": "2026-08-16T09:03:22+00:00"
  },
  "P5846": {
    "problem_number": 5846,
    "slug": "circulant-1399-1-11-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:22+00:00",
    "updated_at": "2026-08-16T09:03:30+00:00"
  },
  "P5848": {
    "problem_number": 5848,
    "slug": "circulant-1409-1-12-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:33+00:00",
    "updated_at": "2026-08-16T09:03:37+00:00"
  },
  "P5850": {
    "problem_number": 5850,
    "slug": "circulant-1423-1-2-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:40+00:00",
    "updated_at": "2026-08-16T09:03:45+00:00"
  },
  "P5852": {
    "problem_number": 5852,
    "slug": "circulant-1427-1-3-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:46+00:00",
    "updated_at": "2026-08-16T09:03:48+00:00"
  },
  "P5854": {
    "problem_number": 5854,
    "slug": "circulant-1429-1-4-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:51+00:00",
    "updated_at": "2026-08-16T09:03:53+00:00"
  },
  "P5856": {
    "problem_number": 5856,
    "slug": "circulant-1433-1-5-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:03:58+00:00",
    "updated_at": "2026-08-16T09:04:02+00:00"
  },
  "P5858": {
    "problem_number": 5858,
    "slug": "circulant-1439-1-6-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:04:10+00:00",
    "updated_at": "2026-08-16T09:04:18+00:00"
  },
  "P5860": {
    "problem_number": 5860,
    "slug": "circulant-1447-1-7-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:04:22+00:00",
    "updated_at": "2026-08-16T09:04:33+00:00"
  },
  "P5862": {
    "problem_number": 5862,
    "slug": "circulant-1451-1-8-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:04:39+00:00",
    "updated_at": "2026-08-16T09:04:49+00:00"
  },
  "P5864": {
    "problem_number": 5864,
    "slug": "circulant-1453-1-9-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:04:56+00:00",
    "updated_at": "2026-08-16T09:04:59+00:00"
  },
  "P5866": {
    "problem_number": 5866,
    "slug": "circulant-1459-1-10-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:05:00+00:00",
    "updated_at": "2026-08-16T09:05:00+00:00"
  },
  "P5868": {
    "problem_number": 5868,
    "slug": "circulant-1471-1-11-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:05:05+00:00",
    "updated_at": "2026-08-16T09:05:18+00:00"
  },
  "P5870": {
    "problem_number": 5870,
    "slug": "circulant-1481-1-12-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:05:27+00:00",
    "updated_at": "2026-08-16T09:05:32+00:00"
  },
  "P5872": {
    "problem_number": 5872,
    "slug": "circulant-1483-1-2-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T09:05:35+00:00",
    "updated_at": "2026-08-16T09:05:43+00:00"
  },
  "P4788": {
    "problem_number": 4788,
    "slug": "circulant-503-1-2-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:07+00:00",
    "updated_at": "2026-08-16T05:43:09+00:00"
  },
  "P4790": {
    "problem_number": 4790,
    "slug": "circulant-509-1-3-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:09+00:00",
    "updated_at": "2026-08-16T05:43:10+00:00"
  },
  "P4792": {
    "problem_number": 4792,
    "slug": "circulant-521-1-4-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:10+00:00",
    "updated_at": "2026-08-16T05:43:11+00:00"
  },
  "P4794": {
    "problem_number": 4794,
    "slug": "circulant-523-1-5-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:11+00:00",
    "updated_at": "2026-08-16T05:43:11+00:00"
  },
  "P4796": {
    "problem_number": 4796,
    "slug": "circulant-541-1-6-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:12+00:00",
    "updated_at": "2026-08-16T05:43:12+00:00"
  },
  "P4798": {
    "problem_number": 4798,
    "slug": "circulant-547-1-7-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:12+00:00",
    "updated_at": "2026-08-16T05:43:13+00:00"
  },
  "P4800": {
    "problem_number": 4800,
    "slug": "circulant-557-1-8-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:13+00:00",
    "updated_at": "2026-08-16T05:43:15+00:00"
  },
  "P4802": {
    "problem_number": 4802,
    "slug": "circulant-563-1-9-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:15+00:00",
    "updated_at": "2026-08-16T05:43:20+00:00"
  },
  "P4804": {
    "problem_number": 4804,
    "slug": "circulant-569-1-10-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:20+00:00",
    "updated_at": "2026-08-16T05:43:25+00:00"
  },
  "P4806": {
    "problem_number": 4806,
    "slug": "circulant-571-1-11-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:26+00:00",
    "updated_at": "2026-08-16T05:43:28+00:00"
  },
  "P4808": {
    "problem_number": 4808,
    "slug": "circulant-577-1-12-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:29+00:00",
    "updated_at": "2026-08-16T05:43:29+00:00"
  },
  "P4810": {
    "problem_number": 4810,
    "slug": "circulant-587-1-2-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:30+00:00",
    "updated_at": "2026-08-16T05:43:35+00:00"
  },
  "P4812": {
    "problem_number": 4812,
    "slug": "circulant-593-1-3-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:38+00:00",
    "updated_at": "2026-08-16T05:43:47+00:00"
  },
  "P4814": {
    "problem_number": 4814,
    "slug": "circulant-599-1-4-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:48+00:00",
    "updated_at": "2026-08-16T05:43:50+00:00"
  },
  "P4816": {
    "problem_number": 4816,
    "slug": "circulant-601-1-5-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:50+00:00",
    "updated_at": "2026-08-16T05:43:51+00:00"
  },
  "P4818": {
    "problem_number": 4818,
    "slug": "circulant-607-1-6-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:52+00:00",
    "updated_at": "2026-08-16T05:43:55+00:00"
  },
  "P4820": {
    "problem_number": 4820,
    "slug": "circulant-613-1-7-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:56+00:00",
    "updated_at": "2026-08-16T05:43:57+00:00"
  },
  "P4822": {
    "problem_number": 4822,
    "slug": "circulant-617-1-8-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:57+00:00",
    "updated_at": "2026-08-16T05:44:04+00:00"
  },
  "P4824": {
    "problem_number": 4824,
    "slug": "circulant-619-1-9-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:06+00:00",
    "updated_at": "2026-08-16T05:44:08+00:00"
  },
  "P4826": {
    "problem_number": 4826,
    "slug": "circulant-631-1-10-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:08+00:00",
    "updated_at": "2026-08-16T05:44:11+00:00"
  },
  "P4828": {
    "problem_number": 4828,
    "slug": "circulant-641-1-11-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:12+00:00",
    "updated_at": "2026-08-16T05:44:14+00:00"
  },
  "P4830": {
    "problem_number": 4830,
    "slug": "circulant-643-1-12-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:14+00:00",
    "updated_at": "2026-08-16T05:44:15+00:00"
  },
  "P4832": {
    "problem_number": 4832,
    "slug": "circulant-647-1-2-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:15+00:00",
    "updated_at": "2026-08-16T05:44:20+00:00"
  },
  "P4834": {
    "problem_number": 4834,
    "slug": "circulant-653-1-3-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:21+00:00",
    "updated_at": "2026-08-16T05:44:22+00:00"
  },
  "P4836": {
    "problem_number": 4836,
    "slug": "circulant-659-1-4-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:23+00:00",
    "updated_at": "2026-08-16T05:44:30+00:00"
  },
  "P4838": {
    "problem_number": 4838,
    "slug": "circulant-661-1-5-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:31+00:00",
    "updated_at": "2026-08-16T05:44:33+00:00"
  },
  "P4840": {
    "problem_number": 4840,
    "slug": "circulant-673-1-6-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:35+00:00",
    "updated_at": "2026-08-16T05:44:37+00:00"
  },
  "P4842": {
    "problem_number": 4842,
    "slug": "circulant-677-1-7-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:38+00:00",
    "updated_at": "2026-08-16T05:44:43+00:00"
  },
  "P4844": {
    "problem_number": 4844,
    "slug": "circulant-683-1-8-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:44+00:00",
    "updated_at": "2026-08-16T05:44:44+00:00"
  },
  "P4846": {
    "problem_number": 4846,
    "slug": "circulant-691-1-9-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:45+00:00",
    "updated_at": "2026-08-16T05:44:47+00:00"
  },
  "P4848": {
    "problem_number": 4848,
    "slug": "circulant-701-1-10-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:49+00:00",
    "updated_at": "2026-08-16T05:44:54+00:00"
  },
  "P4850": {
    "problem_number": 4850,
    "slug": "circulant-709-1-11-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:56+00:00",
    "updated_at": "2026-08-16T05:44:59+00:00"
  },
  "P4852": {
    "problem_number": 4852,
    "slug": "circulant-719-1-12-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:44:59+00:00",
    "updated_at": "2026-08-16T05:45:01+00:00"
  },
  "P4854": {
    "problem_number": 4854,
    "slug": "circulant-727-1-2-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:05+00:00",
    "updated_at": "2026-08-16T05:45:14+00:00"
  },
  "P4856": {
    "problem_number": 4856,
    "slug": "circulant-733-1-3-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:16+00:00",
    "updated_at": "2026-08-16T05:45:17+00:00"
  },
  "P4858": {
    "problem_number": 4858,
    "slug": "circulant-739-1-4-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:17+00:00",
    "updated_at": "2026-08-16T05:45:21+00:00"
  },
  "P4860": {
    "problem_number": 4860,
    "slug": "circulant-743-1-5-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:24+00:00",
    "updated_at": "2026-08-16T05:45:32+00:00"
  },
  "P4862": {
    "problem_number": 4862,
    "slug": "circulant-751-1-6-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:35+00:00",
    "updated_at": "2026-08-16T05:45:41+00:00"
  },
  "P4864": {
    "problem_number": 4864,
    "slug": "circulant-757-1-7-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:43+00:00",
    "updated_at": "2026-08-16T05:45:54+00:00"
  },
  "P4866": {
    "problem_number": 4866,
    "slug": "circulant-761-1-8-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:45:56+00:00",
    "updated_at": "2026-08-16T05:45:57+00:00"
  },
  "P5674": {
    "problem_number": 5674,
    "slug": "circulant-769-1-2-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:16+00:00",
    "updated_at": "2026-08-16T08:45:22+00:00"
  },
  "P5676": {
    "problem_number": 5676,
    "slug": "circulant-773-1-3-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:24+00:00",
    "updated_at": "2026-08-16T08:45:27+00:00"
  },
  "P5678": {
    "problem_number": 5678,
    "slug": "circulant-787-1-4-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:27+00:00",
    "updated_at": "2026-08-16T08:45:28+00:00"
  },
  "P5680": {
    "problem_number": 5680,
    "slug": "circulant-797-1-5-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:29+00:00",
    "updated_at": "2026-08-16T08:45:36+00:00"
  },
  "P5682": {
    "problem_number": 5682,
    "slug": "circulant-809-1-6-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:40+00:00",
    "updated_at": "2026-08-16T08:45:49+00:00"
  },
  "P5684": {
    "problem_number": 5684,
    "slug": "circulant-811-1-7-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:52+00:00",
    "updated_at": "2026-08-16T08:45:53+00:00"
  },
  "P5686": {
    "problem_number": 5686,
    "slug": "circulant-821-1-8-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:53+00:00",
    "updated_at": "2026-08-16T08:45:57+00:00"
  },
  "P5688": {
    "problem_number": 5688,
    "slug": "circulant-823-1-9-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:58+00:00",
    "updated_at": "2026-08-16T08:45:58+00:00"
  },
  "P5690": {
    "problem_number": 5690,
    "slug": "circulant-827-1-10-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:58+00:00",
    "updated_at": "2026-08-16T08:45:59+00:00"
  },
  "P5692": {
    "problem_number": 5692,
    "slug": "circulant-829-1-11-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:59+00:00",
    "updated_at": "2026-08-16T08:46:00+00:00"
  },
  "P5694": {
    "problem_number": 5694,
    "slug": "circulant-839-1-12-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:46:02+00:00",
    "updated_at": "2026-08-16T08:46:11+00:00"
  },
  "P5696": {
    "problem_number": 5696,
    "slug": "circulant-853-1-2-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:46:17+00:00",
    "updated_at": "2026-08-16T08:46:28+00:00"
  },
  "P5698": {
    "problem_number": 5698,
    "slug": "circulant-857-1-3-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:46:33+00:00",
    "updated_at": "2026-08-16T08:46:40+00:00"
  },
  "P5700": {
    "problem_number": 5700,
    "slug": "circulant-859-1-4-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:46:44+00:00",
    "updated_at": "2026-08-16T08:46:55+00:00"
  },
  "P5702": {
    "problem_number": 5702,
    "slug": "circulant-863-1-5-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:47:02+00:00",
    "updated_at": "2026-08-16T08:47:17+00:00"
  },
  "P5704": {
    "problem_number": 5704,
    "slug": "circulant-877-1-6-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:47:25+00:00",
    "updated_at": "2026-08-16T08:47:38+00:00"
  },
  "P5706": {
    "problem_number": 5706,
    "slug": "circulant-881-1-7-30-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:47:44+00:00",
    "updated_at": "2026-08-16T08:47:56+00:00"
  },
  "P5708": {
    "problem_number": 5708,
    "slug": "circulant-883-1-8-14-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:47:58+00:00",
    "updated_at": "2026-08-16T08:48:05+00:00"
  },
  "P5710": {
    "problem_number": 5710,
    "slug": "circulant-887-1-9-15-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:48:12+00:00",
    "updated_at": "2026-08-16T08:48:25+00:00"
  },
  "P5712": {
    "problem_number": 5712,
    "slug": "circulant-907-1-10-16-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:48:33+00:00",
    "updated_at": "2026-08-16T08:48:38+00:00"
  },
  "P5714": {
    "problem_number": 5714,
    "slug": "circulant-911-1-11-17-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:48:43+00:00",
    "updated_at": "2026-08-16T08:48:51+00:00"
  },
  "P5716": {
    "problem_number": 5716,
    "slug": "circulant-919-1-12-18-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:48:59+00:00",
    "updated_at": "2026-08-16T08:49:06+00:00"
  },
  "P5718": {
    "problem_number": 5718,
    "slug": "circulant-929-1-2-19-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:49:10+00:00",
    "updated_at": "2026-08-16T08:49:17+00:00"
  },
  "P5720": {
    "problem_number": 5720,
    "slug": "circulant-937-1-3-20-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:49:25+00:00",
    "updated_at": "2026-08-16T08:49:34+00:00"
  },
  "P5722": {
    "problem_number": 5722,
    "slug": "circulant-941-1-4-21-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:49:41+00:00",
    "updated_at": "2026-08-16T08:49:52+00:00"
  },
  "P5724": {
    "problem_number": 5724,
    "slug": "circulant-947-1-5-22-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:49:55+00:00",
    "updated_at": "2026-08-16T08:50:05+00:00"
  },
  "P5726": {
    "problem_number": 5726,
    "slug": "circulant-953-1-6-23-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:50:10+00:00",
    "updated_at": "2026-08-16T08:50:18+00:00"
  },
  "P5728": {
    "problem_number": 5728,
    "slug": "circulant-967-1-7-24-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:50:20+00:00",
    "updated_at": "2026-08-16T08:50:28+00:00"
  },
  "P5730": {
    "problem_number": 5730,
    "slug": "circulant-971-1-8-25-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:50:32+00:00",
    "updated_at": "2026-08-16T08:50:41+00:00"
  },
  "P5732": {
    "problem_number": 5732,
    "slug": "circulant-977-1-9-26-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:50:47+00:00",
    "updated_at": "2026-08-16T08:51:01+00:00"
  },
  "P5734": {
    "problem_number": 5734,
    "slug": "circulant-983-1-10-27-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:51:10+00:00",
    "updated_at": "2026-08-16T08:51:28+00:00"
  },
  "P5736": {
    "problem_number": 5736,
    "slug": "circulant-991-1-11-28-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:51:36+00:00",
    "updated_at": "2026-08-16T08:51:43+00:00"
  },
  "P5738": {
    "problem_number": 5738,
    "slug": "circulant-997-1-12-29-chromatic-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:51:53+00:00",
    "updated_at": "2026-08-16T08:52:08+00:00"
  },
  "P12401": {
    "problem_number": 12401,
    "slug": "class-numbers-and-cosecant-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:32:08+00:00",
    "updated_at": "2026-09-02T21:32:16+00:00"
  },
  "P8580": {
    "problem_number": 8580,
    "slug": "open-fc-2dadc873d76f77fec6a6-oqp-35",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:14+00:00",
    "updated_at": "2026-08-17T18:56:18+00:00"
  },
  "P2844": {
    "problem_number": 2844,
    "slug": "factorials-interior-pascal-triangle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:37:56+00:00",
    "updated_at": "2026-08-01T12:08:07+00:00"
  },
  "P11222": {
    "problem_number": 11222,
    "slug": "rational-amicable-pair-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:54:33+00:00",
    "updated_at": "2026-08-29T18:49:25+00:00"
  },
  "P11234": {
    "problem_number": 11234,
    "slug": "unitary-divisor-equation-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:59:55+00:00",
    "updated_at": "2026-08-29T18:49:37+00:00"
  },
  "P11618": {
    "problem_number": 11618,
    "slug": "classifying-solutions-of-sigma-n-rad-n-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:39:25+00:00",
    "updated_at": "2026-08-30T04:39:33+00:00"
  },
  "P4708": {
    "problem_number": 4708,
    "slug": "paley-graph-1009-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:01+00:00",
    "updated_at": "2026-08-16T05:41:03+00:00"
  },
  "P4710": {
    "problem_number": 4710,
    "slug": "paley-graph-1013-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:05+00:00",
    "updated_at": "2026-08-16T05:41:06+00:00"
  },
  "P4712": {
    "problem_number": 4712,
    "slug": "paley-graph-1021-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:06+00:00",
    "updated_at": "2026-08-16T05:41:07+00:00"
  },
  "P4714": {
    "problem_number": 4714,
    "slug": "paley-graph-1033-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:07+00:00",
    "updated_at": "2026-08-16T05:41:08+00:00"
  },
  "P4716": {
    "problem_number": 4716,
    "slug": "paley-graph-1049-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:08+00:00",
    "updated_at": "2026-08-16T05:41:17+00:00"
  },
  "P4718": {
    "problem_number": 4718,
    "slug": "paley-graph-1061-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:18+00:00",
    "updated_at": "2026-08-16T05:41:20+00:00"
  },
  "P4720": {
    "problem_number": 4720,
    "slug": "paley-graph-1069-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:22+00:00",
    "updated_at": "2026-08-16T05:41:23+00:00"
  },
  "P4722": {
    "problem_number": 4722,
    "slug": "paley-graph-1093-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:23+00:00",
    "updated_at": "2026-08-16T05:41:23+00:00"
  },
  "P4724": {
    "problem_number": 4724,
    "slug": "paley-graph-1097-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:24+00:00",
    "updated_at": "2026-08-16T05:41:27+00:00"
  },
  "P4726": {
    "problem_number": 4726,
    "slug": "paley-graph-1109-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:29+00:00",
    "updated_at": "2026-08-16T05:41:32+00:00"
  },
  "P4728": {
    "problem_number": 4728,
    "slug": "paley-graph-1117-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:34+00:00",
    "updated_at": "2026-08-16T05:41:45+00:00"
  },
  "P4730": {
    "problem_number": 4730,
    "slug": "paley-graph-1129-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:47+00:00",
    "updated_at": "2026-08-16T05:41:49+00:00"
  },
  "P4732": {
    "problem_number": 4732,
    "slug": "paley-graph-1153-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:50+00:00",
    "updated_at": "2026-08-16T05:41:52+00:00"
  },
  "P4734": {
    "problem_number": 4734,
    "slug": "paley-graph-1181-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:53+00:00",
    "updated_at": "2026-08-16T05:41:54+00:00"
  },
  "P4736": {
    "problem_number": 4736,
    "slug": "paley-graph-1193-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:54+00:00",
    "updated_at": "2026-08-16T05:41:55+00:00"
  },
  "P4738": {
    "problem_number": 4738,
    "slug": "paley-graph-1201-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:55+00:00",
    "updated_at": "2026-08-16T05:41:55+00:00"
  },
  "P4740": {
    "problem_number": 4740,
    "slug": "paley-graph-1213-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:56+00:00",
    "updated_at": "2026-08-16T05:41:57+00:00"
  },
  "P4742": {
    "problem_number": 4742,
    "slug": "paley-graph-1217-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:57+00:00",
    "updated_at": "2026-08-16T05:41:58+00:00"
  },
  "P4744": {
    "problem_number": 4744,
    "slug": "paley-graph-1229-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:59+00:00",
    "updated_at": "2026-08-16T05:42:02+00:00"
  },
  "P4746": {
    "problem_number": 4746,
    "slug": "paley-graph-1237-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:03+00:00",
    "updated_at": "2026-08-16T05:42:04+00:00"
  },
  "P4748": {
    "problem_number": 4748,
    "slug": "paley-graph-1249-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:04+00:00",
    "updated_at": "2026-08-16T05:42:05+00:00"
  },
  "P4750": {
    "problem_number": 4750,
    "slug": "paley-graph-1277-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:07+00:00",
    "updated_at": "2026-08-16T05:42:09+00:00"
  },
  "P4752": {
    "problem_number": 4752,
    "slug": "paley-graph-1289-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:11+00:00",
    "updated_at": "2026-08-16T05:42:11+00:00"
  },
  "P4754": {
    "problem_number": 4754,
    "slug": "paley-graph-1297-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:12+00:00",
    "updated_at": "2026-08-16T05:42:19+00:00"
  },
  "P4756": {
    "problem_number": 4756,
    "slug": "paley-graph-1301-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:21+00:00",
    "updated_at": "2026-08-16T05:42:29+00:00"
  },
  "P4758": {
    "problem_number": 4758,
    "slug": "paley-graph-1321-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:30+00:00",
    "updated_at": "2026-08-16T05:42:34+00:00"
  },
  "P4760": {
    "problem_number": 4760,
    "slug": "paley-graph-1361-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:37+00:00",
    "updated_at": "2026-08-16T05:42:38+00:00"
  },
  "P4762": {
    "problem_number": 4762,
    "slug": "paley-graph-1373-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:39+00:00",
    "updated_at": "2026-08-16T05:42:40+00:00"
  },
  "P4764": {
    "problem_number": 4764,
    "slug": "paley-graph-1381-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:41+00:00",
    "updated_at": "2026-08-16T05:42:47+00:00"
  },
  "P4766": {
    "problem_number": 4766,
    "slug": "paley-graph-1409-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:49+00:00",
    "updated_at": "2026-08-16T05:42:53+00:00"
  },
  "P4768": {
    "problem_number": 4768,
    "slug": "paley-graph-1429-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:55+00:00",
    "updated_at": "2026-08-16T05:42:57+00:00"
  },
  "P4770": {
    "problem_number": 4770,
    "slug": "paley-graph-1433-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:57+00:00",
    "updated_at": "2026-08-16T05:42:58+00:00"
  },
  "P4772": {
    "problem_number": 4772,
    "slug": "paley-graph-1453-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:58+00:00",
    "updated_at": "2026-08-16T05:42:59+00:00"
  },
  "P4774": {
    "problem_number": 4774,
    "slug": "paley-graph-1481-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:59+00:00",
    "updated_at": "2026-08-16T05:42:59+00:00"
  },
  "P4776": {
    "problem_number": 4776,
    "slug": "paley-graph-1489-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:42:59+00:00",
    "updated_at": "2026-08-16T05:43:00+00:00"
  },
  "P4778": {
    "problem_number": 4778,
    "slug": "paley-graph-1493-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:01+00:00",
    "updated_at": "2026-08-16T05:43:02+00:00"
  },
  "P4780": {
    "problem_number": 4780,
    "slug": "paley-graph-1549-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:02+00:00",
    "updated_at": "2026-08-16T05:43:02+00:00"
  },
  "P4782": {
    "problem_number": 4782,
    "slug": "paley-graph-1553-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:02+00:00",
    "updated_at": "2026-08-16T05:43:03+00:00"
  },
  "P4784": {
    "problem_number": 4784,
    "slug": "paley-graph-1597-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:03+00:00",
    "updated_at": "2026-08-16T05:43:04+00:00"
  },
  "P4786": {
    "problem_number": 4786,
    "slug": "paley-graph-1601-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:43:05+00:00",
    "updated_at": "2026-08-16T05:43:07+00:00"
  },
  "P5470": {
    "problem_number": 5470,
    "slug": "paley-graph-1609-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:51+00:00",
    "updated_at": "2026-08-16T08:28:00+00:00"
  },
  "P5472": {
    "problem_number": 5472,
    "slug": "paley-graph-1613-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:28:03+00:00",
    "updated_at": "2026-08-16T08:28:03+00:00"
  },
  "P5474": {
    "problem_number": 5474,
    "slug": "paley-graph-1621-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:28:06+00:00",
    "updated_at": "2026-08-16T08:28:08+00:00"
  },
  "P5476": {
    "problem_number": 5476,
    "slug": "paley-graph-1637-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:28:14+00:00",
    "updated_at": "2026-08-16T08:28:25+00:00"
  },
  "P5478": {
    "problem_number": 5478,
    "slug": "paley-graph-1657-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:28:33+00:00",
    "updated_at": "2026-08-16T08:28:48+00:00"
  },
  "P5480": {
    "problem_number": 5480,
    "slug": "paley-graph-1669-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:28:57+00:00",
    "updated_at": "2026-08-16T08:29:09+00:00"
  },
  "P5482": {
    "problem_number": 5482,
    "slug": "paley-graph-1693-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:15+00:00",
    "updated_at": "2026-08-16T08:29:26+00:00"
  },
  "P5484": {
    "problem_number": 5484,
    "slug": "paley-graph-1697-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:32+00:00",
    "updated_at": "2026-08-16T08:29:37+00:00"
  },
  "P5486": {
    "problem_number": 5486,
    "slug": "paley-graph-1709-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:40+00:00",
    "updated_at": "2026-08-16T08:29:46+00:00"
  },
  "P5488": {
    "problem_number": 5488,
    "slug": "paley-graph-1721-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:50+00:00",
    "updated_at": "2026-08-16T08:29:51+00:00"
  },
  "P5490": {
    "problem_number": 5490,
    "slug": "paley-graph-1733-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:53+00:00",
    "updated_at": "2026-08-16T08:29:55+00:00"
  },
  "P5492": {
    "problem_number": 5492,
    "slug": "paley-graph-1741-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:29:56+00:00",
    "updated_at": "2026-08-16T08:29:58+00:00"
  },
  "P5494": {
    "problem_number": 5494,
    "slug": "paley-graph-1753-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:00+00:00",
    "updated_at": "2026-08-16T08:30:04+00:00"
  },
  "P5496": {
    "problem_number": 5496,
    "slug": "paley-graph-1777-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:05+00:00",
    "updated_at": "2026-08-16T08:30:07+00:00"
  },
  "P5498": {
    "problem_number": 5498,
    "slug": "paley-graph-1789-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:07+00:00",
    "updated_at": "2026-08-16T08:30:11+00:00"
  },
  "P5500": {
    "problem_number": 5500,
    "slug": "paley-graph-1801-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:12+00:00",
    "updated_at": "2026-08-16T08:30:13+00:00"
  },
  "P5502": {
    "problem_number": 5502,
    "slug": "paley-graph-1861-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:15+00:00",
    "updated_at": "2026-08-16T08:30:17+00:00"
  },
  "P5504": {
    "problem_number": 5504,
    "slug": "paley-graph-1873-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:17+00:00",
    "updated_at": "2026-08-16T08:30:18+00:00"
  },
  "P5506": {
    "problem_number": 5506,
    "slug": "paley-graph-1877-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:19+00:00",
    "updated_at": "2026-08-16T08:30:21+00:00"
  },
  "P5508": {
    "problem_number": 5508,
    "slug": "paley-graph-1889-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:21+00:00",
    "updated_at": "2026-08-16T08:30:23+00:00"
  },
  "P5510": {
    "problem_number": 5510,
    "slug": "paley-graph-1901-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:26+00:00",
    "updated_at": "2026-08-16T08:30:27+00:00"
  },
  "P5512": {
    "problem_number": 5512,
    "slug": "paley-graph-1913-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:27+00:00",
    "updated_at": "2026-08-16T08:30:27+00:00"
  },
  "P5514": {
    "problem_number": 5514,
    "slug": "paley-graph-1933-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:28+00:00",
    "updated_at": "2026-08-16T08:30:28+00:00"
  },
  "P5516": {
    "problem_number": 5516,
    "slug": "paley-graph-1949-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:28+00:00",
    "updated_at": "2026-08-16T08:30:32+00:00"
  },
  "P5518": {
    "problem_number": 5518,
    "slug": "paley-graph-1973-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:33+00:00",
    "updated_at": "2026-08-16T08:30:34+00:00"
  },
  "P5520": {
    "problem_number": 5520,
    "slug": "paley-graph-1993-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:36+00:00",
    "updated_at": "2026-08-16T08:30:37+00:00"
  },
  "P5522": {
    "problem_number": 5522,
    "slug": "paley-graph-1997-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:38+00:00",
    "updated_at": "2026-08-16T08:30:43+00:00"
  },
  "P5524": {
    "problem_number": 5524,
    "slug": "paley-graph-2017-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:44+00:00",
    "updated_at": "2026-08-16T08:30:46+00:00"
  },
  "P5526": {
    "problem_number": 5526,
    "slug": "paley-graph-2029-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:48+00:00",
    "updated_at": "2026-08-16T08:30:51+00:00"
  },
  "P5528": {
    "problem_number": 5528,
    "slug": "paley-graph-2053-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:53+00:00",
    "updated_at": "2026-08-16T08:30:55+00:00"
  },
  "P5530": {
    "problem_number": 5530,
    "slug": "paley-graph-2069-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:30:58+00:00",
    "updated_at": "2026-08-16T08:31:03+00:00"
  },
  "P5532": {
    "problem_number": 5532,
    "slug": "paley-graph-2081-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:31:05+00:00",
    "updated_at": "2026-08-16T08:31:12+00:00"
  },
  "P5534": {
    "problem_number": 5534,
    "slug": "paley-graph-2089-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:31:12+00:00",
    "updated_at": "2026-08-16T08:31:14+00:00"
  },
  "P5536": {
    "problem_number": 5536,
    "slug": "paley-graph-2113-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:31:18+00:00",
    "updated_at": "2026-08-16T08:31:21+00:00"
  },
  "P5538": {
    "problem_number": 5538,
    "slug": "paley-graph-2129-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:31:26+00:00",
    "updated_at": "2026-08-16T08:31:32+00:00"
  },
  "P5540": {
    "problem_number": 5540,
    "slug": "paley-graph-2137-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:31:36+00:00",
    "updated_at": "2026-08-16T08:31:46+00:00"
  },
  "P5544": {
    "problem_number": 5544,
    "slug": "paley-graph-2141-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:34:22+00:00",
    "updated_at": "2026-08-16T08:34:48+00:00"
  },
  "P5546": {
    "problem_number": 5546,
    "slug": "paley-graph-2153-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:34:53+00:00",
    "updated_at": "2026-08-16T08:34:56+00:00"
  },
  "P5548": {
    "problem_number": 5548,
    "slug": "paley-graph-2161-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:02+00:00",
    "updated_at": "2026-08-16T08:35:05+00:00"
  },
  "P5550": {
    "problem_number": 5550,
    "slug": "paley-graph-2213-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:06+00:00",
    "updated_at": "2026-08-16T08:35:14+00:00"
  },
  "P5552": {
    "problem_number": 5552,
    "slug": "paley-graph-2221-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:17+00:00",
    "updated_at": "2026-08-16T08:35:26+00:00"
  },
  "P5554": {
    "problem_number": 5554,
    "slug": "paley-graph-2237-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:29+00:00",
    "updated_at": "2026-08-16T08:35:37+00:00"
  },
  "P5556": {
    "problem_number": 5556,
    "slug": "paley-graph-2269-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:42+00:00",
    "updated_at": "2026-08-16T08:35:49+00:00"
  },
  "P5558": {
    "problem_number": 5558,
    "slug": "paley-graph-2273-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:35:52+00:00",
    "updated_at": "2026-08-16T08:35:58+00:00"
  },
  "P5560": {
    "problem_number": 5560,
    "slug": "paley-graph-2281-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:36:04+00:00",
    "updated_at": "2026-08-16T08:36:09+00:00"
  },
  "P5562": {
    "problem_number": 5562,
    "slug": "paley-graph-2293-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:36:14+00:00",
    "updated_at": "2026-08-16T08:36:20+00:00"
  },
  "P5564": {
    "problem_number": 5564,
    "slug": "paley-graph-2297-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:36:23+00:00",
    "updated_at": "2026-08-16T08:36:32+00:00"
  },
  "P5566": {
    "problem_number": 5566,
    "slug": "paley-graph-2309-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:36:35+00:00",
    "updated_at": "2026-08-16T08:36:42+00:00"
  },
  "P5568": {
    "problem_number": 5568,
    "slug": "paley-graph-2333-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:36:45+00:00",
    "updated_at": "2026-08-16T08:36:54+00:00"
  },
  "P5572": {
    "problem_number": 5572,
    "slug": "paley-graph-2341-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:43+00:00",
    "updated_at": "2026-08-16T08:40:44+00:00"
  },
  "P5574": {
    "problem_number": 5574,
    "slug": "paley-graph-2357-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:45+00:00",
    "updated_at": "2026-08-16T08:40:45+00:00"
  },
  "P5576": {
    "problem_number": 5576,
    "slug": "paley-graph-2377-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:45+00:00",
    "updated_at": "2026-08-16T08:40:45+00:00"
  },
  "P5578": {
    "problem_number": 5578,
    "slug": "paley-graph-2381-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:45+00:00",
    "updated_at": "2026-08-16T08:40:46+00:00"
  },
  "P5580": {
    "problem_number": 5580,
    "slug": "paley-graph-2389-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:46+00:00",
    "updated_at": "2026-08-16T08:40:46+00:00"
  },
  "P5582": {
    "problem_number": 5582,
    "slug": "paley-graph-2393-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:46+00:00",
    "updated_at": "2026-08-16T08:40:47+00:00"
  },
  "P5584": {
    "problem_number": 5584,
    "slug": "paley-graph-2417-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:47+00:00",
    "updated_at": "2026-08-16T08:40:47+00:00"
  },
  "P5586": {
    "problem_number": 5586,
    "slug": "paley-graph-2437-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:47+00:00",
    "updated_at": "2026-08-16T08:40:47+00:00"
  },
  "P5588": {
    "problem_number": 5588,
    "slug": "paley-graph-2441-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:48+00:00",
    "updated_at": "2026-08-16T08:40:49+00:00"
  },
  "P5590": {
    "problem_number": 5590,
    "slug": "paley-graph-2473-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:40:50+00:00",
    "updated_at": "2026-08-16T08:40:57+00:00"
  },
  "P5592": {
    "problem_number": 5592,
    "slug": "paley-graph-2477-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:41:06+00:00",
    "updated_at": "2026-08-16T08:41:18+00:00"
  },
  "P5594": {
    "problem_number": 5594,
    "slug": "paley-graph-2521-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:41:25+00:00",
    "updated_at": "2026-08-16T08:41:51+00:00"
  },
  "P5596": {
    "problem_number": 5596,
    "slug": "paley-graph-2549-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:41:57+00:00",
    "updated_at": "2026-08-16T08:42:08+00:00"
  },
  "P5598": {
    "problem_number": 5598,
    "slug": "paley-graph-2557-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:42:13+00:00",
    "updated_at": "2026-08-16T08:42:22+00:00"
  },
  "P5600": {
    "problem_number": 5600,
    "slug": "paley-graph-2593-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:42:27+00:00",
    "updated_at": "2026-08-16T08:42:37+00:00"
  },
  "P5602": {
    "problem_number": 5602,
    "slug": "paley-graph-2609-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:42:41+00:00",
    "updated_at": "2026-08-16T08:42:49+00:00"
  },
  "P5604": {
    "problem_number": 5604,
    "slug": "paley-graph-2617-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:42:51+00:00",
    "updated_at": "2026-08-16T08:42:57+00:00"
  },
  "P5606": {
    "problem_number": 5606,
    "slug": "paley-graph-2621-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:42:58+00:00",
    "updated_at": "2026-08-16T08:43:03+00:00"
  },
  "P5608": {
    "problem_number": 5608,
    "slug": "paley-graph-2633-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:43:04+00:00",
    "updated_at": "2026-08-16T08:43:11+00:00"
  },
  "P5610": {
    "problem_number": 5610,
    "slug": "paley-graph-2657-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:43:17+00:00",
    "updated_at": "2026-08-16T08:43:29+00:00"
  },
  "P5612": {
    "problem_number": 5612,
    "slug": "paley-graph-2677-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:43:32+00:00",
    "updated_at": "2026-08-16T08:43:45+00:00"
  },
  "P5614": {
    "problem_number": 5614,
    "slug": "paley-graph-2689-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:43:50+00:00",
    "updated_at": "2026-08-16T08:44:00+00:00"
  },
  "P5616": {
    "problem_number": 5616,
    "slug": "paley-graph-2693-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:02+00:00",
    "updated_at": "2026-08-16T08:44:05+00:00"
  },
  "P5618": {
    "problem_number": 5618,
    "slug": "paley-graph-2713-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:09+00:00",
    "updated_at": "2026-08-16T08:44:10+00:00"
  },
  "P5620": {
    "problem_number": 5620,
    "slug": "paley-graph-2729-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:11+00:00",
    "updated_at": "2026-08-16T08:44:13+00:00"
  },
  "P5622": {
    "problem_number": 5622,
    "slug": "paley-graph-2741-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:13+00:00",
    "updated_at": "2026-08-16T08:44:14+00:00"
  },
  "P5624": {
    "problem_number": 5624,
    "slug": "paley-graph-2749-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:15+00:00",
    "updated_at": "2026-08-16T08:44:17+00:00"
  },
  "P5626": {
    "problem_number": 5626,
    "slug": "paley-graph-2753-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:19+00:00",
    "updated_at": "2026-08-16T08:44:22+00:00"
  },
  "P5628": {
    "problem_number": 5628,
    "slug": "paley-graph-2777-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:28+00:00",
    "updated_at": "2026-08-16T08:44:29+00:00"
  },
  "P5630": {
    "problem_number": 5630,
    "slug": "paley-graph-2789-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:29+00:00",
    "updated_at": "2026-08-16T08:44:29+00:00"
  },
  "P5632": {
    "problem_number": 5632,
    "slug": "paley-graph-2797-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:31+00:00",
    "updated_at": "2026-08-16T08:44:34+00:00"
  },
  "P5634": {
    "problem_number": 5634,
    "slug": "paley-graph-2801-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:36+00:00",
    "updated_at": "2026-08-16T08:44:36+00:00"
  },
  "P5636": {
    "problem_number": 5636,
    "slug": "paley-graph-2833-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:36+00:00",
    "updated_at": "2026-08-16T08:44:37+00:00"
  },
  "P5638": {
    "problem_number": 5638,
    "slug": "paley-graph-2837-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:38+00:00",
    "updated_at": "2026-08-16T08:44:44+00:00"
  },
  "P5640": {
    "problem_number": 5640,
    "slug": "paley-graph-2857-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:44+00:00",
    "updated_at": "2026-08-16T08:44:46+00:00"
  },
  "P5642": {
    "problem_number": 5642,
    "slug": "paley-graph-2861-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:47+00:00",
    "updated_at": "2026-08-16T08:44:52+00:00"
  },
  "P5644": {
    "problem_number": 5644,
    "slug": "paley-graph-2897-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:53+00:00",
    "updated_at": "2026-08-16T08:44:53+00:00"
  },
  "P5646": {
    "problem_number": 5646,
    "slug": "paley-graph-2909-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:55+00:00",
    "updated_at": "2026-08-16T08:44:56+00:00"
  },
  "P5648": {
    "problem_number": 5648,
    "slug": "paley-graph-2917-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:56+00:00",
    "updated_at": "2026-08-16T08:44:57+00:00"
  },
  "P5650": {
    "problem_number": 5650,
    "slug": "paley-graph-2953-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:57+00:00",
    "updated_at": "2026-08-16T08:44:57+00:00"
  },
  "P5652": {
    "problem_number": 5652,
    "slug": "paley-graph-2957-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:58+00:00",
    "updated_at": "2026-08-16T08:44:58+00:00"
  },
  "P5654": {
    "problem_number": 5654,
    "slug": "paley-graph-2969-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:58+00:00",
    "updated_at": "2026-08-16T08:44:59+00:00"
  },
  "P5656": {
    "problem_number": 5656,
    "slug": "paley-graph-3001-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:44:59+00:00",
    "updated_at": "2026-08-16T08:45:02+00:00"
  },
  "P5658": {
    "problem_number": 5658,
    "slug": "paley-graph-3037-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:03+00:00",
    "updated_at": "2026-08-16T08:45:03+00:00"
  },
  "P5660": {
    "problem_number": 5660,
    "slug": "paley-graph-3041-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:04+00:00",
    "updated_at": "2026-08-16T08:45:05+00:00"
  },
  "P5662": {
    "problem_number": 5662,
    "slug": "paley-graph-3049-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:05+00:00",
    "updated_at": "2026-08-16T08:45:05+00:00"
  },
  "P5664": {
    "problem_number": 5664,
    "slug": "paley-graph-3061-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:06+00:00",
    "updated_at": "2026-08-16T08:45:06+00:00"
  },
  "P5666": {
    "problem_number": 5666,
    "slug": "paley-graph-3089-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:07+00:00",
    "updated_at": "2026-08-16T08:45:07+00:00"
  },
  "P5668": {
    "problem_number": 5668,
    "slug": "paley-graph-3109-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:07+00:00",
    "updated_at": "2026-08-16T08:45:08+00:00"
  },
  "P5670": {
    "problem_number": 5670,
    "slug": "paley-graph-3121-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:08+00:00",
    "updated_at": "2026-08-16T08:45:10+00:00"
  },
  "P5672": {
    "problem_number": 5672,
    "slug": "paley-graph-3137-clique-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:45:11+00:00",
    "updated_at": "2026-08-16T08:45:13+00:00"
  },
  "P2484": {
    "problem_number": 2484,
    "slug": "prime-cube-prime-square-gap-trillion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:02+00:00",
    "updated_at": "2026-07-29T20:56:00+00:00"
  },
  "P3380": {
    "problem_number": 3380,
    "slug": "kourovka-21-17-closure-operators-on-classes-of-metabelian-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:54:24+00:00",
    "updated_at": "2026-08-12T07:54:47+00:00"
  },
  "P12323": {
    "problem_number": 12323,
    "slug": "coefficient-growth-in-a-weighted-distinct-part-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:38:43+00:00",
    "updated_at": "2026-09-01T19:38:48+00:00"
  },
  "P8242": {
    "problem_number": 8242,
    "slug": "open-fc-15020e19317cd9078b28-erdos-340-variants-cofinite-sub",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:37+00:00",
    "updated_at": "2026-08-17T18:37:39+00:00"
  },
  "P3540": {
    "problem_number": 3540,
    "slug": "kourovka-21-141-coherence-of-free-pro-p-products-with-amalgamation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:49+00:00",
    "updated_at": "2026-08-12T08:12:58+00:00"
  },
  "P3430": {
    "problem_number": 3430,
    "slug": "kourovka-21-46-cohomological-dimension-of-finitely-presented-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:00:39+00:00",
    "updated_at": "2026-08-12T08:00:43+00:00"
  },
  "P19": {
    "problem_number": 19,
    "slug": "collatz-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:34:56+00:00"
  },
  "P12535": {
    "problem_number": 12535,
    "slug": "collatz-trajectory-sums-and-stopping-times",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:45:37+00:00",
    "updated_at": "2026-09-02T21:45:49+00:00"
  },
  "P8834": {
    "problem_number": 8834,
    "slug": "open-fc-a24015b03502ecb52735-erdos-193",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:03+00:00",
    "updated_at": "2026-08-17T19:25:14+00:00"
  },
  "P3516": {
    "problem_number": 3516,
    "slug": "kourovka-21-128-commensurability-of-the-spherical-artin-groups-f4-and-h4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:32+00:00",
    "updated_at": "2026-08-12T08:10:42+00:00"
  },
  "P8836": {
    "problem_number": 8836,
    "slug": "open-fc-a31363640108c3100278-erdos-885",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:08+00:00",
    "updated_at": "2026-08-17T19:25:19+00:00"
  },
  "P3398": {
    "problem_number": 3398,
    "slug": "kourovka-21-29-common-regular-two-point-stabilizers-in-primitive-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:50+00:00",
    "updated_at": "2026-08-12T07:57:03+00:00"
  },
  "P3410": {
    "problem_number": 3410,
    "slug": "kourovka-21-35-commutator-values-in-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:04+00:00",
    "updated_at": "2026-08-12T07:58:10+00:00"
  },
  "P12371": {
    "problem_number": 12371,
    "slug": "comparing-iterated-logarithmic-integral-and-prime-counting-descent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:44:37+00:00",
    "updated_at": "2026-09-01T19:44:44+00:00"
  },
  "P3494": {
    "problem_number": 3494,
    "slug": "kourovka-21-112-complete-classes-of-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:07:39+00:00",
    "updated_at": "2026-08-12T08:07:50+00:00"
  },
  "P2936": {
    "problem_number": 2936,
    "slug": "harmonic-random-disk-cover",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:50:21+00:00",
    "updated_at": "2026-08-01T23:29:48+00:00"
  },
  "P11839": {
    "problem_number": 11839,
    "slug": "completeness-of-a-bitwise-and-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:09+00:00",
    "updated_at": "2026-08-30T16:14:15+00:00"
  },
  "P11837": {
    "problem_number": 11837,
    "slug": "completeness-of-a-last-index-recaman-variant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:13:58+00:00",
    "updated_at": "2026-08-30T16:14:05+00:00"
  },
  "P12289": {
    "problem_number": 12289,
    "slug": "completeness-of-a-practical-number-complement-list",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:34:42+00:00",
    "updated_at": "2026-09-01T19:34:48+00:00"
  },
  "P11853": {
    "problem_number": 11853,
    "slug": "completeness-of-a-two-predecessor-gcd-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:09+00:00",
    "updated_at": "2026-08-30T16:15:14+00:00"
  },
  "P9786": {
    "problem_number": 9786,
    "slug": "open-fc-d353cb4da7538d7cdac0-erdos-354-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:39+00:00",
    "updated_at": "2026-08-17T20:02:39+00:00"
  },
  "P11879": {
    "problem_number": 11879,
    "slug": "completeness-of-the-decimal-zero-rows-for-powers-of-nine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:55+00:00",
    "updated_at": "2026-08-30T16:16:59+00:00"
  },
  "P12237": {
    "problem_number": 12237,
    "slug": "completeness-of-the-discriminants-with-class-group-c3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:28:15+00:00",
    "updated_at": "2026-09-01T19:28:21+00:00"
  },
  "P11722": {
    "problem_number": 11722,
    "slug": "completeness-of-the-enots-wolley-sequence-outside-prime-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:34+00:00",
    "updated_at": "2026-08-30T11:17:41+00:00"
  },
  "P11814": {
    "problem_number": 11814,
    "slug": "completeness-of-the-four-known-loops-in-a-prime-factor-collatz-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:52:33+00:00",
    "updated_at": "2026-08-30T16:36:38+00:00"
  },
  "P10038": {
    "problem_number": 10038,
    "slug": "open-fc-dad0e6c96f68480eb470-idoneal-numbers-completeness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:36+00:00",
    "updated_at": "2026-08-17T20:05:37+00:00"
  },
  "P2888": {
    "problem_number": 2888,
    "slug": "line-arrangement-triangular-bounded-completion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:43:52+00:00",
    "updated_at": "2026-08-01T23:34:51+00:00"
  },
  "P9320": {
    "problem_number": 9320,
    "slug": "open-fc-c85e961756b27ceeaf9f-mathoverflow-1973",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:52+00:00",
    "updated_at": "2026-08-17T19:50:53+00:00"
  },
  "P2928": {
    "problem_number": 2928,
    "slug": "binary-code-weight-enumerator-equality-complexity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:49:12+00:00",
    "updated_at": "2026-08-01T23:20:47+00:00"
  },
  "P2788": {
    "problem_number": 2788,
    "slug": "sts15-pasch-switch-graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:03+00:00",
    "updated_at": "2026-08-01T12:31:17+00:00"
  },
  "P8726": {
    "problem_number": 8726,
    "slug": "open-fc-49ef33eaf806873dc94a-fermat-number-are-composite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:19+00:00",
    "updated_at": "2026-08-17T19:11:29+00:00"
  },
  "P12457": {
    "problem_number": 12457,
    "slug": "composite-record-holders-for-euler-s-totient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:37:50+00:00",
    "updated_at": "2026-09-02T21:37:59+00:00"
  },
  "P11919": {
    "problem_number": 11919,
    "slug": "composite-solutions-of-a-totient-exponent-congruence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:23:09+00:00",
    "updated_at": "2026-08-30T16:23:16+00:00"
  },
  "P2906": {
    "problem_number": 2906,
    "slug": "mandelbrot-area-computable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:46:15+00:00",
    "updated_at": "2026-08-01T23:36:07+00:00"
  },
  "P3482": {
    "problem_number": 3482,
    "slug": "kourovka-21-105-concise-words-in-residually-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:48+00:00",
    "updated_at": "2026-08-12T08:06:52+00:00"
  },
  "P9080": {
    "problem_number": 9080,
    "slug": "open-fc-b642551b1efd8c1c530d-mod-216-of-a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:06+00:00",
    "updated_at": "2026-08-17T19:47:07+00:00"
  },
  "P10230": {
    "problem_number": 10230,
    "slug": "open-fc-d65f1640fb79d8aac6ff-conjecture-variants-a-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:55+00:00",
    "updated_at": "2026-08-18T02:51:55+00:00"
  },
  "P10196": {
    "problem_number": 10196,
    "slug": "open-fc-94365b59d743d71dc1ad-conjecture2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:42+00:00",
    "updated_at": "2026-08-18T02:51:43+00:00"
  },
  "P9936": {
    "problem_number": 9936,
    "slug": "open-fc-8b9faf3e8d860648149d-green-16-conjectured-lower-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:41+00:00",
    "updated_at": "2026-08-17T20:04:42+00:00"
  },
  "P3530": {
    "problem_number": 3530,
    "slug": "kourovka-21-136-conjugacy-classes-in-profinite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:20+00:00",
    "updated_at": "2026-08-12T08:12:23+00:00"
  },
  "P3700": {
    "problem_number": 3700,
    "slug": "connected-chord-diagrams-twenty",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:18+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9752": {
    "problem_number": 9752,
    "slug": "open-fc-ba95fc32ba7d894c2ce8-mathoverflow-235893",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:20+00:00",
    "updated_at": "2026-08-17T20:02:21+00:00"
  },
  "P8208": {
    "problem_number": 8208,
    "slug": "open-fc-0e95afe38dcae99caba5-erdos-366",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:08+00:00",
    "updated_at": "2026-08-17T18:37:09+00:00"
  },
  "P3170": {
    "problem_number": 3170,
    "slug": "erdos-problem-366",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:48:03+00:00",
    "updated_at": "2026-08-12T05:48:06+00:00"
  },
  "P8518": {
    "problem_number": 8518,
    "slug": "open-fc-5ecb4aa050e0ea78f2c4-erdos-366-variants-weaker",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:06+00:00",
    "updated_at": "2026-08-17T18:54:07+00:00"
  },
  "P8844": {
    "problem_number": 8844,
    "slug": "open-fc-ab1b1c8f703eafd35ede-erdos-364",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:56+00:00",
    "updated_at": "2026-08-17T19:35:11+00:00"
  },
  "P3160": {
    "problem_number": 3160,
    "slug": "erdos-problem-364",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:43:31+00:00",
    "updated_at": "2026-08-12T05:44:45+00:00"
  },
  "P12531": {
    "problem_number": 12531,
    "slug": "consecutive-prime-palindromes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:45:14+00:00",
    "updated_at": "2026-09-02T21:45:22+00:00"
  },
  "P3046": {
    "problem_number": 3046,
    "slug": "erdos-problem-141",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:18+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8166": {
    "problem_number": 8166,
    "slug": "open-fc-095d5e2c96e280026ea7-erdos-141",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:57+00:00",
    "updated_at": "2026-08-17T18:35:59+00:00"
  },
  "P2870": {
    "problem_number": 2870,
    "slug": "projective-sets-ramsey-consistency-strength",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:41:26+00:00",
    "updated_at": "2026-08-01T23:42:05+00:00"
  },
  "P3414": {
    "problem_number": 3414,
    "slug": "kourovka-21-37-constructibility-of-soluble-tdlc-groups-of-type-fp-infinity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:27+00:00",
    "updated_at": "2026-08-12T07:58:29+00:00"
  },
  "P2884": {
    "problem_number": 2884,
    "slug": "non-cancelling-intersections-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:43:20+00:00",
    "updated_at": "2026-08-01T12:20:06+00:00"
  },
  "P9440": {
    "problem_number": 9440,
    "slug": "open-fc-6c5b3824c8028d2597a5-kotherconjecture-variants-le-kotherradical",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:21+00:00",
    "updated_at": "2026-08-17T19:53:23+00:00"
  },
  "P9830": {
    "problem_number": 9830,
    "slug": "open-fc-f4c4bad5491be592cc78-homogeneousspace-exists-surjective",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:01+00:00",
    "updated_at": "2026-08-17T20:03:01+00:00"
  },
  "P8272": {
    "problem_number": 8272,
    "slug": "open-fc-1a00bc576edf4ef82db2-erdos-143-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:06+00:00",
    "updated_at": "2026-08-17T18:38:07+00:00"
  },
  "P3050": {
    "problem_number": 3050,
    "slug": "erdos-problem-143",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:22+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P2970": {
    "problem_number": 2970,
    "slug": "erdos-problem-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:35+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8316": {
    "problem_number": 8316,
    "slug": "open-fc-1f0d0e8317d9ebdc1ff2-erdos-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:34+00:00",
    "updated_at": "2026-08-17T18:39:35+00:00"
  },
  "P10046": {
    "problem_number": 10046,
    "slug": "open-fc-e1a8bb9a2d05ea98c2ae-erdos-357-variants-infinite-set-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:46+00:00",
    "updated_at": "2026-08-17T20:05:47+00:00"
  },
  "P9358": {
    "problem_number": 9358,
    "slug": "open-fc-e8aae9b6968dd7a5ee1c-cookson-hills-series-converges",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:08+00:00",
    "updated_at": "2026-08-17T19:51:09+00:00"
  },
  "P8976": {
    "problem_number": 8976,
    "slug": "open-fc-6871c2f00e377b7c5b8a-flint-hills-series-converges",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:09+00:00",
    "updated_at": "2026-08-17T19:44:10+00:00"
  },
  "P9832": {
    "problem_number": 9832,
    "slug": "open-fc-f635235db1d5dbdfa421-erdos-12-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:01+00:00",
    "updated_at": "2026-08-17T20:03:01+00:00"
  },
  "P2966": {
    "problem_number": 2966,
    "slug": "erdos-problem-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:32+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8932": {
    "problem_number": 8932,
    "slug": "open-fc-ed611db4dc767384069d-homogeneousspace-exists-inj-tendsto",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:50+00:00",
    "updated_at": "2026-08-17T19:40:52+00:00"
  },
  "P9568": {
    "problem_number": 9568,
    "slug": "open-fc-cd589b3e30f401dd4649-erdos-329-variants-converse-implication",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:34+00:00",
    "updated_at": "2026-08-17T19:55:36+00:00"
  },
  "P9734": {
    "problem_number": 9734,
    "slug": "open-fc-ab852c6b5088daf30359-tunnell-odd-converse",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:09+00:00",
    "updated_at": "2026-08-17T20:02:10+00:00"
  },
  "P9820": {
    "problem_number": 9820,
    "slug": "open-fc-ef7b92eefe68fe2b2307-problem-4-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:57+00:00",
    "updated_at": "2026-08-17T20:02:57+00:00"
  },
  "P9946": {
    "problem_number": 9946,
    "slug": "open-fc-947ee23dcbcf5d7f430a-convex-mosers-worm-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:49+00:00",
    "updated_at": "2026-08-17T20:04:50+00:00"
  },
  "P8668": {
    "problem_number": 8668,
    "slug": "open-fc-2e4ab5d15f4b423f303b-conway99graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:17+00:00",
    "updated_at": "2026-08-17T19:04:21+00:00"
  },
  "P11764": {
    "problem_number": 11764,
    "slug": "conway-s-decimal-rats-orbit-dichotomy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:23:50+00:00",
    "updated_at": "2026-08-30T12:24:01+00:00"
  },
  "P3088": {
    "problem_number": 3088,
    "slug": "conway-thrackle-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:58+00:00",
    "updated_at": "2026-08-02T12:48:08+00:00"
  },
  "P3736": {
    "problem_number": 3736,
    "slug": "knight-seven-cop-number-capture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:48:34+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8132": {
    "problem_number": 8132,
    "slug": "open-fc-0530aa634b9c9ae51183-erdos-307-variants-coprime-one-notmem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:58+00:00",
    "updated_at": "2026-08-17T18:34:59+00:00"
  },
  "P9118": {
    "problem_number": 9118,
    "slug": "open-fc-d1eecd0f8255be9c1af4-green-52",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:41+00:00",
    "updated_at": "2026-08-17T19:47:41+00:00"
  },
  "P3684": {
    "problem_number": 3684,
    "slug": "l-tromino-twelve-torus-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:57+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11516": {
    "problem_number": 11516,
    "slug": "reverse-complement-permutations-with-equal-rsk-recording-tableau",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:41:45+00:00",
    "updated_at": "2026-08-29T18:54:08+00:00"
  },
  "P3658": {
    "problem_number": 3658,
    "slug": "square-sum-avoiding-permutations-thirty",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:08+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3702": {
    "problem_number": 3702,
    "slug": "t-tetromino-twelve-square-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:20+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P10182": {
    "problem_number": 10182,
    "slug": "open-fc-7bbf9ddad08b7220daa1-count-words-in-x-is-a-shifted",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:37+00:00",
    "updated_at": "2026-08-18T02:51:38+00:00"
  },
  "P8750": {
    "problem_number": 8750,
    "slug": "open-fc-5720a49e23b87c9b5585-erdos-592",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:17+00:00",
    "updated_at": "2026-08-17T19:13:29+00:00"
  },
  "P3562": {
    "problem_number": 3562,
    "slug": "connes-rigidity-conjecture",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:51:23+00:00",
    "updated_at": "2026-08-18T06:09:33+00:00"
  },
  "P11710": {
    "problem_number": 11710,
    "slug": "counting-distinct-parenthesized-powers-of-omega",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:42+00:00",
    "updated_at": "2026-08-30T11:16:49+00:00"
  },
  "P12269": {
    "problem_number": 12269,
    "slug": "counting-maximal-2-dense-blocks-of-divisors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:32:15+00:00",
    "updated_at": "2026-09-01T19:32:20+00:00"
  },
  "P12199": {
    "problem_number": 12199,
    "slug": "counting-products-of-two-triangular-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:23:35+00:00",
    "updated_at": "2026-09-01T19:23:40+00:00"
  },
  "P9398": {
    "problem_number": 9398,
    "slug": "open-fc-48a740efeb73b049c116-green-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:16+00:00",
    "updated_at": "2026-08-17T19:52:17+00:00"
  },
  "P12257": {
    "problem_number": 12257,
    "slug": "counting-seidel-permutations-by-genocchi-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:30:44+00:00",
    "updated_at": "2026-09-01T19:30:51+00:00"
  },
  "P3688": {
    "problem_number": 3688,
    "slug": "seven-disks-cover-regular-hexagon",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11865": {
    "problem_number": 11865,
    "slug": "coverage-by-a-prime-factor-symmetric-difference-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:02+00:00",
    "updated_at": "2026-08-30T16:16:08+00:00"
  },
  "P11859": {
    "problem_number": 11859,
    "slug": "coverage-by-the-cumulative-digit-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:34+00:00",
    "updated_at": "2026-08-30T16:15:39+00:00"
  },
  "P11863": {
    "problem_number": 11863,
    "slug": "coverage-by-the-unused-radical-edge-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:52+00:00",
    "updated_at": "2026-08-30T16:15:58+00:00"
  },
  "P12277": {
    "problem_number": 12277,
    "slug": "coverage-of-the-nested-prime-factor-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:33:13+00:00",
    "updated_at": "2026-09-01T19:33:19+00:00"
  },
  "P12639": {
    "problem_number": 12639,
    "slug": "coverage-of-the-novelty-and-divisor-recurrence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:02+00:00",
    "updated_at": "2026-09-02T22:07:07+00:00"
  },
  "P12303": {
    "problem_number": 12303,
    "slug": "coverage-of-the-novelty-and-divisors-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:36:23+00:00",
    "updated_at": "2026-09-01T19:36:28+00:00"
  },
  "P8736": {
    "problem_number": 8736,
    "slug": "open-fc-4979b52c025120d7057c-green-39",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:01+00:00",
    "updated_at": "2026-08-17T19:12:15+00:00"
  },
  "P9844": {
    "problem_number": 9844,
    "slug": "open-fc-3e05077ff1d369bfff23-erdos-689",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:44+00:00",
    "updated_at": "2026-08-17T20:03:53+00:00"
  },
  "P8348": {
    "problem_number": 8348,
    "slug": "open-fc-22ae66e0d6a675e91878-erdos-184-variants-covering",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:13+00:00",
    "updated_at": "2026-08-17T18:40:14+00:00"
  },
  "P2794": {
    "problem_number": 2794,
    "slug": "reed-muller-rm2-8-covering-radius",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:05+00:00",
    "updated_at": "2026-07-30T02:27:19+00:00"
  },
  "P8396": {
    "problem_number": 8396,
    "slug": "open-fc-289fab1bbea36832d7e8-erdos-509",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:17+00:00",
    "updated_at": "2026-08-17T18:49:20+00:00"
  },
  "P9530": {
    "problem_number": 9530,
    "slug": "open-fc-afb9a6b0155bd0cab4a6-erdos-273",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:40+00:00",
    "updated_at": "2026-08-17T19:54:40+00:00"
  },
  "P8284": {
    "problem_number": 8284,
    "slug": "open-fc-1c3d0830fb047874ec2d-rectangles-cover-unit-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:16+00:00",
    "updated_at": "2026-08-17T18:38:17+00:00"
  },
  "P32": {
    "problem_number": 32,
    "slug": "cramers-prime-gap-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:35:17+00:00"
  },
  "P8810": {
    "problem_number": 8810,
    "slug": "open-fc-9258ccc1cd21e2dc4fd8-erdos-942",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:23:24+00:00",
    "updated_at": "2026-08-17T19:35:05+00:00"
  },
  "P12571": {
    "problem_number": 12571,
    "slug": "cubefree-abundant-minima",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:50:06+00:00",
    "updated_at": "2026-09-02T21:50:33+00:00"
  },
  "P11736": {
    "problem_number": 11736,
    "slug": "cubic-supercongruences-from-a-weighted-partition-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:27:11+00:00",
    "updated_at": "2026-08-30T11:30:22+00:00"
  },
  "P11941": {
    "problem_number": 11941,
    "slug": "cutoff-bounds-for-the-least-split-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:31:28+00:00",
    "updated_at": "2026-08-30T16:31:47+00:00"
  },
  "P3062": {
    "problem_number": 3062,
    "slug": "cycle-double-cover-conjecture",
    "resolution_state": "proved_formally",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": true,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "verified",
        "verified": true,
        "kernelAccepted": true,
        "label": "Lean-verified",
        "reason": "A current formalization has a pinned Lean world, a signed accepted verifier result, and an exact binding to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A signed Lean verification is attached.",
      "summary": "Resolved. Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:39+00:00",
    "updated_at": "2026-08-03T06:10:17+00:00"
  },
  "P11911": {
    "problem_number": 11911,
    "slug": "cycle-or-bi-infinite-orbit-through-6-in-the-prime-signature-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:22:13+00:00",
    "updated_at": "2026-08-30T16:22:22+00:00"
  },
  "P8326": {
    "problem_number": 8326,
    "slug": "open-fc-207eae179a82c9577e36-degiorgi-le-eight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:42+00:00",
    "updated_at": "2026-08-17T18:39:46+00:00"
  },
  "P8628": {
    "problem_number": 8628,
    "slug": "open-fc-41ab3536d32b2f145684-degiorgi-seven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:43+00:00",
    "updated_at": "2026-08-17T18:58:48+00:00"
  },
  "P8852": {
    "problem_number": 8852,
    "slug": "open-fc-b082946c719c710e8935-degiorgi-eight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:37+00:00",
    "updated_at": "2026-08-17T19:26:49+00:00"
  },
  "P9952": {
    "problem_number": 9952,
    "slug": "open-fc-989d4ce716a4f345f95d-degiorgi-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:52+00:00",
    "updated_at": "2026-08-17T20:04:53+00:00"
  },
  "P8320": {
    "problem_number": 8320,
    "slug": "open-fc-1f8090ac55edfdb5059f-degiorgi-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:35+00:00",
    "updated_at": "2026-08-17T18:39:38+00:00"
  },
  "P8640": {
    "problem_number": 8640,
    "slug": "open-fc-483a69e8e040b51f7dea-degiorgi-six",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:59+00:00",
    "updated_at": "2026-08-17T18:58:59+00:00"
  },
  "P9776": {
    "problem_number": 9776,
    "slug": "open-fc-cb2ca7c55827282beaaf-erdos-779",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:33+00:00",
    "updated_at": "2026-08-17T20:02:34+00:00"
  },
  "P3158": {
    "problem_number": 3158,
    "slug": "erdos-problem-779",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:42:12+00:00",
    "updated_at": "2026-08-12T05:43:26+00:00"
  },
  "P3116": {
    "problem_number": 3116,
    "slug": "linear-recurrence-positivity-decidability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:04+00:00",
    "updated_at": "2026-08-02T12:52:12+00:00"
  },
  "P3102": {
    "problem_number": 3102,
    "slug": "fp-laurent-series-theory-decidability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:01+00:00",
    "updated_at": "2026-08-02T12:50:21+00:00"
  },
  "P3134": {
    "problem_number": 3134,
    "slug": "real-exponential-field-decidability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:08+00:00",
    "updated_at": "2026-08-02T12:55:00+00:00"
  },
  "P2836": {
    "problem_number": 2836,
    "slug": "skolem-problem-decidability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:06+00:00",
    "updated_at": "2026-07-30T00:55:11+00:00"
  },
  "P3452": {
    "problem_number": 3452,
    "slug": "kourovka-21-69-deciding-hyperbolicity-for-one-relator-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:22+00:00",
    "updated_at": "2026-08-12T08:05:27+00:00"
  },
  "P4272": {
    "problem_number": 4272,
    "slug": "degree-diameter-maximum-3-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:28+00:00",
    "updated_at": "2026-08-16T02:02:33+00:00"
  },
  "P4274": {
    "problem_number": 4274,
    "slug": "degree-diameter-maximum-3-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:29+00:00",
    "updated_at": "2026-08-16T02:02:33+00:00"
  },
  "P4276": {
    "problem_number": 4276,
    "slug": "degree-diameter-maximum-3-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:29+00:00",
    "updated_at": "2026-08-16T02:02:33+00:00"
  },
  "P4278": {
    "problem_number": 4278,
    "slug": "degree-diameter-maximum-3-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:30+00:00",
    "updated_at": "2026-08-16T02:02:33+00:00"
  },
  "P4280": {
    "problem_number": 4280,
    "slug": "degree-diameter-maximum-3-14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:31+00:00",
    "updated_at": "2026-08-16T02:02:34+00:00"
  },
  "P4282": {
    "problem_number": 4282,
    "slug": "degree-diameter-maximum-3-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:34+00:00",
    "updated_at": "2026-08-16T02:02:34+00:00"
  },
  "P4284": {
    "problem_number": 4284,
    "slug": "degree-diameter-maximum-3-16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:35+00:00",
    "updated_at": "2026-08-16T02:02:34+00:00"
  },
  "P4286": {
    "problem_number": 4286,
    "slug": "degree-diameter-maximum-3-17",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:38+00:00",
    "updated_at": "2026-08-16T02:02:34+00:00"
  },
  "P4268": {
    "problem_number": 4268,
    "slug": "degree-diameter-maximum-3-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:25+00:00",
    "updated_at": "2026-08-16T02:02:35+00:00"
  },
  "P4270": {
    "problem_number": 4270,
    "slug": "degree-diameter-maximum-3-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:26+00:00",
    "updated_at": "2026-08-16T02:02:35+00:00"
  },
  "P4292": {
    "problem_number": 4292,
    "slug": "degree-diameter-maximum-4-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:31:31+00:00",
    "updated_at": "2026-08-16T02:02:35+00:00"
  },
  "P4294": {
    "problem_number": 4294,
    "slug": "degree-diameter-maximum-4-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:32:04+00:00",
    "updated_at": "2026-08-16T02:02:35+00:00"
  },
  "P4296": {
    "problem_number": 4296,
    "slug": "degree-diameter-maximum-4-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:32:32+00:00",
    "updated_at": "2026-08-16T02:02:35+00:00"
  },
  "P4298": {
    "problem_number": 4298,
    "slug": "degree-diameter-maximum-4-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:32:41+00:00",
    "updated_at": "2026-08-16T02:02:36+00:00"
  },
  "P4300": {
    "problem_number": 4300,
    "slug": "degree-diameter-maximum-4-14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:32:44+00:00",
    "updated_at": "2026-08-16T02:02:36+00:00"
  },
  "P4302": {
    "problem_number": 4302,
    "slug": "degree-diameter-maximum-4-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:32:53+00:00",
    "updated_at": "2026-08-16T02:02:37+00:00"
  },
  "P4304": {
    "problem_number": 4304,
    "slug": "degree-diameter-maximum-4-16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:33:04+00:00",
    "updated_at": "2026-08-16T02:02:37+00:00"
  },
  "P4306": {
    "problem_number": 4306,
    "slug": "degree-diameter-maximum-4-17",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:33:06+00:00",
    "updated_at": "2026-08-16T02:02:38+00:00"
  },
  "P4288": {
    "problem_number": 4288,
    "slug": "degree-diameter-maximum-4-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:49+00:00",
    "updated_at": "2026-08-16T02:02:38+00:00"
  },
  "P4290": {
    "problem_number": 4290,
    "slug": "degree-diameter-maximum-4-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:31:04+00:00",
    "updated_at": "2026-08-16T02:02:39+00:00"
  },
  "P8944": {
    "problem_number": 8944,
    "slug": "open-fc-f4470795cf2ee68d527d-conjecture133",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:07+00:00",
    "updated_at": "2026-08-17T19:41:09+00:00"
  },
  "P11995": {
    "problem_number": 11995,
    "slug": "denominator-descent-under-approximate-squaring",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:31:53+00:00",
    "updated_at": "2026-09-01T18:32:34+00:00"
  },
  "P9712": {
    "problem_number": 9712,
    "slug": "open-fc-9afaee7149ae8dc3b8e9-erdos-212",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:01+00:00",
    "updated_at": "2026-08-17T20:02:02+00:00"
  },
  "P3426": {
    "problem_number": 3426,
    "slug": "kourovka-21-44-dense-subgroups-of-iterated-alternating-wreath-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:59:41+00:00",
    "updated_at": "2026-08-12T07:59:49+00:00"
  },
  "P2654": {
    "problem_number": 2654,
    "slug": "weight-five-cyclic-inverse-127",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:01+00:00",
    "updated_at": "2026-08-01T02:26:55+00:00"
  },
  "P12713": {
    "problem_number": 12713,
    "slug": "density-of-exponents-with-square-divisible-2-k-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:26:34+00:00",
    "updated_at": "2026-09-02T22:26:58+00:00"
  },
  "P8660": {
    "problem_number": 8660,
    "slug": "open-fc-90d806870ec8efb91dc2-density-of-hyperbolicity-general-exponent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:00:04+00:00",
    "updated_at": "2026-08-17T20:01:54+00:00"
  },
  "P9032": {
    "problem_number": 9032,
    "slug": "open-fc-929e433b26e3982c47d3-density-of-hyperbolicity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:38+00:00",
    "updated_at": "2026-08-17T19:45:40+00:00"
  },
  "P8996": {
    "problem_number": 8996,
    "slug": "open-fc-772e03cfd983b2eaf072-erdos-357-variants-infinite-set-density",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:36+00:00",
    "updated_at": "2026-08-17T19:44:38+00:00"
  },
  "P9122": {
    "problem_number": 9122,
    "slug": "open-fc-d782f415446d103e07ab-erdos-371",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:42+00:00",
    "updated_at": "2026-08-17T19:47:42+00:00"
  },
  "P3216": {
    "problem_number": 3216,
    "slug": "erdos-problem-1201",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:53:12+00:00",
    "updated_at": "2026-08-12T05:53:17+00:00"
  },
  "P9130": {
    "problem_number": 9130,
    "slug": "open-fc-df4de80590e051bd1224-erdos-291-variants-shiu-heuristic-density-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:44+00:00",
    "updated_at": "2026-08-17T19:47:44+00:00"
  },
  "P9324": {
    "problem_number": 9324,
    "slug": "open-fc-cc9fbb867a3d90477782-erdos-409-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:54+00:00",
    "updated_at": "2026-08-17T19:50:54+00:00"
  },
  "P9448": {
    "problem_number": 9448,
    "slug": "open-fc-72f280ad42c1238d9309-artin-primitive-roots-variants-part-ii-power-squarefreepart-not-modeq-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:38+00:00",
    "updated_at": "2026-08-17T19:53:40+00:00"
  },
  "P8818": {
    "problem_number": 8818,
    "slug": "open-fc-9b4b6d624f3fac6db321-artin-primitive-roots-variants-part-ii-power-squarefreepart-modeq-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:21+00:00",
    "updated_at": "2026-08-17T19:24:29+00:00"
  },
  "P9480": {
    "problem_number": 9480,
    "slug": "open-fc-8ad42082394f3b34131d-erdos-940-variants-three-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:08+00:00",
    "updated_at": "2026-08-17T19:54:10+00:00"
  },
  "P3266": {
    "problem_number": 3266,
    "slug": "erdos-problem-488",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:59:45+00:00",
    "updated_at": "2026-08-12T05:59:47+00:00"
  },
  "P8526": {
    "problem_number": 8526,
    "slug": "open-fc-63fb8f53b91ebf97325a-erdos-488",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:12+00:00",
    "updated_at": "2026-08-17T18:54:13+00:00"
  },
  "P9636": {
    "problem_number": 9636,
    "slug": "open-fc-350e17b3288680ef27f4-green-51-one-half",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:06+00:00",
    "updated_at": "2026-08-17T20:00:11+00:00"
  },
  "P8532": {
    "problem_number": 8532,
    "slug": "open-fc-66fac3ee48d86572027b-erdos-340-variants-co-density-zero-sub",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:19+00:00",
    "updated_at": "2026-08-17T18:54:19+00:00"
  },
  "P3490": {
    "problem_number": 3490,
    "slug": "kourovka-21-109-derived-length-from-character-degree-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:07:13+00:00",
    "updated_at": "2026-08-12T08:07:20+00:00"
  },
  "P2": {
    "problem_number": 2,
    "slug": "fib-problem-determinant-range",
    "resolution_state": "proved_formally",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": true,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "verified",
        "verified": true,
        "kernelAccepted": true,
        "label": "Lean-verified",
        "reason": "A current formalization has a pinned Lean world, a signed accepted verifier result, and an exact binding to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A signed Lean verification is attached.",
      "summary": "Resolved. Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T00:55:55+00:00",
    "updated_at": "2026-07-22T00:55:55+00:00"
  },
  "P12375": {
    "problem_number": 12375,
    "slug": "determine-the-unknown-values-of-waring-s-g-k",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:45:08+00:00",
    "updated_at": "2026-09-01T19:45:14+00:00"
  },
  "P9726": {
    "problem_number": 9726,
    "slug": "open-fc-a512c5cad6ba924aeb78-dickson-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:05+00:00",
    "updated_at": "2026-08-17T20:02:07+00:00"
  },
  "P2636": {
    "problem_number": 2636,
    "slug": "difference-basis-z127",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:54+00:00",
    "updated_at": "2026-08-01T23:24:10+00:00"
  },
  "P12467": {
    "problem_number": 12467,
    "slug": "digit-counts-of-partition-numbers-at-perfect-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:38:47+00:00",
    "updated_at": "2026-09-02T21:38:59+00:00"
  },
  "P12559": {
    "problem_number": 12559,
    "slug": "digit-sums-after-a-base-nine-substring-appears",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:48:48+00:00",
    "updated_at": "2026-09-02T21:48:54+00:00"
  },
  "P12539": {
    "problem_number": 12539,
    "slug": "digit-length-rises-in-binomials-of-consecutive-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:46:01+00:00",
    "updated_at": "2026-09-02T21:46:13+00:00"
  },
  "P11584": {
    "problem_number": 11584,
    "slug": "digital-root-divisibility-of-odd-perfect-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:35:52+00:00",
    "updated_at": "2026-08-30T04:35:57+00:00"
  },
  "P9258": {
    "problem_number": 9258,
    "slug": "open-fc-9ac2d267a3156f397daf-erdos-944-variants-dirac-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:27+00:00",
    "updated_at": "2026-08-17T19:50:27+00:00"
  },
  "P3742": {
    "problem_number": 3742,
    "slug": "debruijn-seven-directed-geography",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:50:58+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8256": {
    "problem_number": 8256,
    "slug": "open-fc-17c67bb6b96f36347073-discretetopology-of-t2-of-torontospace",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:48+00:00",
    "updated_at": "2026-08-17T18:37:50+00:00"
  },
  "P3486": {
    "problem_number": 3486,
    "slug": "kourovka-21-107-disjoint-folner-sequences-in-topological-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:57+00:00",
    "updated_at": "2026-08-12T08:07:01+00:00"
  },
  "P3362": {
    "problem_number": 3362,
    "slug": "kourovka-21-3-disjoint-soluble-subgroups-in-symmetric-and-alternating-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:41:00+00:00",
    "updated_at": "2026-08-12T07:42:00+00:00"
  },
  "P3766": {
    "problem_number": 3766,
    "slug": "tree-ten-distance-query-reconstruction",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:52:03+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12515": {
    "problem_number": 12515,
    "slug": "distances-between-twin-prime-gaps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:43:35+00:00",
    "updated_at": "2026-09-02T21:43:42+00:00"
  },
  "P12227": {
    "problem_number": 12227,
    "slug": "distinct-carryless-quotients-in-each-row",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:27:02+00:00",
    "updated_at": "2026-09-01T19:27:08+00:00"
  },
  "P8204": {
    "problem_number": 8204,
    "slug": "open-fc-0e1b83c19e2d08f0db03-erdos-1004",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:04+00:00",
    "updated_at": "2026-08-17T18:37:07+00:00"
  },
  "P3308": {
    "problem_number": 3308,
    "slug": "erdos-problem-1082",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:25+00:00",
    "updated_at": "2026-08-12T06:04:26+00:00"
  },
  "P12743": {
    "problem_number": 12743,
    "slug": "distinct-fractional-parts-of-reciprocal-prime-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:38:53+00:00",
    "updated_at": "2026-09-02T22:39:26+00:00"
  },
  "P11754": {
    "problem_number": 11754,
    "slug": "distinct-fractional-parts-of-reciprocal-totient-interval-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:22:54+00:00",
    "updated_at": "2026-08-30T12:23:02+00:00"
  },
  "P8968": {
    "problem_number": 8968,
    "slug": "open-fc-5e4d9b6888f259a78c3c-erdos-324",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:43:56+00:00",
    "updated_at": "2026-08-17T19:43:58+00:00"
  },
  "P9954": {
    "problem_number": 9954,
    "slug": "open-fc-9988a803ed24becb7dcd-erdos-375",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:53+00:00",
    "updated_at": "2026-08-17T20:04:53+00:00"
  },
  "P3220": {
    "problem_number": 3220,
    "slug": "erdos-problem-375",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:54:23+00:00",
    "updated_at": "2026-08-12T05:54:24+00:00"
  },
  "P11744": {
    "problem_number": 11744,
    "slug": "distinct-smaller-factorials-and-jordan-polya-membership",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:35:54+00:00",
    "updated_at": "2026-08-30T11:38:05+00:00"
  },
  "P8466": {
    "problem_number": 8466,
    "slug": "open-fc-44149f759dd72c9a9c95-erdos-421",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:13+00:00",
    "updated_at": "2026-08-17T18:52:13+00:00"
  },
  "P3348": {
    "problem_number": 3348,
    "slug": "erdos-problem-421",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:08:08+00:00",
    "updated_at": "2026-08-12T06:08:14+00:00"
  },
  "P9264": {
    "problem_number": 9264,
    "slug": "open-fc-9e7ec2fe7f53af8d0112-erdos-324-variants-quintic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:29+00:00",
    "updated_at": "2026-08-17T19:50:29+00:00"
  },
  "P3550": {
    "problem_number": 3550,
    "slug": "kourovka-21-148-distributive-lattices-of-right-relatively-convex-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:14:47+00:00",
    "updated_at": "2026-08-12T08:15:02+00:00"
  },
  "P3252": {
    "problem_number": 3252,
    "slug": "erdos-problem-410",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:07+00:00",
    "updated_at": "2026-08-12T05:58:15+00:00"
  },
  "P8462": {
    "problem_number": 8462,
    "slug": "open-fc-41f6d494410301eb14f1-erdos-410",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:12+00:00",
    "updated_at": "2026-08-17T18:52:12+00:00"
  },
  "P12049": {
    "problem_number": 12049,
    "slug": "divisibility-in-partitions-into-pairs-and-triples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:57:11+00:00",
    "updated_at": "2026-09-01T18:57:21+00:00"
  },
  "P9126": {
    "problem_number": 9126,
    "slug": "open-fc-daf045ac9f5b1bddc4ae-erdos-389",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:43+00:00",
    "updated_at": "2026-08-17T19:47:43+00:00"
  },
  "P12517": {
    "problem_number": 12517,
    "slug": "divisibility-of-mobius-binomial-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:43:42+00:00",
    "updated_at": "2026-09-02T21:43:54+00:00"
  },
  "P12625": {
    "problem_number": 12625,
    "slug": "divisibility-of-starts-of-constant-totient-progressions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:59:24+00:00",
    "updated_at": "2026-09-02T21:59:31+00:00"
  },
  "P8888": {
    "problem_number": 8888,
    "slug": "open-fc-c980ee049a927182bdd9-erdos-396",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:26+00:00",
    "updated_at": "2026-08-17T19:36:30+00:00"
  },
  "P12599": {
    "problem_number": 12599,
    "slug": "do-all-digit-product-orbits-merge-with-the-seed-1-orbit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:54:48+00:00",
    "updated_at": "2026-09-02T21:55:25+00:00"
  },
  "P12607": {
    "problem_number": 12607,
    "slug": "do-all-even-prime-gaps-recur-around-twice-a-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:56:47+00:00",
    "updated_at": "2026-09-02T21:56:54+00:00"
  },
  "P12697": {
    "problem_number": 12697,
    "slug": "do-all-giuga-numbers-satisfy-n-n-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:19:49+00:00",
    "updated_at": "2026-09-02T22:20:16+00:00"
  },
  "P12779": {
    "problem_number": 12779,
    "slug": "do-all-parity-controlled-fibonacci-orbits-have-logarithmic-growth-1-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:55:26+00:00",
    "updated_at": "2026-09-02T22:55:54+00:00"
  },
  "P11212": {
    "problem_number": 11212,
    "slug": "half-frequency-in-square-runlength-fixed-point",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:52:22+00:00",
    "updated_at": "2026-08-29T18:49:15+00:00"
  },
  "P12703": {
    "problem_number": 12703,
    "slug": "do-circle-cut-lattice-grids-supply-almost-all-square-maximizing-point-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:22:06+00:00",
    "updated_at": "2026-09-02T22:22:37+00:00"
  },
  "P12673": {
    "problem_number": 12673,
    "slug": "do-even-faced-dissections-equal-nonnegative-even-drop-path-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:10:57+00:00",
    "updated_at": "2026-09-02T22:11:02+00:00"
  },
  "P11440": {
    "problem_number": 11440,
    "slug": "fibonacci-lcms-avoid-consecutive-residues",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:00:50+00:00",
    "updated_at": "2026-08-29T18:52:59+00:00"
  },
  "P11330": {
    "problem_number": 11330,
    "slug": "complementary-subset-euclid-mullin-prefix-permutations-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:24:56+00:00",
    "updated_at": "2026-08-29T18:51:22+00:00"
  },
  "P11218": {
    "problem_number": 11218,
    "slug": "cyclic-zero-sum-free-four-constructions-exactness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:53:39+00:00",
    "updated_at": "2026-08-29T18:49:20+00:00"
  },
  "P11432": {
    "problem_number": 11432,
    "slug": "folding-numbers-additive-basis-order-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:58:11+00:00",
    "updated_at": "2026-08-29T18:52:53+00:00"
  },
  "P11790": {
    "problem_number": 11790,
    "slug": "do-four-omega-classes-remain-the-most-frequent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:44:26+00:00",
    "updated_at": "2026-08-30T12:44:35+00:00"
  },
  "P12361": {
    "problem_number": 12361,
    "slug": "do-goldbach-representation-counts-eventually-exceed-every-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:43:22+00:00",
    "updated_at": "2026-09-01T19:43:29+00:00"
  },
  "P11400": {
    "problem_number": 11400,
    "slug": "primes-dividing-concatenated-successor-primes-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:48:44+00:00",
    "updated_at": "2026-08-29T18:52:29+00:00"
  },
  "P11466": {
    "problem_number": 11466,
    "slug": "infinitely-many-primorial-least-factor-cycles",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:11:43+00:00",
    "updated_at": "2026-08-29T18:53:31+00:00"
  },
  "P12687": {
    "problem_number": 12687,
    "slug": "do-minimal-triangular-digit-containers-avoid-extra-digits-except-at-n-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:15:19+00:00",
    "updated_at": "2026-09-02T22:15:55+00:00"
  },
  "P3126": {
    "problem_number": 3126,
    "slug": "one-way-functions-exist",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:06+00:00",
    "updated_at": "2026-08-02T12:53:54+00:00"
  },
  "P12267": {
    "problem_number": 12267,
    "slug": "do-only-eleven-primes-enter-a-greedy-sequence-through-triple-multiples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:31:59+00:00",
    "updated_at": "2026-09-01T19:32:06+00:00"
  },
  "P11244": {
    "problem_number": 11244,
    "slug": "prime-gap-local-extrema-arbitrary-zigzags",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:02:55+00:00",
    "updated_at": "2026-08-29T18:49:48+00:00"
  },
  "P11482": {
    "problem_number": 11482,
    "slug": "prime-order-in-asymmetric-semicoprime-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:19:56+00:00",
    "updated_at": "2026-08-29T18:53:44+00:00"
  },
  "P11278": {
    "problem_number": 11278,
    "slug": "positive-density-of-primes-with-mobius-p-minus-one-positive",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:15:41+00:00",
    "updated_at": "2026-08-29T18:50:23+00:00"
  },
  "P12719": {
    "problem_number": 12719,
    "slug": "do-primorial-signatures-set-every-new-factorization-record",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:29:45+00:00",
    "updated_at": "2026-09-02T22:30:12+00:00"
  },
  "P11306": {
    "problem_number": 11306,
    "slug": "quaternary-rooted-identity-tree-universal-law",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:12:41+00:00",
    "updated_at": "2026-08-29T18:50:55+00:00"
  },
  "P11993": {
    "problem_number": 11993,
    "slug": "do-reverse-digits-plus-four-orbits-always-enter-a-cycle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:30:57+00:00",
    "updated_at": "2026-09-01T18:31:31+00:00"
  },
  "P12785": {
    "problem_number": 12785,
    "slug": "do-scaled-recaman-partial-sums-converge-near-0-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T23:07:13+00:00",
    "updated_at": "2026-09-02T23:07:46+00:00"
  },
  "P12731": {
    "problem_number": 12731,
    "slug": "do-solenoidal-flow-counts-give-first-occurrences-of-odd-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:33:26+00:00",
    "updated_at": "2026-09-02T22:34:08+00:00"
  },
  "P11268": {
    "problem_number": 11268,
    "slug": "square-root-consecutive-prime-gaps-tend-to-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:10:46+00:00",
    "updated_at": "2026-08-29T18:50:15+00:00"
  },
  "P12757": {
    "problem_number": 12757,
    "slug": "do-squarefree-a068991-terms-divide-their-bernoulli-denominators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:45:05+00:00",
    "updated_at": "2026-09-02T22:45:47+00:00"
  },
  "P12725": {
    "problem_number": 12725,
    "slug": "do-stirling-transform-residues-have-period-dividing-euler-s-totient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:31:27+00:00",
    "updated_at": "2026-09-02T22:43:41+00:00"
  },
  "P11304": {
    "problem_number": 11304,
    "slug": "universal-law-for-ternary-rooted-identity-trees",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:11:23+00:00",
    "updated_at": "2026-08-29T18:50:53+00:00"
  },
  "P11442": {
    "problem_number": 11442,
    "slug": "slater-velez-differences-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:01:14+00:00",
    "updated_at": "2026-08-29T18:53:02+00:00"
  },
  "P11502": {
    "problem_number": 11502,
    "slug": "even-class-number-maxima-mod-24",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:31:55+00:00",
    "updated_at": "2026-08-29T18:53:58+00:00"
  },
  "P11284": {
    "problem_number": 11284,
    "slug": "exact-even-consecutive-prime-gap-runs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:17:51+00:00",
    "updated_at": "2026-08-29T18:50:30+00:00"
  },
  "P12661": {
    "problem_number": 12661,
    "slug": "do-the-jacobsthal-and-mersenne-tests-select-the-same-composites",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:09:31+00:00",
    "updated_at": "2026-09-02T22:09:36+00:00"
  },
  "P12773": {
    "problem_number": 12773,
    "slug": "do-the-lagarias-based-integer-values-eventually-become-pairwise-distinct",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:52:41+00:00",
    "updated_at": "2026-09-02T22:53:13+00:00"
  },
  "P11506": {
    "problem_number": 11506,
    "slug": "least-factorial-divisor-count-chain",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:35:08+00:00",
    "updated_at": "2026-08-29T18:54:01+00:00"
  },
  "P12055": {
    "problem_number": 12055,
    "slug": "do-the-sigma-trajectories-of-2-and-5-ever-merge",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:58:18+00:00",
    "updated_at": "2026-09-01T18:58:31+00:00"
  },
  "P11220": {
    "problem_number": 11220,
    "slug": "alternating-prime-parity-lead-changes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:54:04+00:00",
    "updated_at": "2026-08-29T18:49:22+00:00"
  },
  "P11478": {
    "problem_number": 11478,
    "slug": "equal-fibers-for-two-arithmetic-invariant-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:18:11+00:00",
    "updated_at": "2026-08-29T18:53:40+00:00"
  },
  "P11867": {
    "problem_number": 11867,
    "slug": "does-13-occur-in-the-last-index-recaman-variant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:12+00:00",
    "updated_at": "2026-08-30T16:16:16+00:00"
  },
  "P11242": {
    "problem_number": 11242,
    "slug": "two-prime-factor-test-for-two-to-1048592-plus-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:02:31+00:00",
    "updated_at": "2026-08-29T18:49:46+00:00"
  },
  "P11957": {
    "problem_number": 11957,
    "slug": "does-387-occur-in-the-self-describing-digit-sum-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:53:23+00:00",
    "updated_at": "2026-08-31T03:53:26+00:00"
  },
  "P11638": {
    "problem_number": 11638,
    "slug": "does-5-occur-in-the-prime-modulus-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:42:06+00:00",
    "updated_at": "2026-08-30T04:42:15+00:00"
  },
  "P11676": {
    "problem_number": 11676,
    "slug": "does-6-appear-in-the-sydney-opera-house-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:06:33+00:00",
    "updated_at": "2026-08-30T11:09:05+00:00"
  },
  "P11404": {
    "problem_number": 11404,
    "slug": "common-carmichael-lucas-carmichael-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:49:37+00:00",
    "updated_at": "2026-08-29T18:52:34+00:00"
  },
  "P11528": {
    "problem_number": 11528,
    "slug": "semiprime-five-power-minus-four-power-forces-prime-exponent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:47:38+00:00",
    "updated_at": "2026-08-29T18:54:18+00:00"
  },
  "P11350": {
    "problem_number": 11350,
    "slug": "shifted-prime-factorial-as-bhargava-factorial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:33:11+00:00",
    "updated_at": "2026-08-29T18:51:40+00:00"
  },
  "P11188": {
    "problem_number": 11188,
    "slug": "existence-of-a-sixth-unitary-perfect-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:47:01+00:00",
    "updated_at": "2026-08-29T18:48:52+00:00"
  },
  "P12735": {
    "problem_number": 12735,
    "slug": "does-a-n-n-2-have-a-limit-superior-strictly-between-0-and-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:35:37+00:00",
    "updated_at": "2026-09-02T22:36:14+00:00"
  },
  "P12669": {
    "problem_number": 12669,
    "slug": "does-a066820-produce-infinitely-many-odd-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:10:05+00:00",
    "updated_at": "2026-09-02T22:10:40+00:00"
  },
  "P11430": {
    "problem_number": 11430,
    "slug": "arithmetic-derivative-reaches-primorial-exp",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:57:46+00:00",
    "updated_at": "2026-08-29T18:52:52+00:00"
  },
  "P11448": {
    "problem_number": 11448,
    "slug": "rapid-recurrence-consecutive-divisibility",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:03:20+00:00",
    "updated_at": "2026-08-29T18:53:11+00:00"
  },
  "P11474": {
    "problem_number": 11474,
    "slug": "totality-of-the-a349876-residue-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:16:26+00:00",
    "updated_at": "2026-08-29T18:53:37+00:00"
  },
  "P12659": {
    "problem_number": 12659,
    "slug": "does-every-alternating-phi-sigma-orbit-become-periodic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:09:19+00:00",
    "updated_at": "2026-09-02T22:09:24+00:00"
  },
  "P11512": {
    "problem_number": 11512,
    "slug": "binary-complement-times-three-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:38:31+00:00",
    "updated_at": "2026-08-29T18:54:06+00:00"
  },
  "P11702": {
    "problem_number": 11702,
    "slug": "does-every-card-reach-the-top-in-guy-s-growing-shuffle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:02+00:00",
    "updated_at": "2026-08-30T11:16:09+00:00"
  },
  "P11358": {
    "problem_number": 11358,
    "slug": "clockwise-gaussian-prime-spirals-all-close",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:35:52+00:00",
    "updated_at": "2026-08-29T18:51:46+00:00"
  },
  "P11510": {
    "problem_number": 11510,
    "slug": "hamming-unused-permutation-finite-cycles",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:36:55+00:00",
    "updated_at": "2026-08-29T18:54:04+00:00"
  },
  "P11280": {
    "problem_number": 11280,
    "slug": "prime-suffix-for-every-decimal-prefix",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:17:00+00:00",
    "updated_at": "2026-08-29T18:50:25+00:00"
  },
  "P11456": {
    "problem_number": 11456,
    "slug": "eventual-periodicity-of-delete-exponent-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:07:40+00:00",
    "updated_at": "2026-08-29T18:53:21+00:00"
  },
  "P11292": {
    "problem_number": 11292,
    "slug": "digit-square-increment-orbits-reach-a-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:22:14+00:00",
    "updated_at": "2026-08-29T18:50:38+00:00"
  },
  "P11384": {
    "problem_number": 11384,
    "slug": "prime-in-divisor-controlled-strict-interval",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:43:40+00:00",
    "updated_at": "2026-08-29T18:52:08+00:00"
  },
  "P11320": {
    "problem_number": 11320,
    "slug": "prime-in-every-four-x-plus-minus-one-tree-generation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:21:10+00:00",
    "updated_at": "2026-08-29T18:51:09+00:00"
  },
  "P12681": {
    "problem_number": 12681,
    "slug": "does-every-integer-admit-a-prime-descending-power-concatenation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:11:51+00:00",
    "updated_at": "2026-09-02T22:12:39+00:00"
  },
  "P12667": {
    "problem_number": 12667,
    "slug": "does-every-integer-reach-a-prime-after-adding-safe-prime-partial-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:10:00+00:00",
    "updated_at": "2026-09-02T22:10:05+00:00"
  },
  "P11356": {
    "problem_number": 11356,
    "slug": "least-divisor-ratio-numerators-repeat-infinitely",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:35:23+00:00",
    "updated_at": "2026-08-29T18:51:44+00:00"
  },
  "P11204": {
    "problem_number": 11204,
    "slug": "modified-juggler-nearest-integer-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:50:32+00:00",
    "updated_at": "2026-08-29T18:49:07+00:00"
  },
  "P12335": {
    "problem_number": 12335,
    "slug": "does-every-multiplicity-occur-in-a-least-prime-factor-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:40:08+00:00",
    "updated_at": "2026-09-01T19:40:14+00:00"
  },
  "P12365": {
    "problem_number": 12365,
    "slug": "does-every-nonnegative-integer-appear-in-van-eck-s-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:43:53+00:00",
    "updated_at": "2026-09-01T19:43:58+00:00"
  },
  "P12671": {
    "problem_number": 12671,
    "slug": "does-every-nontrivial-primorial-determine-a-unique-pell-discriminant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:10:48+00:00",
    "updated_at": "2026-09-02T22:10:53+00:00"
  },
  "P11476": {
    "problem_number": 11476,
    "slug": "gcd-six-five-x-plus-one-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:16:52+00:00",
    "updated_at": "2026-08-29T18:53:39+00:00"
  },
  "P11626": {
    "problem_number": 11626,
    "slug": "does-every-positive-integer-appear-in-the-divisor-count-avoidance-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:40:28+00:00",
    "updated_at": "2026-08-30T04:40:36+00:00"
  },
  "P11628": {
    "problem_number": 11628,
    "slug": "does-every-positive-integer-appear-in-the-divisor-count-sum-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:40:43+00:00",
    "updated_at": "2026-08-30T04:40:52+00:00"
  },
  "P11554": {
    "problem_number": 11554,
    "slug": "completeness-of-the-mian-chowla-difference-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:03:10+00:00",
    "updated_at": "2026-08-29T18:54:36+00:00"
  },
  "P11989": {
    "problem_number": 11989,
    "slug": "does-every-positive-integer-occur-as-a-simultaneous-coprimality-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:28:57+00:00",
    "updated_at": "2026-09-01T18:29:33+00:00"
  },
  "P11312": {
    "problem_number": 11312,
    "slug": "integer-edge-tetrahedra-for-every-multiple-of-three-volume",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:15:47+00:00",
    "updated_at": "2026-08-29T18:51:01+00:00"
  },
  "P11985": {
    "problem_number": 11985,
    "slug": "does-every-positive-odd-number-occur-in-the-harmonic-denominator-quotient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:28:14+00:00",
    "updated_at": "2026-09-01T18:28:22+00:00"
  },
  "P12013": {
    "problem_number": 12013,
    "slug": "does-every-powertrain-orbit-reach-a-fixed-point",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:49:45+00:00",
    "updated_at": "2026-09-01T18:50:15+00:00"
  },
  "P11424": {
    "problem_number": 11424,
    "slug": "greedy-prime-offset-unique-forbidden-residue",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:54:41+00:00",
    "updated_at": "2026-08-29T18:52:48+00:00"
  },
  "P11366": {
    "problem_number": 11366,
    "slug": "signed-square-greedy-walk-covers-every-square-magnitude",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:39:14+00:00",
    "updated_at": "2026-08-29T18:51:53+00:00"
  },
  "P12787": {
    "problem_number": 12787,
    "slug": "does-every-squarefree-integer-occur-as-a-squarefree-cubefree-rank-gcd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T23:08:53+00:00",
    "updated_at": "2026-09-02T23:09:23+00:00"
  },
  "P12675": {
    "problem_number": 12675,
    "slug": "does-every-triangular-digit-sum-occur-infinitely-often",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:11:07+00:00",
    "updated_at": "2026-09-02T22:11:12+00:00"
  },
  "P12727": {
    "problem_number": 12727,
    "slug": "does-every-triangular-interval-contain-a-number-outside-6xy-x-y",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:32:23+00:00",
    "updated_at": "2026-09-02T22:32:52+00:00"
  },
  "P11386": {
    "problem_number": 11386,
    "slug": "wrecker-ball-rows-all-reach-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:44:05+00:00",
    "updated_at": "2026-08-29T18:52:11+00:00"
  },
  "P12649": {
    "problem_number": 12649,
    "slug": "does-increasing-prime-gap-characterize-strict-prime-log-convexity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:51+00:00",
    "updated_at": "2026-09-02T22:07:56+00:00"
  },
  "P11987": {
    "problem_number": 11987,
    "slug": "does-iterating-the-odd-part-of-the-divisor-sum-always-reach-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:28:34+00:00",
    "updated_at": "2026-09-01T18:28:43+00:00"
  },
  "P11730": {
    "problem_number": 11730,
    "slug": "does-kimberling-s-expulsion-diagonal-contain-every-positive-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:22:15+00:00",
    "updated_at": "2026-08-30T11:23:19+00:00"
  },
  "P12683": {
    "problem_number": 12683,
    "slug": "does-n-2-n-2-1-parametrize-a069187-outside-a049532",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:13:04+00:00",
    "updated_at": "2026-09-02T22:13:49+00:00"
  },
  "P11454": {
    "problem_number": 11454,
    "slug": "permutation-property-of-the-three-prime-sum-window-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:06:22+00:00",
    "updated_at": "2026-08-29T18:53:18+00:00"
  },
  "P11326": {
    "problem_number": 11326,
    "slug": "quet-greedy-sequence-contains-every-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:24:10+00:00",
    "updated_at": "2026-08-29T18:51:17+00:00"
  },
  "P11184": {
    "problem_number": 11184,
    "slug": "radoux-artin-schreier-root-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:46:08+00:00",
    "updated_at": "2026-08-29T18:48:48+00:00"
  },
  "P11724": {
    "problem_number": 11724,
    "slug": "does-recaman-s-sequence-visit-every-nonnegative-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:43+00:00",
    "updated_at": "2026-08-30T11:18:26+00:00"
  },
  "P12357": {
    "problem_number": 12357,
    "slug": "does-reverse-and-add-starting-at-196-reach-a-palindrome",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:42:53+00:00",
    "updated_at": "2026-09-01T19:42:58+00:00"
  },
  "P12579": {
    "problem_number": 12579,
    "slug": "does-sigma-x-n-phi-x-have-a-positive-solution-for-every-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:52:01+00:00",
    "updated_at": "2026-09-02T21:52:07+00:00"
  },
  "P12733": {
    "problem_number": 12733,
    "slug": "does-sopfr-of-consecutive-prime-square-differences-miss-exactly-eight-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:34:33+00:00",
    "updated_at": "2026-09-02T22:35:10+00:00"
  },
  "P12771": {
    "problem_number": 12771,
    "slug": "does-substitution-by-x-2-x-1-preserve-all-ones-irreducibility-exponents",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:51:43+00:00",
    "updated_at": "2026-09-02T22:52:11+00:00"
  },
  "P11939": {
    "problem_number": 11939,
    "slug": "does-the-1373-adjacent-digit-sum-orbit-ever-cycle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:31:05+00:00",
    "updated_at": "2026-08-30T16:31:19+00:00"
  },
  "P12605": {
    "problem_number": 12605,
    "slug": "does-the-a006369-trajectory-from-64-avoid-every-prior-state",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:55:56+00:00",
    "updated_at": "2026-09-02T21:56:34+00:00"
  },
  "P12169": {
    "problem_number": 12169,
    "slug": "does-the-a006369-trajectory-of-40-ever-repeat",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:19:58+00:00",
    "updated_at": "2026-09-01T19:20:05+00:00"
  },
  "P11488": {
    "problem_number": 11488,
    "slug": "surjectivity-of-the-a355483-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:23:12+00:00",
    "updated_at": "2026-08-29T18:53:48+00:00"
  },
  "P11270": {
    "problem_number": 11270,
    "slug": "absolute-three-halves-recurrence-divergence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:11:12+00:00",
    "updated_at": "2026-08-29T18:50:16+00:00"
  },
  "P11224": {
    "problem_number": 11224,
    "slug": "aliquot-orbit-276-fate",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:55:51+00:00",
    "updated_at": "2026-08-29T18:49:27+00:00"
  },
  "P11650": {
    "problem_number": 11650,
    "slug": "does-the-aliquot-divisor-orbit-from-222-enter-a-two-cycle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:50:45+00:00",
    "updated_at": "2026-08-30T04:51:48+00:00"
  },
  "P11622": {
    "problem_number": 11622,
    "slug": "does-the-aliquot-divisor-orbit-from-222-reach-a-fixed-point",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:39:54+00:00",
    "updated_at": "2026-08-30T04:40:02+00:00"
  },
  "P11208": {
    "problem_number": 11208,
    "slug": "alternating-prime-sum-ratio-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:51:29+00:00",
    "updated_at": "2026-08-29T18:49:11+00:00"
  },
  "P11214": {
    "problem_number": 11214,
    "slug": "amusical-orbit-of-eight-repetition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:52:51+00:00",
    "updated_at": "2026-08-29T18:49:16+00:00"
  },
  "P12651": {
    "problem_number": 12651,
    "slug": "does-the-binary-factorization-tree-contain-every-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:56+00:00",
    "updated_at": "2026-09-02T22:08:36+00:00"
  },
  "P11414": {
    "problem_number": 11414,
    "slug": "infinitely-many-same-length-binary-greedy-matches",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:52:42+00:00",
    "updated_at": "2026-08-29T18:52:40+00:00"
  },
  "P11536": {
    "problem_number": 11536,
    "slug": "coprime-zigzag-permutation-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:53:21+00:00",
    "updated_at": "2026-08-29T18:54:23+00:00"
  },
  "P12695": {
    "problem_number": 12695,
    "slug": "does-the-cubic-binomial-congruence-characterize-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:18:53+00:00",
    "updated_at": "2026-09-02T22:19:26+00:00"
  },
  "P12653": {
    "problem_number": 12653,
    "slug": "does-the-digit-sum-recurrence-contain-every-positive-nonmultiple-of-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:08:47+00:00",
    "updated_at": "2026-09-02T22:08:51+00:00"
  },
  "P11460": {
    "problem_number": 11460,
    "slug": "greedy-distinct-exponent-partial-products-infinitely-many-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:08:29+00:00",
    "updated_at": "2026-08-29T18:53:26+00:00"
  },
  "P11630": {
    "problem_number": 11630,
    "slug": "does-the-distinct-visible-sum-spiral-contain-every-positive-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:40:58+00:00",
    "updated_at": "2026-08-30T04:41:05+00:00"
  },
  "P11260": {
    "problem_number": 11260,
    "slug": "approximate-squaring-dyadic-step-ratio-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:07:10+00:00",
    "updated_at": "2026-08-29T18:50:06+00:00"
  },
  "P11352": {
    "problem_number": 11352,
    "slug": "earlier-products-plus-two-greedy-prime-sequence-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:34:29+00:00",
    "updated_at": "2026-08-29T18:51:42+00:00"
  },
  "P12655": {
    "problem_number": 12655,
    "slug": "does-the-fibbinary-least-unused-recurrence-permute-the-positive-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:08:57+00:00",
    "updated_at": "2026-09-02T22:09:02+00:00"
  },
  "P12067": {
    "problem_number": 12067,
    "slug": "does-the-fibbinary-adjacency-greedy-injection-hit-every-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:07:36+00:00",
    "updated_at": "2026-09-01T19:07:42+00:00"
  },
  "P12377": {
    "problem_number": 12377,
    "slug": "does-the-five-thirds-floor-iteration-always-return-to-an-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:45:22+00:00",
    "updated_at": "2026-09-01T19:45:29+00:00"
  },
  "P12685": {
    "problem_number": 12685,
    "slug": "does-the-gcd-with-4-recurrence-diverge",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:14:26+00:00",
    "updated_at": "2026-09-02T22:15:00+00:00"
  },
  "P11262": {
    "problem_number": 11262,
    "slug": "greedy-prime-concatenation-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:07:37+00:00",
    "updated_at": "2026-08-29T18:50:09+00:00"
  },
  "P12279": {
    "problem_number": 12279,
    "slug": "does-the-greedy-coprime-spiral-use-every-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:33:28+00:00",
    "updated_at": "2026-09-01T19:33:34+00:00"
  },
  "P11412": {
    "problem_number": 11412,
    "slug": "greedy-decimal-overlap-sequence-covers-all-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:52:17+00:00",
    "updated_at": "2026-08-29T18:52:39+00:00"
  },
  "P11522": {
    "problem_number": 11522,
    "slug": "surjectivity-of-greedy-fibonacci-jump-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:44:13+00:00",
    "updated_at": "2026-08-29T18:54:13+00:00"
  },
  "P11452": {
    "problem_number": 11452,
    "slug": "spiral-board-greedy-knight-walk-completeness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:05:03+00:00",
    "updated_at": "2026-08-29T18:53:16+00:00"
  },
  "P2458": {
    "problem_number": 2458,
    "slug": "greedy-one-common-bit-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:56:52+00:00",
    "updated_at": "2026-08-01T02:08:25+00:00"
  },
  "P11530": {
    "problem_number": 11530,
    "slug": "permutation-property-of-pairwise-coprime-spiral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:48:59+00:00",
    "updated_at": "2026-08-29T18:54:19+00:00"
  },
  "P12593": {
    "problem_number": 12593,
    "slug": "does-the-greedy-prime-sum-permutation-contain-every-even-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:54:13+00:00",
    "updated_at": "2026-09-02T21:54:20+00:00"
  },
  "P11254": {
    "problem_number": 11254,
    "slug": "greedy-product-avoidance-square-root-gap-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:05:59+00:00",
    "updated_at": "2026-08-29T18:49:59+00:00"
  },
  "P11504": {
    "problem_number": 11504,
    "slug": "consecutive-sum-power-avoiding-greedy-completeness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:33:32+00:00",
    "updated_at": "2026-08-29T18:54:00+00:00"
  },
  "P11274": {
    "problem_number": 11274,
    "slug": "greedy-complex-unit-vector-limiting-geometry",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:13:52+00:00",
    "updated_at": "2026-08-29T18:50:20+00:00"
  },
  "P11294": {
    "problem_number": 11294,
    "slug": "harmonic-denominator-equals-initial-lcm-infinitely-often",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:22:38+00:00",
    "updated_at": "2026-08-29T18:50:40+00:00"
  },
  "P11328": {
    "problem_number": 11328,
    "slug": "harmonic-divisor-mean-greedy-sequence-terminates",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:24:33+00:00",
    "updated_at": "2026-08-29T18:51:19+00:00"
  },
  "P11232": {
    "problem_number": 11232,
    "slug": "increasing-digit-prime-walk-infinitude",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:59:27+00:00",
    "updated_at": "2026-08-29T18:49:35+00:00"
  },
  "P11266": {
    "problem_number": 11266,
    "slug": "kolakoski-sequence-density-one-half",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:10:21+00:00",
    "updated_at": "2026-08-29T18:50:12+00:00"
  },
  "P12699": {
    "problem_number": 12699,
    "slug": "does-the-least-prime-multiplier-stay-below-2-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:20:28+00:00",
    "updated_at": "2026-09-02T22:21:00+00:00"
  },
  "P3118": {
    "problem_number": 3118,
    "slug": "matrix-multiplication-exponent-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:04+00:00",
    "updated_at": "2026-08-02T12:52:37+00:00"
  },
  "P12657": {
    "problem_number": 12657,
    "slug": "does-the-maximal-representation-degree-equal-twice-dedekind-psi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:09:08+00:00",
    "updated_at": "2026-09-02T22:09:13+00:00"
  },
  "P11198": {
    "problem_number": 11198,
    "slug": "three-color-queen-density-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:49:04+00:00",
    "updated_at": "2026-08-29T18:49:01+00:00"
  },
  "P12689": {
    "problem_number": 12689,
    "slug": "does-the-modulo-5-obstruction-exactly-predict-missing-endpoint-block-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:16:22+00:00",
    "updated_at": "2026-09-02T22:16:53+00:00"
  },
  "P11462": {
    "problem_number": 11462,
    "slug": "novel-repeat-pool-sequence-upper-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:08:53+00:00",
    "updated_at": "2026-08-29T18:53:29+00:00"
  },
  "P11658": {
    "problem_number": 11658,
    "slug": "does-the-orthogonal-digit-avoiding-square-spiral-terminate",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:03:39+00:00",
    "updated_at": "2026-08-30T11:03:46+00:00"
  },
  "P11392": {
    "problem_number": 11392,
    "slug": "prime-count-factor-concatenation-sixth-term",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:46:12+00:00",
    "updated_at": "2026-08-29T18:52:18+00:00"
  },
  "P12693": {
    "problem_number": 12693,
    "slug": "does-the-proportion-of-holey-polyominoes-tend-to-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:17:54+00:00",
    "updated_at": "2026-09-02T22:18:26+00:00"
  },
  "P11881": {
    "problem_number": 11881,
    "slug": "does-the-rotating-prime-sisyphus-sequence-visit-every-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:17:04+00:00",
    "updated_at": "2026-08-30T16:17:09+00:00"
  },
  "P11492": {
    "problem_number": 11492,
    "slug": "staged-recaman-path-infinitude",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:26:15+00:00",
    "updated_at": "2026-08-29T18:53:50+00:00"
  },
  "P12723": {
    "problem_number": 12723,
    "slug": "does-the-totient-rank-identity-characterize-universal-fibonacci-divisors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:31:22+00:00",
    "updated_at": "2026-09-02T22:31:53+00:00"
  },
  "P11258": {
    "problem_number": 11258,
    "slug": "weighted-mobius-second-sum-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:06:46+00:00",
    "updated_at": "2026-08-29T18:50:04+00:00"
  },
  "P4548": {
    "problem_number": 4548,
    "slug": "toroidal-knight-18-19-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:20+00:00",
    "updated_at": "2026-08-16T05:33:22+00:00"
  },
  "P4550": {
    "problem_number": 4550,
    "slug": "toroidal-knight-18-20-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:22+00:00",
    "updated_at": "2026-08-16T05:33:23+00:00"
  },
  "P4552": {
    "problem_number": 4552,
    "slug": "toroidal-knight-18-21-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:25+00:00",
    "updated_at": "2026-08-16T05:33:26+00:00"
  },
  "P4554": {
    "problem_number": 4554,
    "slug": "toroidal-knight-18-22-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:29+00:00",
    "updated_at": "2026-08-16T05:33:37+00:00"
  },
  "P4556": {
    "problem_number": 4556,
    "slug": "toroidal-knight-18-23-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:38+00:00",
    "updated_at": "2026-08-16T05:33:40+00:00"
  },
  "P4558": {
    "problem_number": 4558,
    "slug": "toroidal-knight-19-20-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:41+00:00",
    "updated_at": "2026-08-16T05:33:46+00:00"
  },
  "P4560": {
    "problem_number": 4560,
    "slug": "toroidal-knight-19-21-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:46+00:00",
    "updated_at": "2026-08-16T05:33:51+00:00"
  },
  "P4562": {
    "problem_number": 4562,
    "slug": "toroidal-knight-19-22-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:51+00:00",
    "updated_at": "2026-08-16T05:33:52+00:00"
  },
  "P4564": {
    "problem_number": 4564,
    "slug": "toroidal-knight-19-23-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:54+00:00",
    "updated_at": "2026-08-16T05:34:03+00:00"
  },
  "P4566": {
    "problem_number": 4566,
    "slug": "toroidal-knight-19-24-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:04+00:00",
    "updated_at": "2026-08-16T05:34:04+00:00"
  },
  "P4568": {
    "problem_number": 4568,
    "slug": "toroidal-knight-20-21-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:04+00:00",
    "updated_at": "2026-08-16T05:34:06+00:00"
  },
  "P4570": {
    "problem_number": 4570,
    "slug": "toroidal-knight-20-22-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:10+00:00",
    "updated_at": "2026-08-16T05:34:21+00:00"
  },
  "P4572": {
    "problem_number": 4572,
    "slug": "toroidal-knight-20-23-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:26+00:00",
    "updated_at": "2026-08-16T05:34:35+00:00"
  },
  "P4574": {
    "problem_number": 4574,
    "slug": "toroidal-knight-20-24-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:36+00:00",
    "updated_at": "2026-08-16T05:34:37+00:00"
  },
  "P4576": {
    "problem_number": 4576,
    "slug": "toroidal-knight-20-25-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:37+00:00",
    "updated_at": "2026-08-16T05:34:44+00:00"
  },
  "P4578": {
    "problem_number": 4578,
    "slug": "toroidal-knight-21-22-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:46+00:00",
    "updated_at": "2026-08-16T05:34:50+00:00"
  },
  "P4580": {
    "problem_number": 4580,
    "slug": "toroidal-knight-21-23-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:34:52+00:00",
    "updated_at": "2026-08-16T05:34:58+00:00"
  },
  "P4582": {
    "problem_number": 4582,
    "slug": "toroidal-knight-21-24-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:35:00+00:00",
    "updated_at": "2026-08-16T05:35:04+00:00"
  },
  "P4584": {
    "problem_number": 4584,
    "slug": "toroidal-knight-21-25-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:35:07+00:00",
    "updated_at": "2026-08-16T05:35:17+00:00"
  },
  "P4586": {
    "problem_number": 4586,
    "slug": "toroidal-knight-21-26-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:35:22+00:00",
    "updated_at": "2026-08-16T05:35:35+00:00"
  },
  "P4588": {
    "problem_number": 4588,
    "slug": "toroidal-knight-22-23-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:35:39+00:00",
    "updated_at": "2026-08-16T05:35:48+00:00"
  },
  "P4590": {
    "problem_number": 4590,
    "slug": "toroidal-knight-22-24-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:35:52+00:00",
    "updated_at": "2026-08-16T05:36:02+00:00"
  },
  "P4592": {
    "problem_number": 4592,
    "slug": "toroidal-knight-22-25-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:07+00:00",
    "updated_at": "2026-08-16T05:36:08+00:00"
  },
  "P4594": {
    "problem_number": 4594,
    "slug": "toroidal-knight-22-26-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:08+00:00",
    "updated_at": "2026-08-16T05:36:09+00:00"
  },
  "P4596": {
    "problem_number": 4596,
    "slug": "toroidal-knight-22-27-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:09+00:00",
    "updated_at": "2026-08-16T05:36:11+00:00"
  },
  "P4598": {
    "problem_number": 4598,
    "slug": "toroidal-knight-23-24-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:11+00:00",
    "updated_at": "2026-08-16T05:36:17+00:00"
  },
  "P4600": {
    "problem_number": 4600,
    "slug": "toroidal-knight-23-25-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:19+00:00",
    "updated_at": "2026-08-16T05:36:20+00:00"
  },
  "P4602": {
    "problem_number": 4602,
    "slug": "toroidal-knight-23-26-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:21+00:00",
    "updated_at": "2026-08-16T05:36:22+00:00"
  },
  "P4604": {
    "problem_number": 4604,
    "slug": "toroidal-knight-23-27-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:25+00:00",
    "updated_at": "2026-08-16T05:36:33+00:00"
  },
  "P4606": {
    "problem_number": 4606,
    "slug": "toroidal-knight-23-28-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:41+00:00",
    "updated_at": "2026-08-16T05:36:46+00:00"
  },
  "P4608": {
    "problem_number": 4608,
    "slug": "toroidal-knight-24-25-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:47+00:00",
    "updated_at": "2026-08-16T05:36:53+00:00"
  },
  "P4610": {
    "problem_number": 4610,
    "slug": "toroidal-knight-24-26-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:54+00:00",
    "updated_at": "2026-08-16T05:36:55+00:00"
  },
  "P4612": {
    "problem_number": 4612,
    "slug": "toroidal-knight-24-27-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:56+00:00",
    "updated_at": "2026-08-16T05:36:57+00:00"
  },
  "P4614": {
    "problem_number": 4614,
    "slug": "toroidal-knight-24-28-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:58+00:00",
    "updated_at": "2026-08-16T05:36:58+00:00"
  },
  "P4616": {
    "problem_number": 4616,
    "slug": "toroidal-knight-24-29-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:59+00:00",
    "updated_at": "2026-08-16T05:36:59+00:00"
  },
  "P4618": {
    "problem_number": 4618,
    "slug": "toroidal-knight-25-26-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:36:59+00:00",
    "updated_at": "2026-08-16T05:37:01+00:00"
  },
  "P4620": {
    "problem_number": 4620,
    "slug": "toroidal-knight-25-27-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:01+00:00",
    "updated_at": "2026-08-16T05:37:03+00:00"
  },
  "P4622": {
    "problem_number": 4622,
    "slug": "toroidal-knight-25-28-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:04+00:00",
    "updated_at": "2026-08-16T05:37:05+00:00"
  },
  "P4624": {
    "problem_number": 4624,
    "slug": "toroidal-knight-25-29-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:06+00:00",
    "updated_at": "2026-08-16T05:37:06+00:00"
  },
  "P4626": {
    "problem_number": 4626,
    "slug": "toroidal-knight-25-30-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:09+00:00",
    "updated_at": "2026-08-16T05:37:17+00:00"
  },
  "P5080": {
    "problem_number": 5080,
    "slug": "toroidal-knight-26-27-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:53+00:00",
    "updated_at": "2026-08-16T08:04:57+00:00"
  },
  "P5082": {
    "problem_number": 5082,
    "slug": "toroidal-knight-26-28-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:58+00:00",
    "updated_at": "2026-08-16T08:04:58+00:00"
  },
  "P5084": {
    "problem_number": 5084,
    "slug": "toroidal-knight-26-29-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:05:00+00:00",
    "updated_at": "2026-08-16T08:05:03+00:00"
  },
  "P5086": {
    "problem_number": 5086,
    "slug": "toroidal-knight-26-30-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:05:12+00:00",
    "updated_at": "2026-08-16T08:05:22+00:00"
  },
  "P5088": {
    "problem_number": 5088,
    "slug": "toroidal-knight-26-31-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:05:28+00:00",
    "updated_at": "2026-08-16T08:05:39+00:00"
  },
  "P5090": {
    "problem_number": 5090,
    "slug": "toroidal-knight-27-28-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:05:44+00:00",
    "updated_at": "2026-08-16T08:05:56+00:00"
  },
  "P5092": {
    "problem_number": 5092,
    "slug": "toroidal-knight-27-29-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:06:04+00:00",
    "updated_at": "2026-08-16T08:06:15+00:00"
  },
  "P5094": {
    "problem_number": 5094,
    "slug": "toroidal-knight-27-30-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:06:25+00:00",
    "updated_at": "2026-08-16T08:06:40+00:00"
  },
  "P5096": {
    "problem_number": 5096,
    "slug": "toroidal-knight-27-31-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:08:37+00:00",
    "updated_at": "2026-08-16T08:08:44+00:00"
  },
  "P5098": {
    "problem_number": 5098,
    "slug": "toroidal-knight-27-32-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:08:46+00:00",
    "updated_at": "2026-08-16T08:08:47+00:00"
  },
  "P5100": {
    "problem_number": 5100,
    "slug": "toroidal-knight-28-29-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:08:48+00:00",
    "updated_at": "2026-08-16T08:08:49+00:00"
  },
  "P5102": {
    "problem_number": 5102,
    "slug": "toroidal-knight-28-30-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:08:49+00:00",
    "updated_at": "2026-08-16T08:08:55+00:00"
  },
  "P5104": {
    "problem_number": 5104,
    "slug": "toroidal-knight-28-31-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:08:58+00:00",
    "updated_at": "2026-08-16T08:09:08+00:00"
  },
  "P5106": {
    "problem_number": 5106,
    "slug": "toroidal-knight-28-32-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:09:15+00:00",
    "updated_at": "2026-08-16T08:09:28+00:00"
  },
  "P5108": {
    "problem_number": 5108,
    "slug": "toroidal-knight-28-33-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:09:30+00:00",
    "updated_at": "2026-08-16T08:09:36+00:00"
  },
  "P5110": {
    "problem_number": 5110,
    "slug": "toroidal-knight-29-30-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:09:40+00:00",
    "updated_at": "2026-08-16T08:09:53+00:00"
  },
  "P5112": {
    "problem_number": 5112,
    "slug": "toroidal-knight-29-31-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:09:55+00:00",
    "updated_at": "2026-08-16T08:10:06+00:00"
  },
  "P5114": {
    "problem_number": 5114,
    "slug": "toroidal-knight-29-32-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:10:10+00:00",
    "updated_at": "2026-08-16T08:10:16+00:00"
  },
  "P5116": {
    "problem_number": 5116,
    "slug": "toroidal-knight-29-33-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:10:19+00:00",
    "updated_at": "2026-08-16T08:10:26+00:00"
  },
  "P5118": {
    "problem_number": 5118,
    "slug": "toroidal-knight-29-34-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:10:27+00:00",
    "updated_at": "2026-08-16T08:10:37+00:00"
  },
  "P5120": {
    "problem_number": 5120,
    "slug": "toroidal-knight-30-31-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:10:40+00:00",
    "updated_at": "2026-08-16T08:10:45+00:00"
  },
  "P5122": {
    "problem_number": 5122,
    "slug": "toroidal-knight-30-32-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:10:50+00:00",
    "updated_at": "2026-08-16T08:11:03+00:00"
  },
  "P5124": {
    "problem_number": 5124,
    "slug": "toroidal-knight-30-33-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:07+00:00",
    "updated_at": "2026-08-16T08:11:08+00:00"
  },
  "P5126": {
    "problem_number": 5126,
    "slug": "toroidal-knight-30-34-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:08+00:00",
    "updated_at": "2026-08-16T08:11:12+00:00"
  },
  "P5128": {
    "problem_number": 5128,
    "slug": "toroidal-knight-30-35-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:12+00:00",
    "updated_at": "2026-08-16T08:11:16+00:00"
  },
  "P5130": {
    "problem_number": 5130,
    "slug": "toroidal-knight-31-32-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:18+00:00",
    "updated_at": "2026-08-16T08:11:26+00:00"
  },
  "P5132": {
    "problem_number": 5132,
    "slug": "toroidal-knight-31-33-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:30+00:00",
    "updated_at": "2026-08-16T08:11:35+00:00"
  },
  "P5134": {
    "problem_number": 5134,
    "slug": "toroidal-knight-31-34-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:36+00:00",
    "updated_at": "2026-08-16T08:11:41+00:00"
  },
  "P5136": {
    "problem_number": 5136,
    "slug": "toroidal-knight-31-35-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:43+00:00",
    "updated_at": "2026-08-16T08:11:48+00:00"
  },
  "P5138": {
    "problem_number": 5138,
    "slug": "toroidal-knight-31-36-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:49+00:00",
    "updated_at": "2026-08-16T08:11:55+00:00"
  },
  "P5140": {
    "problem_number": 5140,
    "slug": "toroidal-knight-32-33-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:57+00:00",
    "updated_at": "2026-08-16T08:11:58+00:00"
  },
  "P5142": {
    "problem_number": 5142,
    "slug": "toroidal-knight-32-34-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:11:58+00:00",
    "updated_at": "2026-08-16T08:11:59+00:00"
  },
  "P5144": {
    "problem_number": 5144,
    "slug": "toroidal-knight-32-35-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:00+00:00",
    "updated_at": "2026-08-16T08:12:04+00:00"
  },
  "P5146": {
    "problem_number": 5146,
    "slug": "toroidal-knight-32-36-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:04+00:00",
    "updated_at": "2026-08-16T08:12:06+00:00"
  },
  "P5148": {
    "problem_number": 5148,
    "slug": "toroidal-knight-32-37-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:07+00:00",
    "updated_at": "2026-08-16T08:12:08+00:00"
  },
  "P5150": {
    "problem_number": 5150,
    "slug": "toroidal-knight-33-34-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:08+00:00",
    "updated_at": "2026-08-16T08:12:10+00:00"
  },
  "P5152": {
    "problem_number": 5152,
    "slug": "toroidal-knight-33-35-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:11+00:00",
    "updated_at": "2026-08-16T08:12:14+00:00"
  },
  "P5154": {
    "problem_number": 5154,
    "slug": "toroidal-knight-33-36-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:20+00:00",
    "updated_at": "2026-08-16T08:12:32+00:00"
  },
  "P5156": {
    "problem_number": 5156,
    "slug": "toroidal-knight-33-37-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:37+00:00",
    "updated_at": "2026-08-16T08:12:40+00:00"
  },
  "P5158": {
    "problem_number": 5158,
    "slug": "toroidal-knight-33-38-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:40+00:00",
    "updated_at": "2026-08-16T08:12:41+00:00"
  },
  "P5160": {
    "problem_number": 5160,
    "slug": "toroidal-knight-34-35-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:42+00:00",
    "updated_at": "2026-08-16T08:12:42+00:00"
  },
  "P5162": {
    "problem_number": 5162,
    "slug": "toroidal-knight-34-36-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:44+00:00",
    "updated_at": "2026-08-16T08:12:46+00:00"
  },
  "P5164": {
    "problem_number": 5164,
    "slug": "toroidal-knight-34-37-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:48+00:00",
    "updated_at": "2026-08-16T08:12:49+00:00"
  },
  "P5166": {
    "problem_number": 5166,
    "slug": "toroidal-knight-34-38-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:50+00:00",
    "updated_at": "2026-08-16T08:12:50+00:00"
  },
  "P5168": {
    "problem_number": 5168,
    "slug": "toroidal-knight-34-39-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:51+00:00",
    "updated_at": "2026-08-16T08:12:56+00:00"
  },
  "P5170": {
    "problem_number": 5170,
    "slug": "toroidal-knight-35-36-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:12:57+00:00",
    "updated_at": "2026-08-16T08:13:01+00:00"
  },
  "P5172": {
    "problem_number": 5172,
    "slug": "toroidal-knight-35-37-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:01+00:00",
    "updated_at": "2026-08-16T08:13:01+00:00"
  },
  "P5174": {
    "problem_number": 5174,
    "slug": "toroidal-knight-35-38-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:02+00:00",
    "updated_at": "2026-08-16T08:13:02+00:00"
  },
  "P5176": {
    "problem_number": 5176,
    "slug": "toroidal-knight-35-39-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:03+00:00",
    "updated_at": "2026-08-16T08:13:06+00:00"
  },
  "P5178": {
    "problem_number": 5178,
    "slug": "toroidal-knight-35-40-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:07+00:00",
    "updated_at": "2026-08-16T08:13:09+00:00"
  },
  "P5180": {
    "problem_number": 5180,
    "slug": "toroidal-knight-36-37-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:11+00:00",
    "updated_at": "2026-08-16T08:13:12+00:00"
  },
  "P5182": {
    "problem_number": 5182,
    "slug": "toroidal-knight-36-38-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:13+00:00",
    "updated_at": "2026-08-16T08:13:15+00:00"
  },
  "P5184": {
    "problem_number": 5184,
    "slug": "toroidal-knight-36-39-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:16+00:00",
    "updated_at": "2026-08-16T08:13:18+00:00"
  },
  "P5186": {
    "problem_number": 5186,
    "slug": "toroidal-knight-36-40-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:18+00:00",
    "updated_at": "2026-08-16T08:13:19+00:00"
  },
  "P5188": {
    "problem_number": 5188,
    "slug": "toroidal-knight-36-41-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:19+00:00",
    "updated_at": "2026-08-16T08:13:20+00:00"
  },
  "P5190": {
    "problem_number": 5190,
    "slug": "toroidal-knight-37-38-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:21+00:00",
    "updated_at": "2026-08-16T08:13:26+00:00"
  },
  "P5192": {
    "problem_number": 5192,
    "slug": "toroidal-knight-37-39-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:27+00:00",
    "updated_at": "2026-08-16T08:13:28+00:00"
  },
  "P5194": {
    "problem_number": 5194,
    "slug": "toroidal-knight-37-40-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:29+00:00",
    "updated_at": "2026-08-16T08:13:30+00:00"
  },
  "P5196": {
    "problem_number": 5196,
    "slug": "toroidal-knight-37-41-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:30+00:00",
    "updated_at": "2026-08-16T08:13:32+00:00"
  },
  "P5198": {
    "problem_number": 5198,
    "slug": "toroidal-knight-37-42-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:33+00:00",
    "updated_at": "2026-08-16T08:13:35+00:00"
  },
  "P5200": {
    "problem_number": 5200,
    "slug": "toroidal-knight-38-39-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:36+00:00",
    "updated_at": "2026-08-16T08:13:37+00:00"
  },
  "P5202": {
    "problem_number": 5202,
    "slug": "toroidal-knight-38-40-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:38+00:00",
    "updated_at": "2026-08-16T08:13:38+00:00"
  },
  "P5204": {
    "problem_number": 5204,
    "slug": "toroidal-knight-38-41-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:38+00:00",
    "updated_at": "2026-08-16T08:13:41+00:00"
  },
  "P5206": {
    "problem_number": 5206,
    "slug": "toroidal-knight-38-42-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:46+00:00",
    "updated_at": "2026-08-16T08:13:53+00:00"
  },
  "P5208": {
    "problem_number": 5208,
    "slug": "toroidal-knight-38-43-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:54+00:00",
    "updated_at": "2026-08-16T08:13:55+00:00"
  },
  "P5210": {
    "problem_number": 5210,
    "slug": "toroidal-knight-39-40-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:55+00:00",
    "updated_at": "2026-08-16T08:13:56+00:00"
  },
  "P5212": {
    "problem_number": 5212,
    "slug": "toroidal-knight-39-41-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:56+00:00",
    "updated_at": "2026-08-16T08:13:57+00:00"
  },
  "P5214": {
    "problem_number": 5214,
    "slug": "toroidal-knight-39-42-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:57+00:00",
    "updated_at": "2026-08-16T08:13:57+00:00"
  },
  "P5216": {
    "problem_number": 5216,
    "slug": "toroidal-knight-39-43-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:58+00:00",
    "updated_at": "2026-08-16T08:13:59+00:00"
  },
  "P5218": {
    "problem_number": 5218,
    "slug": "toroidal-knight-39-44-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:59+00:00",
    "updated_at": "2026-08-16T08:13:59+00:00"
  },
  "P5220": {
    "problem_number": 5220,
    "slug": "toroidal-knight-40-41-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:13:59+00:00",
    "updated_at": "2026-08-16T08:14:00+00:00"
  },
  "P5222": {
    "problem_number": 5222,
    "slug": "toroidal-knight-40-42-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:01+00:00",
    "updated_at": "2026-08-16T08:14:01+00:00"
  },
  "P5224": {
    "problem_number": 5224,
    "slug": "toroidal-knight-40-43-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:03+00:00",
    "updated_at": "2026-08-16T08:14:11+00:00"
  },
  "P5226": {
    "problem_number": 5226,
    "slug": "toroidal-knight-40-44-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:11+00:00",
    "updated_at": "2026-08-16T08:14:13+00:00"
  },
  "P5228": {
    "problem_number": 5228,
    "slug": "toroidal-knight-40-45-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:14+00:00",
    "updated_at": "2026-08-16T08:14:14+00:00"
  },
  "P5230": {
    "problem_number": 5230,
    "slug": "toroidal-knight-41-42-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:15+00:00",
    "updated_at": "2026-08-16T08:14:15+00:00"
  },
  "P5232": {
    "problem_number": 5232,
    "slug": "toroidal-knight-41-43-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:16+00:00",
    "updated_at": "2026-08-16T08:14:19+00:00"
  },
  "P5234": {
    "problem_number": 5234,
    "slug": "toroidal-knight-41-44-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:22+00:00",
    "updated_at": "2026-08-16T08:14:24+00:00"
  },
  "P5236": {
    "problem_number": 5236,
    "slug": "toroidal-knight-41-45-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:28+00:00",
    "updated_at": "2026-08-16T08:14:29+00:00"
  },
  "P5238": {
    "problem_number": 5238,
    "slug": "toroidal-knight-41-46-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:31+00:00",
    "updated_at": "2026-08-16T08:14:34+00:00"
  },
  "P5240": {
    "problem_number": 5240,
    "slug": "toroidal-knight-42-43-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:34+00:00",
    "updated_at": "2026-08-16T08:14:37+00:00"
  },
  "P5242": {
    "problem_number": 5242,
    "slug": "toroidal-knight-42-44-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:38+00:00",
    "updated_at": "2026-08-16T08:14:39+00:00"
  },
  "P5244": {
    "problem_number": 5244,
    "slug": "toroidal-knight-42-45-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:40+00:00",
    "updated_at": "2026-08-16T08:14:46+00:00"
  },
  "P5246": {
    "problem_number": 5246,
    "slug": "toroidal-knight-42-46-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:48+00:00",
    "updated_at": "2026-08-16T08:14:52+00:00"
  },
  "P5248": {
    "problem_number": 5248,
    "slug": "toroidal-knight-42-47-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:52+00:00",
    "updated_at": "2026-08-16T08:14:55+00:00"
  },
  "P5250": {
    "problem_number": 5250,
    "slug": "toroidal-knight-43-44-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:14:56+00:00",
    "updated_at": "2026-08-16T08:14:57+00:00"
  },
  "P5252": {
    "problem_number": 5252,
    "slug": "toroidal-knight-43-45-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:15:01+00:00",
    "updated_at": "2026-08-16T08:15:05+00:00"
  },
  "P5254": {
    "problem_number": 5254,
    "slug": "toroidal-knight-43-46-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:15:09+00:00",
    "updated_at": "2026-08-16T08:15:11+00:00"
  },
  "P5256": {
    "problem_number": 5256,
    "slug": "toroidal-knight-43-47-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:15:14+00:00",
    "updated_at": "2026-08-16T08:15:20+00:00"
  },
  "P5258": {
    "problem_number": 5258,
    "slug": "toroidal-knight-43-48-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:15:23+00:00",
    "updated_at": "2026-08-16T08:15:32+00:00"
  },
  "P5260": {
    "problem_number": 5260,
    "slug": "toroidal-knight-44-45-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:15:39+00:00",
    "updated_at": "2026-08-16T08:15:50+00:00"
  },
  "P5264": {
    "problem_number": 5264,
    "slug": "toroidal-knight-44-46-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:09+00:00",
    "updated_at": "2026-08-16T08:19:17+00:00"
  },
  "P5266": {
    "problem_number": 5266,
    "slug": "toroidal-knight-44-47-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:21+00:00",
    "updated_at": "2026-08-16T08:19:30+00:00"
  },
  "P5268": {
    "problem_number": 5268,
    "slug": "toroidal-knight-44-48-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:35+00:00",
    "updated_at": "2026-08-16T08:19:38+00:00"
  },
  "P5270": {
    "problem_number": 5270,
    "slug": "toroidal-knight-44-49-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:39+00:00",
    "updated_at": "2026-08-16T08:19:40+00:00"
  },
  "P5272": {
    "problem_number": 5272,
    "slug": "toroidal-knight-45-46-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:41+00:00",
    "updated_at": "2026-08-16T08:19:47+00:00"
  },
  "P5274": {
    "problem_number": 5274,
    "slug": "toroidal-knight-45-47-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:49+00:00",
    "updated_at": "2026-08-16T08:19:54+00:00"
  },
  "P5276": {
    "problem_number": 5276,
    "slug": "toroidal-knight-45-48-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:19:54+00:00",
    "updated_at": "2026-08-16T08:19:58+00:00"
  },
  "P5278": {
    "problem_number": 5278,
    "slug": "toroidal-knight-45-49-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:00+00:00",
    "updated_at": "2026-08-16T08:20:01+00:00"
  },
  "P5280": {
    "problem_number": 5280,
    "slug": "toroidal-knight-45-50-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:01+00:00",
    "updated_at": "2026-08-16T08:20:02+00:00"
  },
  "P3824": {
    "problem_number": 3824,
    "slug": "circulant-211-2-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:14+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3826": {
    "problem_number": 3826,
    "slug": "circulant-223-3-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:28+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3828": {
    "problem_number": 3828,
    "slug": "circulant-227-4-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:29+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3830": {
    "problem_number": 3830,
    "slug": "circulant-229-5-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:30+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3832": {
    "problem_number": 3832,
    "slug": "circulant-233-6-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:34+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3834": {
    "problem_number": 3834,
    "slug": "circulant-239-7-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3836": {
    "problem_number": 3836,
    "slug": "circulant-241-8-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:43+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3838": {
    "problem_number": 3838,
    "slug": "circulant-251-9-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:45+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3840": {
    "problem_number": 3840,
    "slug": "circulant-257-10-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:46+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3842": {
    "problem_number": 3842,
    "slug": "circulant-263-11-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:49+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3844": {
    "problem_number": 3844,
    "slug": "circulant-269-12-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:53+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3846": {
    "problem_number": 3846,
    "slug": "circulant-271-13-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:32:57+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3848": {
    "problem_number": 3848,
    "slug": "circulant-277-14-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:00+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3850": {
    "problem_number": 3850,
    "slug": "circulant-281-15-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:02+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3852": {
    "problem_number": 3852,
    "slug": "circulant-283-16-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:06+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3854": {
    "problem_number": 3854,
    "slug": "circulant-293-17-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:08+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3856": {
    "problem_number": 3856,
    "slug": "circulant-307-18-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:11+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3858": {
    "problem_number": 3858,
    "slug": "circulant-311-19-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:12+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3860": {
    "problem_number": 3860,
    "slug": "circulant-313-20-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:13+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3862": {
    "problem_number": 3862,
    "slug": "circulant-317-21-domination-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:14+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3680": {
    "problem_number": 3680,
    "slug": "domino-thirty-square-central-hole-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:49+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11796": {
    "problem_number": 11796,
    "slug": "double-exponential-growth-in-the-greedy-expansion-of-square-root-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:44:57+00:00",
    "updated_at": "2026-08-30T12:45:06+00:00"
  },
  "P12075": {
    "problem_number": 12075,
    "slug": "doubling-before-terminal-naked-primes-in-the-cup-of-coffee-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:23+00:00",
    "updated_at": "2026-09-01T19:08:29+00:00"
  },
  "P11945": {
    "problem_number": 11945,
    "slug": "doubling-law-for-rotated-xor-cycle-lengths",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:32:29+00:00",
    "updated_at": "2026-08-30T16:32:42+00:00"
  },
  "P10090": {
    "problem_number": 10090,
    "slug": "doubling-the-dimension-yields-a-benign-landscape-for-the-squared-stress",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:02:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9966": {
    "problem_number": 9966,
    "slug": "open-fc-a133208166f3d9eed4cd-dubner-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:59+00:00",
    "updated_at": "2026-08-17T20:05:00+00:00"
  },
  "P3406": {
    "problem_number": 3406,
    "slug": "kourovka-21-33-dunwoody-accessibility-for-totally-disconnected-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:57:45+00:00",
    "updated_at": "2026-08-12T07:57:49+00:00"
  },
  "P3094": {
    "problem_number": 3094,
    "slug": "durers-edge-unfolding-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:59+00:00",
    "updated_at": "2026-08-02T12:48:58+00:00"
  },
  "P8940": {
    "problem_number": 8940,
    "slug": "open-fc-f216fd27c8211c39a4c6-abc-variants-lt-constant-mul",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:01+00:00",
    "updated_at": "2026-08-17T19:41:03+00:00"
  },
  "P2934": {
    "problem_number": 2934,
    "slug": "cmon-cocongruences-effective",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:50:04+00:00",
    "updated_at": "2026-08-01T11:33:57+00:00"
  },
  "P11756": {
    "problem_number": 11756,
    "slug": "egyptian-fractions-from-sums-of-consecutive-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:23:04+00:00",
    "updated_at": "2026-08-30T12:23:11+00:00"
  },
  "P8990": {
    "problem_number": 8990,
    "slug": "open-fc-727eb21073d8394ed5d8-erdos-306",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:27+00:00",
    "updated_at": "2026-08-17T19:44:29+00:00"
  },
  "P3570": {
    "problem_number": 3570,
    "slug": "ehrhart-volume-conjecture",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:53:07+00:00",
    "updated_at": "2026-08-18T06:09:34+00:00"
  },
  "P3100": {
    "problem_number": 3100,
    "slug": "finite-group-power-semigroup-embeddability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:00+00:00",
    "updated_at": "2026-08-02T12:50:01+00:00"
  },
  "P3548": {
    "problem_number": 3548,
    "slug": "kourovka-21-146-embedding-groups-of-type-f-into-higher-finiteness-types",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:14:22+00:00",
    "updated_at": "2026-08-12T08:14:36+00:00"
  },
  "P8438": {
    "problem_number": 8438,
    "slug": "open-fc-353fe97b15f035b9b2a5-erdos-536",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:06+00:00",
    "updated_at": "2026-08-17T18:52:06+00:00"
  },
  "P9234": {
    "problem_number": 9234,
    "slug": "open-fc-83499cacfe773fe7de79-erdos-677",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:13+00:00",
    "updated_at": "2026-08-17T19:50:14+00:00"
  },
  "P8214": {
    "problem_number": 8214,
    "slug": "open-fc-0f9f6f11e040fefb8ea3-mathoverflow-347178-variants-bounded-only",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:12+00:00",
    "updated_at": "2026-08-17T18:37:13+00:00"
  },
  "P3338": {
    "problem_number": 3338,
    "slug": "erdos-problem-412",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:45+00:00",
    "updated_at": "2026-08-12T06:06:47+00:00"
  },
  "P8232": {
    "problem_number": 8232,
    "slug": "open-fc-138a36eaa8cb33772f9d-erdos-412",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:26+00:00",
    "updated_at": "2026-08-17T18:37:28+00:00"
  },
  "P9206": {
    "problem_number": 9206,
    "slug": "open-fc-5c7ac190176f150ac904-kotherconjecture-variants-matrixover-kotherradical",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:17+00:00",
    "updated_at": "2026-08-17T19:49:20+00:00"
  },
  "P9314": {
    "problem_number": 9314,
    "slug": "open-fc-c54fe525d3f15c3be706-isequidistributedmoduloone-three-halves-pow",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:51+00:00",
    "updated_at": "2026-08-17T19:50:51+00:00"
  },
  "P8936": {
    "problem_number": 8936,
    "slug": "open-fc-f00c1480a07530f48aff-isequidistributedmoduloone-transcendental-three-halves-pow",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:55+00:00",
    "updated_at": "2026-08-17T19:40:56+00:00"
  },
  "P3028": {
    "problem_number": 3028,
    "slug": "erdos-problem-99",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:58+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9352": {
    "problem_number": 9352,
    "slug": "open-fc-e45e4cf62876d45d299f-erdos-99",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:05+00:00",
    "updated_at": "2026-08-17T19:51:05+00:00"
  },
  "P12381": {
    "problem_number": 12381,
    "slug": "equinumerous-inversion-sequence-avoidance-classes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:45:58+00:00",
    "updated_at": "2026-09-01T19:46:03+00:00"
  },
  "P10200": {
    "problem_number": 10200,
    "slug": "open-fc-9e13e4ff394c607f2fc6-erdos-moser-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:44+00:00",
    "updated_at": "2026-08-18T02:51:44+00:00"
  },
  "P9162": {
    "problem_number": 9162,
    "slug": "open-fc-f493d5e9017ee8d42b61-erdos-982",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:53+00:00",
    "updated_at": "2026-08-17T19:47:53+00:00"
  },
  "P3262": {
    "problem_number": 3262,
    "slug": "erdos-problem-982",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:59:33+00:00",
    "updated_at": "2026-08-12T05:59:37+00:00"
  },
  "P9780": {
    "problem_number": 9780,
    "slug": "open-fc-ced3b0afe5dfaf90b4cc-erdos-89",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:36+00:00",
    "updated_at": "2026-08-17T20:02:36+00:00"
  },
  "P3020": {
    "problem_number": 3020,
    "slug": "erdos-problem-89",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:47+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P10686": {
    "problem_number": 10686,
    "slug": "erdos-problem-1005",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:44+00:00",
    "updated_at": "2026-08-18T02:54:45+00:00"
  },
  "P10688": {
    "problem_number": 10688,
    "slug": "erdos-problem-1011",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:45+00:00",
    "updated_at": "2026-08-18T02:54:45+00:00"
  },
  "P10690": {
    "problem_number": 10690,
    "slug": "erdos-problem-1013",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:45+00:00",
    "updated_at": "2026-08-18T02:54:46+00:00"
  },
  "P10692": {
    "problem_number": 10692,
    "slug": "erdos-problem-1016",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:46+00:00",
    "updated_at": "2026-08-18T02:54:46+00:00"
  },
  "P10694": {
    "problem_number": 10694,
    "slug": "erdos-problem-1017",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:47+00:00",
    "updated_at": "2026-08-18T02:54:47+00:00"
  },
  "P10696": {
    "problem_number": 10696,
    "slug": "erdos-problem-1029",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:47+00:00",
    "updated_at": "2026-08-18T02:54:48+00:00"
  },
  "P10268": {
    "problem_number": 10268,
    "slug": "erdos-problem-102",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:44+00:00",
    "updated_at": "2026-08-18T02:52:45+00:00"
  },
  "P10698": {
    "problem_number": 10698,
    "slug": "erdos-problem-1030",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:48+00:00",
    "updated_at": "2026-08-18T02:54:48+00:00"
  },
  "P10700": {
    "problem_number": 10700,
    "slug": "erdos-problem-1032",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:48+00:00",
    "updated_at": "2026-08-18T02:54:49+00:00"
  },
  "P10702": {
    "problem_number": 10702,
    "slug": "erdos-problem-1033",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:49+00:00",
    "updated_at": "2026-08-18T02:54:49+00:00"
  },
  "P10704": {
    "problem_number": 10704,
    "slug": "erdos-problem-1035",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:49+00:00",
    "updated_at": "2026-08-18T02:54:50+00:00"
  },
  "P10706": {
    "problem_number": 10706,
    "slug": "erdos-problem-1039",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:50+00:00",
    "updated_at": "2026-08-18T02:54:50+00:00"
  },
  "P10270": {
    "problem_number": 10270,
    "slug": "erdos-problem-103",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:45+00:00",
    "updated_at": "2026-08-18T02:52:45+00:00"
  },
  "P10708": {
    "problem_number": 10708,
    "slug": "erdos-problem-1040",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:51+00:00",
    "updated_at": "2026-08-18T02:54:51+00:00"
  },
  "P8234": {
    "problem_number": 8234,
    "slug": "open-fc-13d7bf3925773a1eb6a7-erdos-1041",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:29+00:00",
    "updated_at": "2026-08-17T18:37:31+00:00"
  },
  "P3224": {
    "problem_number": 3224,
    "slug": "erdos-problem-1041",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:54:48+00:00",
    "updated_at": "2026-08-12T05:54:54+00:00"
  },
  "P10272": {
    "problem_number": 10272,
    "slug": "erdos-problem-104",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:46+00:00",
    "updated_at": "2026-08-18T02:52:46+00:00"
  },
  "P10710": {
    "problem_number": 10710,
    "slug": "erdos-problem-1053",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:51+00:00",
    "updated_at": "2026-08-18T02:54:52+00:00"
  },
  "P10190": {
    "problem_number": 10190,
    "slug": "open-fc-8d77a614d79530ae1fa6-erdos-1056-variants-noll-simmons",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:40+00:00",
    "updated_at": "2026-08-18T02:51:40+00:00"
  },
  "P10162": {
    "problem_number": 10162,
    "slug": "open-fc-45c0c594235357f0abfc-erdos-1056",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:30+00:00",
    "updated_at": "2026-08-18T02:51:30+00:00"
  },
  "P10186": {
    "problem_number": 10186,
    "slug": "open-fc-7feee4bb5d29c6fd78dc-erdos-1057-variants-pomerance",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:38+00:00",
    "updated_at": "2026-08-18T02:51:39+00:00"
  },
  "P10166": {
    "problem_number": 10166,
    "slug": "open-fc-49f8eb6b40c0dd56896b-erdos-1057",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:31+00:00",
    "updated_at": "2026-08-18T02:51:32+00:00"
  },
  "P10214": {
    "problem_number": 10214,
    "slug": "open-fc-bf6b549faacdb183b826-erdos-1060-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:49+00:00",
    "updated_at": "2026-08-18T02:51:49+00:00"
  },
  "P10100": {
    "problem_number": 10100,
    "slug": "open-fc-11d03e1c913792a48635-erdos-1060-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:09+00:00",
    "updated_at": "2026-08-18T02:51:10+00:00"
  },
  "P10712": {
    "problem_number": 10712,
    "slug": "erdos-problem-1062",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:52+00:00",
    "updated_at": "2026-08-18T02:54:52+00:00"
  },
  "P10714": {
    "problem_number": 10714,
    "slug": "erdos-problem-1063",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:53+00:00",
    "updated_at": "2026-08-18T02:54:53+00:00"
  },
  "P10716": {
    "problem_number": 10716,
    "slug": "erdos-problem-1066",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:53+00:00",
    "updated_at": "2026-08-18T02:54:54+00:00"
  },
  "P10246": {
    "problem_number": 10246,
    "slug": "open-fc-ee1305fea7edc12355b3-erdos-1068",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:01+00:00",
    "updated_at": "2026-08-18T02:52:02+00:00"
  },
  "P10718": {
    "problem_number": 10718,
    "slug": "erdos-problem-1070",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:54+00:00",
    "updated_at": "2026-08-18T02:54:54+00:00"
  },
  "P10720": {
    "problem_number": 10720,
    "slug": "erdos-problem-1073",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:54+00:00",
    "updated_at": "2026-08-18T02:54:55+00:00"
  },
  "P10722": {
    "problem_number": 10722,
    "slug": "erdos-problem-1075",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:55+00:00",
    "updated_at": "2026-08-18T02:54:56+00:00"
  },
  "P10724": {
    "problem_number": 10724,
    "slug": "erdos-problem-1083",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:56+00:00",
    "updated_at": "2026-08-18T02:54:56+00:00"
  },
  "P10726": {
    "problem_number": 10726,
    "slug": "erdos-problem-1086",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:56+00:00",
    "updated_at": "2026-08-18T02:54:57+00:00"
  },
  "P10728": {
    "problem_number": 10728,
    "slug": "erdos-problem-1087",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:57+00:00",
    "updated_at": "2026-08-18T02:54:57+00:00"
  },
  "P10730": {
    "problem_number": 10730,
    "slug": "erdos-problem-1088",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:57+00:00",
    "updated_at": "2026-08-18T02:54:58+00:00"
  },
  "P10732": {
    "problem_number": 10732,
    "slug": "erdos-problem-1093",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:58+00:00",
    "updated_at": "2026-08-18T02:54:58+00:00"
  },
  "P10204": {
    "problem_number": 10204,
    "slug": "open-fc-a8b93600040b910dfd81-erdos-1094",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:45+00:00",
    "updated_at": "2026-08-18T02:51:46+00:00"
  },
  "P10174": {
    "problem_number": 10174,
    "slug": "open-fc-5d80db16d5ead3990761-erdos-1095-variants-log-equivalent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:34+00:00",
    "updated_at": "2026-08-18T02:51:35+00:00"
  },
  "P10184": {
    "problem_number": 10184,
    "slug": "open-fc-7c010ee67c58f90f1d89-erdos-1095-variants-lower-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:38+00:00",
    "updated_at": "2026-08-18T02:51:38+00:00"
  },
  "P10178": {
    "problem_number": 10178,
    "slug": "open-fc-6a56a9d83b4949581a2f-erdos-1095-variants-upper-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:36+00:00",
    "updated_at": "2026-08-18T02:51:36+00:00"
  },
  "P10734": {
    "problem_number": 10734,
    "slug": "erdos-problem-1097",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:59+00:00",
    "updated_at": "2026-08-18T02:54:59+00:00"
  },
  "P10736": {
    "problem_number": 10736,
    "slug": "erdos-problem-1100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:59+00:00",
    "updated_at": "2026-08-18T02:55:00+00:00"
  },
  "P10738": {
    "problem_number": 10738,
    "slug": "erdos-problem-1101",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:00+00:00",
    "updated_at": "2026-08-18T02:55:00+00:00"
  },
  "P10740": {
    "problem_number": 10740,
    "slug": "erdos-problem-1103",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:00+00:00",
    "updated_at": "2026-08-18T02:55:01+00:00"
  },
  "P10742": {
    "problem_number": 10742,
    "slug": "erdos-problem-1104",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:01+00:00",
    "updated_at": "2026-08-18T02:55:01+00:00"
  },
  "P10252": {
    "problem_number": 10252,
    "slug": "open-fc-ff3eba8709ef2b0209bc-erdos-1109-variants-polylog",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:03+00:00",
    "updated_at": "2026-08-18T02:52:04+00:00"
  },
  "P10152": {
    "problem_number": 10152,
    "slug": "open-fc-3dd90e503855d1409d5b-erdos-1110",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:26+00:00",
    "updated_at": "2026-08-18T02:51:27+00:00"
  },
  "P10744": {
    "problem_number": 10744,
    "slug": "erdos-problem-1111",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:01+00:00",
    "updated_at": "2026-08-18T02:55:02+00:00"
  },
  "P10746": {
    "problem_number": 10746,
    "slug": "erdos-problem-1113",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:02+00:00",
    "updated_at": "2026-08-18T02:55:02+00:00"
  },
  "P10748": {
    "problem_number": 10748,
    "slug": "erdos-problem-1117",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:03+00:00",
    "updated_at": "2026-08-18T02:55:03+00:00"
  },
  "P10274": {
    "problem_number": 10274,
    "slug": "erdos-problem-111",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:46+00:00",
    "updated_at": "2026-08-18T02:52:47+00:00"
  },
  "P10750": {
    "problem_number": 10750,
    "slug": "erdos-problem-1120",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:03+00:00",
    "updated_at": "2026-08-18T02:55:04+00:00"
  },
  "P10752": {
    "problem_number": 10752,
    "slug": "erdos-problem-1122",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:04+00:00",
    "updated_at": "2026-08-18T02:55:04+00:00"
  },
  "P10276": {
    "problem_number": 10276,
    "slug": "erdos-problem-112",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:47+00:00",
    "updated_at": "2026-08-18T02:52:47+00:00"
  },
  "P10754": {
    "problem_number": 10754,
    "slug": "erdos-problem-1131",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:04+00:00",
    "updated_at": "2026-08-18T02:55:05+00:00"
  },
  "P10756": {
    "problem_number": 10756,
    "slug": "erdos-problem-1132",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:05+00:00",
    "updated_at": "2026-08-18T02:55:05+00:00"
  },
  "P10758": {
    "problem_number": 10758,
    "slug": "erdos-problem-1133",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:05+00:00",
    "updated_at": "2026-08-18T02:55:06+00:00"
  },
  "P10160": {
    "problem_number": 10160,
    "slug": "open-fc-42e39886b2b9beb4d9f1-erdos-1135",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:29+00:00",
    "updated_at": "2026-08-18T02:51:30+00:00"
  },
  "P10130": {
    "problem_number": 10130,
    "slug": "open-fc-253b028d43849d1fbe54-erdos-1145",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:19+00:00",
    "updated_at": "2026-08-18T02:51:19+00:00"
  },
  "P10278": {
    "problem_number": 10278,
    "slug": "erdos-problem-117",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:47+00:00",
    "updated_at": "2026-08-18T02:52:48+00:00"
  },
  "P10142": {
    "problem_number": 10142,
    "slug": "open-fc-300b86a3ed2f65815068-erdos-1209-parts-iii-b",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:23+00:00",
    "updated_at": "2026-08-18T02:51:23+00:00"
  },
  "P10154": {
    "problem_number": 10154,
    "slug": "open-fc-3f603cdfb2676093c776-erdos-1209-parts-iii-d",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:27+00:00",
    "updated_at": "2026-08-18T02:51:27+00:00"
  },
  "P10218": {
    "problem_number": 10218,
    "slug": "open-fc-c0988eb1aef3823fc935-erdos-1209-parts-iii-c",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:50+00:00",
    "updated_at": "2026-08-18T02:51:51+00:00"
  },
  "P10172": {
    "problem_number": 10172,
    "slug": "open-fc-56ea46c3761b263c517f-erdos-1210",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:33+00:00",
    "updated_at": "2026-08-18T02:51:34+00:00"
  },
  "P10122": {
    "problem_number": 10122,
    "slug": "open-fc-216463a3549a2b3c590c-erdos-1210-variants-er80-correction",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:16+00:00",
    "updated_at": "2026-08-18T02:51:17+00:00"
  },
  "P10280": {
    "problem_number": 10280,
    "slug": "erdos-problem-122",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:48+00:00",
    "updated_at": "2026-08-18T02:52:48+00:00"
  },
  "P3038": {
    "problem_number": 3038,
    "slug": "erdos-problem-124",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:10+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8528": {
    "problem_number": 8528,
    "slug": "open-fc-658ce2a82ce0788c0585-erdos124-ne-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:14+00:00",
    "updated_at": "2026-08-17T18:54:15+00:00"
  },
  "P10282": {
    "problem_number": 10282,
    "slug": "erdos-problem-129",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:49+00:00",
    "updated_at": "2026-08-18T02:52:49+00:00"
  },
  "P10284": {
    "problem_number": 10284,
    "slug": "erdos-problem-130",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:49+00:00",
    "updated_at": "2026-08-18T02:52:49+00:00"
  },
  "P10286": {
    "problem_number": 10286,
    "slug": "erdos-problem-131",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:50+00:00",
    "updated_at": "2026-08-18T02:52:50+00:00"
  },
  "P10288": {
    "problem_number": 10288,
    "slug": "erdos-problem-132",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:50+00:00",
    "updated_at": "2026-08-18T02:52:51+00:00"
  },
  "P9882": {
    "problem_number": 9882,
    "slug": "open-fc-63242c5db67f5696358a-erdos-14-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:13+00:00",
    "updated_at": "2026-08-17T20:04:14+00:00"
  },
  "P9536": {
    "problem_number": 9536,
    "slug": "open-fc-b55c2f36ffd409a11300-erdos-143-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:46+00:00",
    "updated_at": "2026-08-17T19:54:48+00:00"
  },
  "P10290": {
    "problem_number": 10290,
    "slug": "erdos-problem-148",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:51+00:00",
    "updated_at": "2026-08-18T02:52:51+00:00"
  },
  "P10292": {
    "problem_number": 10292,
    "slug": "erdos-problem-149",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:51+00:00",
    "updated_at": "2026-08-18T02:52:52+00:00"
  },
  "P10294": {
    "problem_number": 10294,
    "slug": "erdos-problem-151",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:52+00:00",
    "updated_at": "2026-08-18T02:52:53+00:00"
  },
  "P3066": {
    "problem_number": 3066,
    "slug": "erdos-152-isolated-sidon-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:41+00:00",
    "updated_at": "2026-08-02T12:48:59+00:00"
  },
  "P10296": {
    "problem_number": 10296,
    "slug": "erdos-problem-159",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:53+00:00",
    "updated_at": "2026-08-18T02:52:53+00:00"
  },
  "P10298": {
    "problem_number": 10298,
    "slug": "erdos-problem-161",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:53+00:00",
    "updated_at": "2026-08-18T02:52:54+00:00"
  },
  "P10300": {
    "problem_number": 10300,
    "slug": "erdos-problem-162",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:54+00:00",
    "updated_at": "2026-08-18T02:52:54+00:00"
  },
  "P10302": {
    "problem_number": 10302,
    "slug": "erdos-problem-165",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:54+00:00",
    "updated_at": "2026-08-18T02:52:55+00:00"
  },
  "P10304": {
    "problem_number": 10304,
    "slug": "erdos-problem-169",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:55+00:00",
    "updated_at": "2026-08-18T02:52:55+00:00"
  },
  "P10306": {
    "problem_number": 10306,
    "slug": "erdos-problem-173",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:56+00:00",
    "updated_at": "2026-08-18T02:52:56+00:00"
  },
  "P10308": {
    "problem_number": 10308,
    "slug": "erdos-problem-174",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:56+00:00",
    "updated_at": "2026-08-18T02:52:57+00:00"
  },
  "P10310": {
    "problem_number": 10310,
    "slug": "erdos-problem-176",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:57+00:00",
    "updated_at": "2026-08-18T02:52:57+00:00"
  },
  "P10312": {
    "problem_number": 10312,
    "slug": "erdos-problem-177",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:57+00:00",
    "updated_at": "2026-08-18T02:52:58+00:00"
  },
  "P10314": {
    "problem_number": 10314,
    "slug": "erdos-problem-181",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:58+00:00",
    "updated_at": "2026-08-18T02:52:58+00:00"
  },
  "P3572": {
    "problem_number": 3572,
    "slug": "erdos-183",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:53:25+00:00",
    "updated_at": "2026-08-18T05:54:04+00:00"
  },
  "P10316": {
    "problem_number": 10316,
    "slug": "erdos-problem-187",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:58+00:00",
    "updated_at": "2026-08-18T02:52:59+00:00"
  },
  "P10318": {
    "problem_number": 10318,
    "slug": "erdos-problem-201",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:59+00:00",
    "updated_at": "2026-08-18T02:52:59+00:00"
  },
  "P8418": {
    "problem_number": 8418,
    "slug": "open-fc-2bafe800eb2e37a93524-erdos-203",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:39+00:00",
    "updated_at": "2026-08-17T18:50:46+00:00"
  },
  "P10320": {
    "problem_number": 10320,
    "slug": "erdos-problem-217",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:00+00:00",
    "updated_at": "2026-08-18T02:53:00+00:00"
  },
  "P10322": {
    "problem_number": 10322,
    "slug": "erdos-problem-222",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:00+00:00",
    "updated_at": "2026-08-18T02:53:01+00:00"
  },
  "P10324": {
    "problem_number": 10324,
    "slug": "erdos-problem-254",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:01+00:00",
    "updated_at": "2026-08-18T02:53:01+00:00"
  },
  "P10326": {
    "problem_number": 10326,
    "slug": "erdos-problem-256",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:01+00:00",
    "updated_at": "2026-08-18T02:53:02+00:00"
  },
  "P2978": {
    "problem_number": 2978,
    "slug": "erdos-problem-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:44+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8588": {
    "problem_number": 8588,
    "slug": "open-fc-30e4c73a8b744a32adf8-erdos-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:28+00:00",
    "updated_at": "2026-08-17T18:56:28+00:00"
  },
  "P10328": {
    "problem_number": 10328,
    "slug": "erdos-problem-261",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:02+00:00",
    "updated_at": "2026-08-18T02:53:02+00:00"
  },
  "P10330": {
    "problem_number": 10330,
    "slug": "erdos-problem-265",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:03+00:00",
    "updated_at": "2026-08-18T02:53:03+00:00"
  },
  "P10332": {
    "problem_number": 10332,
    "slug": "erdos-problem-271",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:03+00:00",
    "updated_at": "2026-08-18T02:53:04+00:00"
  },
  "P10334": {
    "problem_number": 10334,
    "slug": "erdos-problem-278",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:04+00:00",
    "updated_at": "2026-08-18T02:53:04+00:00"
  },
  "P9990": {
    "problem_number": 9990,
    "slug": "open-fc-b3bdc7d3d295bbd27d1f-erdos-279",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:15+00:00",
    "updated_at": "2026-08-17T20:05:15+00:00"
  },
  "P10336": {
    "problem_number": 10336,
    "slug": "erdos-problem-293",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:04+00:00",
    "updated_at": "2026-08-18T02:53:05+00:00"
  },
  "P2982": {
    "problem_number": 2982,
    "slug": "erdos-problem-30",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:49+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9054": {
    "problem_number": 9054,
    "slug": "open-fc-a16e7d0018af330f7017-erdos-30",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:22+00:00",
    "updated_at": "2026-08-17T19:46:24+00:00"
  },
  "P10338": {
    "problem_number": 10338,
    "slug": "erdos-problem-301",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:05+00:00",
    "updated_at": "2026-08-18T02:53:05+00:00"
  },
  "P10340": {
    "problem_number": 10340,
    "slug": "erdos-problem-302",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:05+00:00",
    "updated_at": "2026-08-18T02:53:06+00:00"
  },
  "P8290": {
    "problem_number": 8290,
    "slug": "open-fc-1c83ef6ec943d12a27a3-erdos-307",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:19+00:00",
    "updated_at": "2026-08-17T18:38:22+00:00"
  },
  "P3312": {
    "problem_number": 3312,
    "slug": "erdos-problem-307",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:28+00:00",
    "updated_at": "2026-08-12T06:04:30+00:00"
  },
  "P10342": {
    "problem_number": 10342,
    "slug": "erdos-problem-311",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:06+00:00",
    "updated_at": "2026-08-18T02:53:06+00:00"
  },
  "P9392": {
    "problem_number": 9392,
    "slug": "open-fc-401eb872edc63786f51c-erdos-317",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:09+00:00",
    "updated_at": "2026-08-17T19:52:11+00:00"
  },
  "P10344": {
    "problem_number": 10344,
    "slug": "erdos-problem-322",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:07+00:00",
    "updated_at": "2026-08-18T02:53:07+00:00"
  },
  "P10346": {
    "problem_number": 10346,
    "slug": "erdos-problem-327",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:07+00:00",
    "updated_at": "2026-08-18T02:53:08+00:00"
  },
  "P10348": {
    "problem_number": 10348,
    "slug": "erdos-problem-334",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:08+00:00",
    "updated_at": "2026-08-18T02:53:08+00:00"
  },
  "P10350": {
    "problem_number": 10350,
    "slug": "erdos-problem-335",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:08+00:00",
    "updated_at": "2026-08-18T02:53:09+00:00"
  },
  "P10352": {
    "problem_number": 10352,
    "slug": "erdos-problem-336",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:09+00:00",
    "updated_at": "2026-08-18T02:53:09+00:00"
  },
  "P10354": {
    "problem_number": 10354,
    "slug": "erdos-problem-338",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:09+00:00",
    "updated_at": "2026-08-18T02:53:10+00:00"
  },
  "P10356": {
    "problem_number": 10356,
    "slug": "erdos-problem-345",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:10+00:00",
    "updated_at": "2026-08-18T02:53:10+00:00"
  },
  "P9532": {
    "problem_number": 9532,
    "slug": "open-fc-b1cee316b4daa7125438-erdos-348",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:40+00:00",
    "updated_at": "2026-08-17T19:54:40+00:00"
  },
  "P10146": {
    "problem_number": 10146,
    "slug": "open-fc-363eb3caed3071b62ef1-erdos-361-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:24+00:00",
    "updated_at": "2026-08-18T02:51:24+00:00"
  },
  "P10104": {
    "problem_number": 10104,
    "slug": "open-fc-1225db26a4262ecc61e8-erdos-361",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:10+00:00",
    "updated_at": "2026-08-18T02:51:11+00:00"
  },
  "P10358": {
    "problem_number": 10358,
    "slug": "erdos-problem-365",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:11+00:00",
    "updated_at": "2026-08-18T02:53:11+00:00"
  },
  "P10360": {
    "problem_number": 10360,
    "slug": "erdos-problem-367",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:11+00:00",
    "updated_at": "2026-08-18T02:53:11+00:00"
  },
  "P10362": {
    "problem_number": 10362,
    "slug": "erdos-problem-368",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:12+00:00",
    "updated_at": "2026-08-18T02:53:12+00:00"
  },
  "P10364": {
    "problem_number": 10364,
    "slug": "erdos-problem-374",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:12+00:00",
    "updated_at": "2026-08-18T02:53:13+00:00"
  },
  "P10366": {
    "problem_number": 10366,
    "slug": "erdos-problem-382",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:13+00:00",
    "updated_at": "2026-08-18T02:53:13+00:00"
  },
  "P8824": {
    "problem_number": 8824,
    "slug": "open-fc-989e46dbee8ebbf146df-erdos-385-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:33+00:00",
    "updated_at": "2026-08-17T19:24:40+00:00"
  },
  "P10368": {
    "problem_number": 10368,
    "slug": "erdos-problem-388",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:13+00:00",
    "updated_at": "2026-08-18T02:53:14+00:00"
  },
  "P10370": {
    "problem_number": 10370,
    "slug": "erdos-problem-393",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:14+00:00",
    "updated_at": "2026-08-18T02:53:14+00:00"
  },
  "P2992": {
    "problem_number": 2992,
    "slug": "erdos-problem-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:03+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8458": {
    "problem_number": 8458,
    "slug": "open-fc-40215f03705a2b2faddd-erdos-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:11+00:00",
    "updated_at": "2026-08-17T18:52:11+00:00"
  },
  "P10372": {
    "problem_number": 10372,
    "slug": "erdos-problem-404",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:14+00:00",
    "updated_at": "2026-08-18T02:53:15+00:00"
  },
  "P10374": {
    "problem_number": 10374,
    "slug": "erdos-problem-408",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:15+00:00",
    "updated_at": "2026-08-18T02:53:15+00:00"
  },
  "P2994": {
    "problem_number": 2994,
    "slug": "erdos-problem-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:06+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9704": {
    "problem_number": 9704,
    "slug": "open-fc-971b5c3ff0400c5d769f-erdos-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:57+00:00",
    "updated_at": "2026-08-17T20:01:57+00:00"
  },
  "P10376": {
    "problem_number": 10376,
    "slug": "erdos-problem-411",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:16+00:00",
    "updated_at": "2026-08-18T02:53:16+00:00"
  },
  "P9158": {
    "problem_number": 9158,
    "slug": "open-fc-f2328d2ea61208561dfc-erdos-414",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:52+00:00",
    "updated_at": "2026-08-17T19:47:52+00:00"
  },
  "P3202": {
    "problem_number": 3202,
    "slug": "erdos-problem-414",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:07+00:00",
    "updated_at": "2026-08-12T05:52:19+00:00"
  },
  "P10378": {
    "problem_number": 10378,
    "slug": "erdos-problem-415",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:16+00:00",
    "updated_at": "2026-08-18T02:53:16+00:00"
  },
  "P10380": {
    "problem_number": 10380,
    "slug": "erdos-problem-420",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:17+00:00",
    "updated_at": "2026-08-18T02:53:17+00:00"
  },
  "P10382": {
    "problem_number": 10382,
    "slug": "erdos-problem-423",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:17+00:00",
    "updated_at": "2026-08-18T02:53:18+00:00"
  },
  "P10384": {
    "problem_number": 10384,
    "slug": "erdos-problem-425",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:18+00:00",
    "updated_at": "2026-08-18T02:53:18+00:00"
  },
  "P10386": {
    "problem_number": 10386,
    "slug": "erdos-problem-430",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:18+00:00",
    "updated_at": "2026-08-18T02:53:19+00:00"
  },
  "P10388": {
    "problem_number": 10388,
    "slug": "erdos-problem-431",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:19+00:00",
    "updated_at": "2026-08-18T02:53:19+00:00"
  },
  "P10390": {
    "problem_number": 10390,
    "slug": "erdos-problem-432",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:20+00:00",
    "updated_at": "2026-08-18T02:53:20+00:00"
  },
  "P10392": {
    "problem_number": 10392,
    "slug": "erdos-problem-436",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:20+00:00",
    "updated_at": "2026-08-18T02:53:21+00:00"
  },
  "P8958": {
    "problem_number": 8958,
    "slug": "open-fc-feb96f92acf5c3d8e594-erdos-445",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:20+00:00",
    "updated_at": "2026-08-17T19:41:21+00:00"
  },
  "P9520": {
    "problem_number": 9520,
    "slug": "open-fc-a933a5e378445d57bb20-erdos-44",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:36+00:00",
    "updated_at": "2026-08-17T19:54:36+00:00"
  },
  "P10394": {
    "problem_number": 10394,
    "slug": "erdos-problem-450",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:21+00:00",
    "updated_at": "2026-08-18T02:53:21+00:00"
  },
  "P10396": {
    "problem_number": 10396,
    "slug": "erdos-problem-451",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:21+00:00",
    "updated_at": "2026-08-18T02:53:22+00:00"
  },
  "P10398": {
    "problem_number": 10398,
    "slug": "erdos-problem-452",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:22+00:00",
    "updated_at": "2026-08-18T02:53:22+00:00"
  },
  "P9534": {
    "problem_number": 9534,
    "slug": "open-fc-b375ea95cd546c329e63-erdos-458",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:42+00:00",
    "updated_at": "2026-08-17T19:54:44+00:00"
  },
  "P3164": {
    "problem_number": 3164,
    "slug": "erdos-problem-458",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:45:17+00:00",
    "updated_at": "2026-08-12T05:45:51+00:00"
  },
  "P10400": {
    "problem_number": 10400,
    "slug": "erdos-problem-460",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:23+00:00",
    "updated_at": "2026-08-18T02:53:23+00:00"
  },
  "P10402": {
    "problem_number": 10402,
    "slug": "erdos-problem-461",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:23+00:00",
    "updated_at": "2026-08-18T02:53:24+00:00"
  },
  "P10404": {
    "problem_number": 10404,
    "slug": "erdos-problem-467",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:24+00:00",
    "updated_at": "2026-08-18T02:53:24+00:00"
  },
  "P10406": {
    "problem_number": 10406,
    "slug": "erdos-problem-472",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:24+00:00",
    "updated_at": "2026-08-18T02:53:25+00:00"
  },
  "P10408": {
    "problem_number": 10408,
    "slug": "erdos-problem-478",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:25+00:00",
    "updated_at": "2026-08-18T02:53:25+00:00"
  },
  "P10410": {
    "problem_number": 10410,
    "slug": "erdos-problem-483",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:26+00:00",
    "updated_at": "2026-08-18T02:53:26+00:00"
  },
  "P10412": {
    "problem_number": 10412,
    "slug": "erdos-problem-489",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:26+00:00",
    "updated_at": "2026-08-18T02:53:26+00:00"
  },
  "P10414": {
    "problem_number": 10414,
    "slug": "erdos-problem-500",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:27+00:00",
    "updated_at": "2026-08-18T02:53:27+00:00"
  },
  "P10416": {
    "problem_number": 10416,
    "slug": "erdos-problem-514",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:27+00:00",
    "updated_at": "2026-08-18T02:53:28+00:00"
  },
  "P10418": {
    "problem_number": 10418,
    "slug": "erdos-problem-521",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:28+00:00",
    "updated_at": "2026-08-18T02:53:28+00:00"
  },
  "P10420": {
    "problem_number": 10420,
    "slug": "erdos-problem-524",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:28+00:00",
    "updated_at": "2026-08-18T02:53:29+00:00"
  },
  "P10422": {
    "problem_number": 10422,
    "slug": "erdos-problem-528",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:29+00:00",
    "updated_at": "2026-08-18T02:53:29+00:00"
  },
  "P10424": {
    "problem_number": 10424,
    "slug": "erdos-problem-529",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:29+00:00",
    "updated_at": "2026-08-18T02:53:30+00:00"
  },
  "P10426": {
    "problem_number": 10426,
    "slug": "erdos-problem-530",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:30+00:00",
    "updated_at": "2026-08-18T02:53:30+00:00"
  },
  "P10428": {
    "problem_number": 10428,
    "slug": "erdos-problem-531",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:30+00:00",
    "updated_at": "2026-08-18T02:53:31+00:00"
  },
  "P9048": {
    "problem_number": 9048,
    "slug": "open-fc-9ce347c6636dc31679de-erdos-535-variants-first-open-case",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:10+00:00",
    "updated_at": "2026-08-17T19:46:12+00:00"
  },
  "P10430": {
    "problem_number": 10430,
    "slug": "erdos-problem-538",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:31+00:00",
    "updated_at": "2026-08-18T02:53:31+00:00"
  },
  "P10432": {
    "problem_number": 10432,
    "slug": "erdos-problem-544",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:32+00:00",
    "updated_at": "2026-08-18T02:53:32+00:00"
  },
  "P10434": {
    "problem_number": 10434,
    "slug": "erdos-problem-545",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:32+00:00",
    "updated_at": "2026-08-18T02:53:33+00:00"
  },
  "P10436": {
    "problem_number": 10436,
    "slug": "erdos-problem-550",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:33+00:00",
    "updated_at": "2026-08-18T02:53:33+00:00"
  },
  "P10438": {
    "problem_number": 10438,
    "slug": "erdos-problem-552",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:33+00:00",
    "updated_at": "2026-08-18T02:53:34+00:00"
  },
  "P10440": {
    "problem_number": 10440,
    "slug": "erdos-problem-554",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:34+00:00",
    "updated_at": "2026-08-18T02:53:34+00:00"
  },
  "P10442": {
    "problem_number": 10442,
    "slug": "erdos-problem-555",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:34+00:00",
    "updated_at": "2026-08-18T02:53:35+00:00"
  },
  "P10444": {
    "problem_number": 10444,
    "slug": "erdos-problem-557",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:35+00:00",
    "updated_at": "2026-08-18T02:53:35+00:00"
  },
  "P10446": {
    "problem_number": 10446,
    "slug": "erdos-problem-558",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:36+00:00",
    "updated_at": "2026-08-18T02:53:36+00:00"
  },
  "P10448": {
    "problem_number": 10448,
    "slug": "erdos-problem-560",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:36+00:00",
    "updated_at": "2026-08-18T02:53:36+00:00"
  },
  "P10450": {
    "problem_number": 10450,
    "slug": "erdos-problem-561",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:37+00:00",
    "updated_at": "2026-08-18T02:53:37+00:00"
  },
  "P10452": {
    "problem_number": 10452,
    "slug": "erdos-problem-563",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:37+00:00",
    "updated_at": "2026-08-18T02:53:38+00:00"
  },
  "P10454": {
    "problem_number": 10454,
    "slug": "erdos-problem-568",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:38+00:00",
    "updated_at": "2026-08-18T02:53:38+00:00"
  },
  "P10456": {
    "problem_number": 10456,
    "slug": "erdos-problem-569",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:38+00:00",
    "updated_at": "2026-08-18T02:53:39+00:00"
  },
  "P10458": {
    "problem_number": 10458,
    "slug": "erdos-problem-571",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:39+00:00",
    "updated_at": "2026-08-18T02:53:39+00:00"
  },
  "P10460": {
    "problem_number": 10460,
    "slug": "erdos-problem-572",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:39+00:00",
    "updated_at": "2026-08-18T02:53:40+00:00"
  },
  "P10462": {
    "problem_number": 10462,
    "slug": "erdos-problem-573",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:40+00:00",
    "updated_at": "2026-08-18T02:53:40+00:00"
  },
  "P10464": {
    "problem_number": 10464,
    "slug": "erdos-problem-575",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:40+00:00",
    "updated_at": "2026-08-18T02:53:41+00:00"
  },
  "P10466": {
    "problem_number": 10466,
    "slug": "erdos-problem-576",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:41+00:00",
    "updated_at": "2026-08-18T02:53:41+00:00"
  },
  "P10468": {
    "problem_number": 10468,
    "slug": "erdos-problem-585",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:42+00:00",
    "updated_at": "2026-08-18T02:53:42+00:00"
  },
  "P10470": {
    "problem_number": 10470,
    "slug": "erdos-problem-588",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:42+00:00",
    "updated_at": "2026-08-18T02:53:42+00:00"
  },
  "P10472": {
    "problem_number": 10472,
    "slug": "erdos-problem-589",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:43+00:00",
    "updated_at": "2026-08-18T02:53:43+00:00"
  },
  "P9740": {
    "problem_number": 9740,
    "slug": "open-fc-b02e00fd948c3d9b8708-erdos-595",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:12+00:00",
    "updated_at": "2026-08-17T20:02:13+00:00"
  },
  "P10474": {
    "problem_number": 10474,
    "slug": "erdos-problem-597",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:43+00:00",
    "updated_at": "2026-08-18T02:53:44+00:00"
  },
  "P8728": {
    "problem_number": 8728,
    "slug": "open-fc-40c30be510245621e9ac-erdos-598",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:21+00:00",
    "updated_at": "2026-08-17T19:11:38+00:00"
  },
  "P10202": {
    "problem_number": 10202,
    "slug": "open-fc-a6d2b30296a280a9ef92-erdos-5-variants-dense",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:44+00:00",
    "updated_at": "2026-08-18T02:51:45+00:00"
  },
  "P10476": {
    "problem_number": 10476,
    "slug": "erdos-problem-601",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:44+00:00",
    "updated_at": "2026-08-18T02:53:44+00:00"
  },
  "P10478": {
    "problem_number": 10478,
    "slug": "erdos-problem-604",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:44+00:00",
    "updated_at": "2026-08-18T02:53:45+00:00"
  },
  "P10480": {
    "problem_number": 10480,
    "slug": "erdos-problem-609",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:45+00:00",
    "updated_at": "2026-08-18T02:53:45+00:00"
  },
  "P10138": {
    "problem_number": 10138,
    "slug": "open-fc-2eaf5cfcf8b78757e064-erdos-60",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:21+00:00",
    "updated_at": "2026-08-18T02:51:22+00:00"
  },
  "P10482": {
    "problem_number": 10482,
    "slug": "erdos-problem-611",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:46+00:00",
    "updated_at": "2026-08-18T02:53:46+00:00"
  },
  "P10484": {
    "problem_number": 10484,
    "slug": "erdos-problem-612",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:46+00:00",
    "updated_at": "2026-08-18T02:53:46+00:00"
  },
  "P10486": {
    "problem_number": 10486,
    "slug": "erdos-problem-616",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:47+00:00",
    "updated_at": "2026-08-18T02:53:47+00:00"
  },
  "P10488": {
    "problem_number": 10488,
    "slug": "erdos-problem-620",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:47+00:00",
    "updated_at": "2026-08-18T02:53:48+00:00"
  },
  "P8784": {
    "problem_number": 8784,
    "slug": "open-fc-5ee558fe8cc44751fe9f-erdos-623",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:20:25+00:00",
    "updated_at": "2026-08-17T19:20:31+00:00"
  },
  "P10490": {
    "problem_number": 10490,
    "slug": "erdos-problem-625",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:48+00:00",
    "updated_at": "2026-08-18T02:53:48+00:00"
  },
  "P10492": {
    "problem_number": 10492,
    "slug": "erdos-problem-626",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:48+00:00",
    "updated_at": "2026-08-18T02:53:49+00:00"
  },
  "P10494": {
    "problem_number": 10494,
    "slug": "erdos-problem-627",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:49+00:00",
    "updated_at": "2026-08-18T02:53:49+00:00"
  },
  "P10496": {
    "problem_number": 10496,
    "slug": "erdos-problem-629",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:49+00:00",
    "updated_at": "2026-08-18T02:53:50+00:00"
  },
  "P10254": {
    "problem_number": 10254,
    "slug": "erdos-problem-62",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:40+00:00",
    "updated_at": "2026-08-18T02:52:41+00:00"
  },
  "P10498": {
    "problem_number": 10498,
    "slug": "erdos-problem-634",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:50+00:00",
    "updated_at": "2026-08-18T02:53:50+00:00"
  },
  "P10500": {
    "problem_number": 10500,
    "slug": "erdos-problem-635",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:51+00:00",
    "updated_at": "2026-08-18T02:53:51+00:00"
  },
  "P10502": {
    "problem_number": 10502,
    "slug": "erdos-problem-638",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:51+00:00",
    "updated_at": "2026-08-18T02:53:52+00:00"
  },
  "P10504": {
    "problem_number": 10504,
    "slug": "erdos-problem-642",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:52+00:00",
    "updated_at": "2026-08-18T02:53:52+00:00"
  },
  "P10506": {
    "problem_number": 10506,
    "slug": "erdos-problem-643",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:52+00:00",
    "updated_at": "2026-08-18T02:53:53+00:00"
  },
  "P10508": {
    "problem_number": 10508,
    "slug": "erdos-problem-644",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:53+00:00",
    "updated_at": "2026-08-18T02:53:53+00:00"
  },
  "P10510": {
    "problem_number": 10510,
    "slug": "erdos-problem-654",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:54+00:00",
    "updated_at": "2026-08-18T02:53:54+00:00"
  },
  "P9120": {
    "problem_number": 9120,
    "slug": "open-fc-d453dbff88a96e113731-erdos-655-variants-general-position",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:41+00:00",
    "updated_at": "2026-08-17T19:47:42+00:00"
  },
  "P10512": {
    "problem_number": 10512,
    "slug": "erdos-problem-657",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:54+00:00",
    "updated_at": "2026-08-18T02:53:55+00:00"
  },
  "P10256": {
    "problem_number": 10256,
    "slug": "erdos-problem-65",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:41+00:00",
    "updated_at": "2026-08-18T02:52:41+00:00"
  },
  "P10242": {
    "problem_number": 10242,
    "slug": "open-fc-eb31a6a9f78f852578bd-erdos-660-variants-er75f",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:00+00:00",
    "updated_at": "2026-08-18T02:52:00+00:00"
  },
  "P10136": {
    "problem_number": 10136,
    "slug": "open-fc-29d97e1a3a1cb29cbecc-erdos-660",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:21+00:00",
    "updated_at": "2026-08-18T02:51:21+00:00"
  },
  "P10514": {
    "problem_number": 10514,
    "slug": "erdos-problem-661",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:55+00:00",
    "updated_at": "2026-08-18T02:53:55+00:00"
  },
  "P10516": {
    "problem_number": 10516,
    "slug": "erdos-problem-662",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:55+00:00",
    "updated_at": "2026-08-18T02:53:56+00:00"
  },
  "P10518": {
    "problem_number": 10518,
    "slug": "erdos-problem-663",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:56+00:00",
    "updated_at": "2026-08-18T02:53:56+00:00"
  },
  "P10520": {
    "problem_number": 10520,
    "slug": "erdos-problem-665",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:57+00:00",
    "updated_at": "2026-08-18T02:53:57+00:00"
  },
  "P10522": {
    "problem_number": 10522,
    "slug": "erdos-problem-667",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:57+00:00",
    "updated_at": "2026-08-18T02:53:57+00:00"
  },
  "P10524": {
    "problem_number": 10524,
    "slug": "erdos-problem-668",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:58+00:00",
    "updated_at": "2026-08-18T02:53:58+00:00"
  },
  "P10526": {
    "problem_number": 10526,
    "slug": "erdos-problem-669",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:58+00:00",
    "updated_at": "2026-08-18T02:53:59+00:00"
  },
  "P10528": {
    "problem_number": 10528,
    "slug": "erdos-problem-670",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:59+00:00",
    "updated_at": "2026-08-18T02:53:59+00:00"
  },
  "P10530": {
    "problem_number": 10530,
    "slug": "erdos-problem-671",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:53:59+00:00",
    "updated_at": "2026-08-18T02:54:00+00:00"
  },
  "P10532": {
    "problem_number": 10532,
    "slug": "erdos-problem-676",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:00+00:00",
    "updated_at": "2026-08-18T02:54:00+00:00"
  },
  "P10534": {
    "problem_number": 10534,
    "slug": "erdos-problem-679",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:00+00:00",
    "updated_at": "2026-08-18T02:54:01+00:00"
  },
  "P8240": {
    "problem_number": 8240,
    "slug": "open-fc-149559f0911324529df5-erdos-680-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:36+00:00",
    "updated_at": "2026-08-17T18:37:38+00:00"
  },
  "P9544": {
    "problem_number": 9544,
    "slug": "open-fc-bbd88c642b5c2f636a0c-erdos-680-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:56+00:00",
    "updated_at": "2026-08-17T19:54:58+00:00"
  },
  "P10536": {
    "problem_number": 10536,
    "slug": "erdos-problem-684",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:01+00:00",
    "updated_at": "2026-08-18T02:54:01+00:00"
  },
  "P10538": {
    "problem_number": 10538,
    "slug": "erdos-problem-685",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:02+00:00",
    "updated_at": "2026-08-18T02:54:02+00:00"
  },
  "P10540": {
    "problem_number": 10540,
    "slug": "erdos-problem-687",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:02+00:00",
    "updated_at": "2026-08-18T02:54:03+00:00"
  },
  "P10542": {
    "problem_number": 10542,
    "slug": "erdos-problem-691",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:03+00:00",
    "updated_at": "2026-08-18T02:54:03+00:00"
  },
  "P3268": {
    "problem_number": 3268,
    "slug": "erdos-problem-699",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:59:49+00:00",
    "updated_at": "2026-08-12T05:59:51+00:00"
  },
  "P8148": {
    "problem_number": 8148,
    "slug": "open-fc-074cec4cbc36a1a885e9-erdos-699",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:19+00:00",
    "updated_at": "2026-08-17T18:35:19+00:00"
  },
  "P10544": {
    "problem_number": 10544,
    "slug": "erdos-problem-704",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:03+00:00",
    "updated_at": "2026-08-18T02:54:04+00:00"
  },
  "P10546": {
    "problem_number": 10546,
    "slug": "erdos-problem-706",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:04+00:00",
    "updated_at": "2026-08-18T02:54:04+00:00"
  },
  "P10548": {
    "problem_number": 10548,
    "slug": "erdos-problem-708",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:05+00:00",
    "updated_at": "2026-08-18T02:54:05+00:00"
  },
  "P10550": {
    "problem_number": 10550,
    "slug": "erdos-problem-709",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:05+00:00",
    "updated_at": "2026-08-18T02:54:05+00:00"
  },
  "P10552": {
    "problem_number": 10552,
    "slug": "erdos-problem-710",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:06+00:00",
    "updated_at": "2026-08-18T02:54:06+00:00"
  },
  "P10554": {
    "problem_number": 10554,
    "slug": "erdos-problem-711",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:06+00:00",
    "updated_at": "2026-08-18T02:54:07+00:00"
  },
  "P10556": {
    "problem_number": 10556,
    "slug": "erdos-problem-712",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:07+00:00",
    "updated_at": "2026-08-18T02:54:07+00:00"
  },
  "P10558": {
    "problem_number": 10558,
    "slug": "erdos-problem-713",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:07+00:00",
    "updated_at": "2026-08-18T02:54:08+00:00"
  },
  "P10560": {
    "problem_number": 10560,
    "slug": "erdos-problem-714",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:08+00:00",
    "updated_at": "2026-08-18T02:54:08+00:00"
  },
  "P10562": {
    "problem_number": 10562,
    "slug": "erdos-problem-724",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:09+00:00",
    "updated_at": "2026-08-18T02:54:09+00:00"
  },
  "P10564": {
    "problem_number": 10564,
    "slug": "erdos-problem-725",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:09+00:00",
    "updated_at": "2026-08-18T02:54:09+00:00"
  },
  "P10566": {
    "problem_number": 10566,
    "slug": "erdos-problem-731",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:10+00:00",
    "updated_at": "2026-08-18T02:54:10+00:00"
  },
  "P10568": {
    "problem_number": 10568,
    "slug": "erdos-problem-734",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:10+00:00",
    "updated_at": "2026-08-18T02:54:11+00:00"
  },
  "P10570": {
    "problem_number": 10570,
    "slug": "erdos-problem-761",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:11+00:00",
    "updated_at": "2026-08-18T02:54:11+00:00"
  },
  "P10572": {
    "problem_number": 10572,
    "slug": "erdos-problem-766",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:11+00:00",
    "updated_at": "2026-08-18T02:54:12+00:00"
  },
  "P10574": {
    "problem_number": 10574,
    "slug": "erdos-problem-768",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:12+00:00",
    "updated_at": "2026-08-18T02:54:12+00:00"
  },
  "P10216": {
    "problem_number": 10216,
    "slug": "open-fc-c01def9e14fed2ec1eaf-erdos-769-variants-growth-rate",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:49+00:00",
    "updated_at": "2026-08-18T02:51:50+00:00"
  },
  "P10576": {
    "problem_number": 10576,
    "slug": "erdos-problem-773",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:12+00:00",
    "updated_at": "2026-08-18T02:54:13+00:00"
  },
  "P8842": {
    "problem_number": 8842,
    "slug": "open-fc-a9a0fc4948f71fa919ec-erdos-774",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:45+00:00",
    "updated_at": "2026-08-17T19:25:51+00:00"
  },
  "P10578": {
    "problem_number": 10578,
    "slug": "erdos-problem-776",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:13+00:00",
    "updated_at": "2026-08-18T02:54:13+00:00"
  },
  "P10580": {
    "problem_number": 10580,
    "slug": "erdos-problem-778",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:14+00:00",
    "updated_at": "2026-08-18T02:54:14+00:00"
  },
  "P10582": {
    "problem_number": 10582,
    "slug": "erdos-problem-782",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:14+00:00",
    "updated_at": "2026-08-18T02:54:15+00:00"
  },
  "P10584": {
    "problem_number": 10584,
    "slug": "erdos-problem-787",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:15+00:00",
    "updated_at": "2026-08-18T02:54:15+00:00"
  },
  "P10586": {
    "problem_number": 10586,
    "slug": "erdos-problem-788",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:15+00:00",
    "updated_at": "2026-08-18T02:54:16+00:00"
  },
  "P10258": {
    "problem_number": 10258,
    "slug": "erdos-problem-78",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:42+00:00",
    "updated_at": "2026-08-18T02:52:42+00:00"
  },
  "P10588": {
    "problem_number": 10588,
    "slug": "erdos-problem-790",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:16+00:00",
    "updated_at": "2026-08-18T02:54:16+00:00"
  },
  "P10590": {
    "problem_number": 10590,
    "slug": "erdos-problem-791",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:17+00:00",
    "updated_at": "2026-08-18T02:54:17+00:00"
  },
  "P10592": {
    "problem_number": 10592,
    "slug": "erdos-problem-792",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:17+00:00",
    "updated_at": "2026-08-18T02:54:17+00:00"
  },
  "P10594": {
    "problem_number": 10594,
    "slug": "erdos-problem-796",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:18+00:00",
    "updated_at": "2026-08-18T02:54:18+00:00"
  },
  "P10596": {
    "problem_number": 10596,
    "slug": "erdos-problem-802",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:18+00:00",
    "updated_at": "2026-08-18T02:54:19+00:00"
  },
  "P10598": {
    "problem_number": 10598,
    "slug": "erdos-problem-805",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:19+00:00",
    "updated_at": "2026-08-18T02:54:19+00:00"
  },
  "P10600": {
    "problem_number": 10600,
    "slug": "erdos-problem-809",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:19+00:00",
    "updated_at": "2026-08-18T02:54:20+00:00"
  },
  "P10126": {
    "problem_number": 10126,
    "slug": "open-fc-23d702f360c2816c37fd-erdos-80",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:18+00:00",
    "updated_at": "2026-08-18T02:51:18+00:00"
  },
  "P10602": {
    "problem_number": 10602,
    "slug": "erdos-problem-810",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:20+00:00",
    "updated_at": "2026-08-18T02:54:20+00:00"
  },
  "P10604": {
    "problem_number": 10604,
    "slug": "erdos-problem-811",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:21+00:00",
    "updated_at": "2026-08-18T02:54:21+00:00"
  },
  "P10606": {
    "problem_number": 10606,
    "slug": "erdos-problem-813",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:21+00:00",
    "updated_at": "2026-08-18T02:54:22+00:00"
  },
  "P10608": {
    "problem_number": 10608,
    "slug": "erdos-problem-819",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:22+00:00",
    "updated_at": "2026-08-18T02:54:22+00:00"
  },
  "P10260": {
    "problem_number": 10260,
    "slug": "erdos-problem-81",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:42+00:00",
    "updated_at": "2026-08-18T02:52:42+00:00"
  },
  "P10610": {
    "problem_number": 10610,
    "slug": "erdos-problem-820",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:22+00:00",
    "updated_at": "2026-08-18T02:54:23+00:00"
  },
  "P10612": {
    "problem_number": 10612,
    "slug": "erdos-problem-824",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:23+00:00",
    "updated_at": "2026-08-18T02:54:23+00:00"
  },
  "P10614": {
    "problem_number": 10614,
    "slug": "erdos-problem-827",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:24+00:00",
    "updated_at": "2026-08-18T02:54:24+00:00"
  },
  "P8578": {
    "problem_number": 8578,
    "slug": "open-fc-2d0e3e2d57553ebb9154-erdos-835-variants-johnson",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:11+00:00",
    "updated_at": "2026-08-17T18:56:14+00:00"
  },
  "P10616": {
    "problem_number": 10616,
    "slug": "erdos-problem-836",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:24+00:00",
    "updated_at": "2026-08-18T02:54:25+00:00"
  },
  "P10618": {
    "problem_number": 10618,
    "slug": "erdos-problem-837",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:25+00:00",
    "updated_at": "2026-08-18T02:54:25+00:00"
  },
  "P10620": {
    "problem_number": 10620,
    "slug": "erdos-problem-838",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:26+00:00",
    "updated_at": "2026-08-18T02:54:26+00:00"
  },
  "P10622": {
    "problem_number": 10622,
    "slug": "erdos-problem-839",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:26+00:00",
    "updated_at": "2026-08-18T02:54:27+00:00"
  },
  "P10624": {
    "problem_number": 10624,
    "slug": "erdos-problem-840",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:27+00:00",
    "updated_at": "2026-08-18T02:54:27+00:00"
  },
  "P10262": {
    "problem_number": 10262,
    "slug": "erdos-problem-84",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:43+00:00",
    "updated_at": "2026-08-18T02:52:43+00:00"
  },
  "P10626": {
    "problem_number": 10626,
    "slug": "erdos-problem-852",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:27+00:00",
    "updated_at": "2026-08-18T02:54:28+00:00"
  },
  "P10628": {
    "problem_number": 10628,
    "slug": "erdos-problem-854",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:28+00:00",
    "updated_at": "2026-08-18T02:54:28+00:00"
  },
  "P10630": {
    "problem_number": 10630,
    "slug": "erdos-problem-856",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:28+00:00",
    "updated_at": "2026-08-18T02:54:29+00:00"
  },
  "P10632": {
    "problem_number": 10632,
    "slug": "erdos-problem-860",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:29+00:00",
    "updated_at": "2026-08-18T02:54:29+00:00"
  },
  "P10634": {
    "problem_number": 10634,
    "slug": "erdos-problem-864",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:30+00:00",
    "updated_at": "2026-08-18T02:54:30+00:00"
  },
  "P10636": {
    "problem_number": 10636,
    "slug": "erdos-problem-866",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:30+00:00",
    "updated_at": "2026-08-18T02:54:30+00:00"
  },
  "P10264": {
    "problem_number": 10264,
    "slug": "erdos-problem-86",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:43+00:00",
    "updated_at": "2026-08-18T02:52:44+00:00"
  },
  "P10638": {
    "problem_number": 10638,
    "slug": "erdos-problem-870",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:31+00:00",
    "updated_at": "2026-08-18T02:54:31+00:00"
  },
  "P10640": {
    "problem_number": 10640,
    "slug": "erdos-problem-875",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:31+00:00",
    "updated_at": "2026-08-18T02:54:32+00:00"
  },
  "P10642": {
    "problem_number": 10642,
    "slug": "erdos-problem-876",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:32+00:00",
    "updated_at": "2026-08-18T02:54:32+00:00"
  },
  "P10644": {
    "problem_number": 10644,
    "slug": "erdos-problem-879",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:32+00:00",
    "updated_at": "2026-08-18T02:54:33+00:00"
  },
  "P10266": {
    "problem_number": 10266,
    "slug": "erdos-problem-87",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:44+00:00",
    "updated_at": "2026-08-18T02:52:44+00:00"
  },
  "P10646": {
    "problem_number": 10646,
    "slug": "erdos-problem-883",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:33+00:00",
    "updated_at": "2026-08-18T02:54:33+00:00"
  },
  "P9332": {
    "problem_number": 9332,
    "slug": "open-fc-d2311b58573d2c1e63f6-erdos-891-variants-case-k-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:57+00:00",
    "updated_at": "2026-08-17T19:50:58+00:00"
  },
  "P10648": {
    "problem_number": 10648,
    "slug": "erdos-problem-892",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:34+00:00",
    "updated_at": "2026-08-18T02:54:34+00:00"
  },
  "P10650": {
    "problem_number": 10650,
    "slug": "erdos-problem-901",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:34+00:00",
    "updated_at": "2026-08-18T02:54:34+00:00"
  },
  "P10652": {
    "problem_number": 10652,
    "slug": "erdos-problem-902",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:35+00:00",
    "updated_at": "2026-08-18T02:54:35+00:00"
  },
  "P10654": {
    "problem_number": 10654,
    "slug": "erdos-problem-917",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:35+00:00",
    "updated_at": "2026-08-18T02:54:36+00:00"
  },
  "P10656": {
    "problem_number": 10656,
    "slug": "erdos-problem-919",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:36+00:00",
    "updated_at": "2026-08-18T02:54:36+00:00"
  },
  "P10658": {
    "problem_number": 10658,
    "slug": "erdos-problem-928",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:36+00:00",
    "updated_at": "2026-08-18T02:54:37+00:00"
  },
  "P10660": {
    "problem_number": 10660,
    "slug": "erdos-problem-929",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:37+00:00",
    "updated_at": "2026-08-18T02:54:37+00:00"
  },
  "P8910": {
    "problem_number": 8910,
    "slug": "open-fc-dca0deba708061190c75-erdos-933",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:16+00:00",
    "updated_at": "2026-08-17T19:40:17+00:00"
  },
  "P10662": {
    "problem_number": 10662,
    "slug": "erdos-problem-934",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:38+00:00",
    "updated_at": "2026-08-18T02:54:38+00:00"
  },
  "P10664": {
    "problem_number": 10664,
    "slug": "erdos-problem-935",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:38+00:00",
    "updated_at": "2026-08-18T02:54:38+00:00"
  },
  "P9666": {
    "problem_number": 9666,
    "slug": "open-fc-6506025b24ce0ecab2fa-erdos-951",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:56+00:00",
    "updated_at": "2026-08-17T20:00:57+00:00"
  },
  "P10666": {
    "problem_number": 10666,
    "slug": "erdos-problem-953",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:39+00:00",
    "updated_at": "2026-08-18T02:54:39+00:00"
  },
  "P10668": {
    "problem_number": 10668,
    "slug": "erdos-problem-954",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:39+00:00",
    "updated_at": "2026-08-18T02:54:40+00:00"
  },
  "P10208": {
    "problem_number": 10208,
    "slug": "open-fc-b98563fb54ad26790ef0-erdos-955",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:47+00:00",
    "updated_at": "2026-08-18T02:51:47+00:00"
  },
  "P10670": {
    "problem_number": 10670,
    "slug": "erdos-problem-956",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:40+00:00",
    "updated_at": "2026-08-18T02:54:40+00:00"
  },
  "P10672": {
    "problem_number": 10672,
    "slug": "erdos-problem-959",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:40+00:00",
    "updated_at": "2026-08-18T02:54:41+00:00"
  },
  "P10674": {
    "problem_number": 10674,
    "slug": "erdos-problem-963",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:41+00:00",
    "updated_at": "2026-08-18T02:54:41+00:00"
  },
  "P10676": {
    "problem_number": 10676,
    "slug": "erdos-problem-969",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:41+00:00",
    "updated_at": "2026-08-18T02:54:42+00:00"
  },
  "P10678": {
    "problem_number": 10678,
    "slug": "erdos-problem-970",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:42+00:00",
    "updated_at": "2026-08-18T02:54:42+00:00"
  },
  "P10680": {
    "problem_number": 10680,
    "slug": "erdos-problem-976",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:43+00:00",
    "updated_at": "2026-08-18T02:54:43+00:00"
  },
  "P10682": {
    "problem_number": 10682,
    "slug": "erdos-problem-983",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:43+00:00",
    "updated_at": "2026-08-18T02:54:43+00:00"
  },
  "P10684": {
    "problem_number": 10684,
    "slug": "erdos-problem-995",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:54:44+00:00",
    "updated_at": "2026-08-18T02:54:44+00:00"
  },
  "P8582": {
    "problem_number": 8582,
    "slug": "open-fc-2ebdfa1b5c59a570a834-erdos-940",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:18+00:00",
    "updated_at": "2026-08-17T18:56:19+00:00"
  },
  "P3006": {
    "problem_number": 3006,
    "slug": "erdos-problem-66",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:24+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8090": {
    "problem_number": 8090,
    "slug": "open-fc-018eee102266355873a2-erdos-66",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:38+00:00",
    "updated_at": "2026-08-17T18:34:39+00:00"
  },
  "P8722": {
    "problem_number": 8722,
    "slug": "open-fc-4581c84ebe0aa3f9b045-erdos-996",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:03+00:00",
    "updated_at": "2026-08-17T19:11:13+00:00"
  },
  "P9984": {
    "problem_number": 9984,
    "slug": "open-fc-ad8a821e73fe2e053c1e-erdos-23",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:13+00:00",
    "updated_at": "2026-08-17T20:05:14+00:00"
  },
  "P3168": {
    "problem_number": 3168,
    "slug": "erdos-problem-23",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:47:41+00:00",
    "updated_at": "2026-08-12T05:47:56+00:00"
  },
  "P3310": {
    "problem_number": 3310,
    "slug": "erdos-problem-835",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:27+00:00",
    "updated_at": "2026-08-12T06:04:28+00:00"
  },
  "P9570": {
    "problem_number": 9570,
    "slug": "open-fc-cecbcba5b3bac14cc88f-erdos-835",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:38+00:00",
    "updated_at": "2026-08-17T19:55:40+00:00"
  },
  "P9044": {
    "problem_number": 9044,
    "slug": "open-fc-9ab93a0240916dafee8d-erdos-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:03+00:00",
    "updated_at": "2026-08-17T19:46:05+00:00"
  },
  "P2958": {
    "problem_number": 2958,
    "slug": "erdos-problem-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:25+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8250": {
    "problem_number": 8250,
    "slug": "open-fc-15c4e383280e72542c73-erdos-137-variants-multiple-powerful-factors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:43+00:00",
    "updated_at": "2026-08-17T18:37:44+00:00"
  },
  "P9962": {
    "problem_number": 9962,
    "slug": "open-fc-9d446e997a89fc4fb7e5-erdos-18a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:56+00:00",
    "updated_at": "2026-08-17T20:04:57+00:00"
  },
  "P2974": {
    "problem_number": 2974,
    "slug": "erdos-problem-18",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:39+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8520": {
    "problem_number": 8520,
    "slug": "open-fc-5fb76acb33c2324abf57-erdos-686",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:08+00:00",
    "updated_at": "2026-08-17T18:54:09+00:00"
  },
  "P9182": {
    "problem_number": 9182,
    "slug": "open-fc-35920f1429f8f1b59c66-erdos-535",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:02+00:00",
    "updated_at": "2026-08-17T19:49:03+00:00"
  },
  "P8342": {
    "problem_number": 8342,
    "slug": "open-fc-225f996fedaa433eb3ff-erdos-100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:06+00:00",
    "updated_at": "2026-08-17T18:40:07+00:00"
  },
  "P3030": {
    "problem_number": 3030,
    "slug": "erdos-problem-100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:01+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9732": {
    "problem_number": 9732,
    "slug": "open-fc-aaf28bd602ecad79a310-erdos-647",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:08+00:00",
    "updated_at": "2026-08-17T20:02:09+00:00"
  },
  "P3162": {
    "problem_number": 3162,
    "slug": "erdos-problem-647",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:44:48+00:00",
    "updated_at": "2026-08-12T05:45:11+00:00"
  },
  "P9974": {
    "problem_number": 9974,
    "slug": "open-fc-a82b201008fdf67842cb-erdos-242",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:05+00:00",
    "updated_at": "2026-08-17T20:05:07+00:00"
  },
  "P3156": {
    "problem_number": 3156,
    "slug": "erdos-problem-242",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:41:04+00:00",
    "updated_at": "2026-08-12T05:42:08+00:00"
  },
  "P10054": {
    "problem_number": 10054,
    "slug": "open-fc-e70d82fbad1c8ae28cb7-erdos-289",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:56+00:00",
    "updated_at": "2026-08-17T20:05:57+00:00"
  },
  "P8228": {
    "problem_number": 8228,
    "slug": "open-fc-12e5cf5f83c04a9ab7b3-erdos-287",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:24+00:00",
    "updated_at": "2026-08-17T18:37:25+00:00"
  },
  "P3222": {
    "problem_number": 3222,
    "slug": "erdos-problem-287",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:54:33+00:00",
    "updated_at": "2026-08-12T05:54:39+00:00"
  },
  "P3180": {
    "problem_number": 3180,
    "slug": "erdos-problem-97",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:49:39+00:00",
    "updated_at": "2026-08-12T05:49:41+00:00"
  },
  "P9518": {
    "problem_number": 9518,
    "slug": "open-fc-a739b79b0912f53dda18-erdos-97",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:36+00:00",
    "updated_at": "2026-08-17T19:54:36+00:00"
  },
  "P8676": {
    "problem_number": 8676,
    "slug": "open-fc-32a795a14c3210d6b793-erdos-701",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:35+00:00",
    "updated_at": "2026-08-17T19:04:38+00:00"
  },
  "P9464": {
    "problem_number": 9464,
    "slug": "open-fc-8024921104a53659b83c-erdos-513",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:58+00:00",
    "updated_at": "2026-08-17T19:53:58+00:00"
  },
  "P9634": {
    "problem_number": 9634,
    "slug": "open-fc-ffb5dd9e72f92f80a520-erdos-477",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:48+00:00",
    "updated_at": "2026-08-17T19:57:51+00:00"
  },
  "P3036": {
    "problem_number": 3036,
    "slug": "erdos-problem-120",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:08+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8080": {
    "problem_number": 8080,
    "slug": "open-fc-003a969fe697c00ce91d-erdos-120",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:35+00:00",
    "updated_at": "2026-08-17T18:34:35+00:00"
  },
  "P8802": {
    "problem_number": 8802,
    "slug": "open-fc-8877bb467aa4df818d76-erdos-74",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:22:20+00:00",
    "updated_at": "2026-08-17T19:22:32+00:00"
  },
  "P9064": {
    "problem_number": 9064,
    "slug": "open-fc-a9fea9c8228fb471ccb0-erdos-386",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:38+00:00",
    "updated_at": "2026-08-17T19:46:40+00:00"
  },
  "P3200": {
    "problem_number": 3200,
    "slug": "erdos-problem-463",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:51:49+00:00",
    "updated_at": "2026-08-12T05:51:57+00:00"
  },
  "P8126": {
    "problem_number": 8126,
    "slug": "open-fc-04cacfe5f1a605791eab-erdos-463",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:53+00:00",
    "updated_at": "2026-08-17T18:34:54+00:00"
  },
  "P9910": {
    "problem_number": 9910,
    "slug": "open-fc-7a047994a8af86390f6a-erdos-727",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:29+00:00",
    "updated_at": "2026-08-17T20:04:30+00:00"
  },
  "P3186": {
    "problem_number": 3186,
    "slug": "erdos-problem-727",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:50:08+00:00",
    "updated_at": "2026-08-12T05:50:09+00:00"
  },
  "P9002": {
    "problem_number": 9002,
    "slug": "open-fc-7dd0fa646985e0db9b8e-erdos-108",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:43+00:00",
    "updated_at": "2026-08-17T19:44:44+00:00"
  },
  "P3034": {
    "problem_number": 3034,
    "slug": "erdos-problem-108",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:06+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9950": {
    "problem_number": 9950,
    "slug": "open-fc-971fa0a4b448f69870c8-erdos-740",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:52+00:00",
    "updated_at": "2026-08-17T20:04:52+00:00"
  },
  "P9374": {
    "problem_number": 9374,
    "slug": "open-fc-f2d7af87ab4e16832879-erdos-501",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:15+00:00",
    "updated_at": "2026-08-17T19:51:15+00:00"
  },
  "P9784": {
    "problem_number": 9784,
    "slug": "open-fc-d17e1279886be375a0e8-erdos-891",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:36+00:00",
    "updated_at": "2026-08-17T20:02:37+00:00"
  },
  "P9318": {
    "problem_number": 9318,
    "slug": "open-fc-c7cee977a2933504482e-erdos-932",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:51+00:00",
    "updated_at": "2026-08-17T19:50:52+00:00"
  },
  "P3182": {
    "problem_number": 3182,
    "slug": "erdos-problem-683",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:49:52+00:00",
    "updated_at": "2026-08-12T05:49:57+00:00"
  },
  "P9244": {
    "problem_number": 9244,
    "slug": "open-fc-9154364e389caf6c4716-erdos-683",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:18+00:00",
    "updated_at": "2026-08-17T19:50:20+00:00"
  },
  "P3306": {
    "problem_number": 3306,
    "slug": "erdos-problem-786",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:46+00:00",
    "updated_at": "2026-08-12T06:03:48+00:00"
  },
  "P8960": {
    "problem_number": 8960,
    "slug": "open-fc-434c796b86279c5021b6-erdos-786-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:43:17+00:00",
    "updated_at": "2026-08-17T19:43:44+00:00"
  },
  "P2968": {
    "problem_number": 2968,
    "slug": "erdos-problem-14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:34+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8354": {
    "problem_number": 8354,
    "slug": "open-fc-2309d4113bfacc199130-erdos-14-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:16+00:00",
    "updated_at": "2026-08-17T18:40:17+00:00"
  },
  "P8776": {
    "problem_number": 8776,
    "slug": "open-fc-34266a2bdf8961ea1f14-erdos-889",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:18:34+00:00",
    "updated_at": "2026-08-17T19:19:18+00:00"
  },
  "P8612": {
    "problem_number": 8612,
    "slug": "open-fc-842efc2d25297d398fc6-erdos-243",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:40+00:00",
    "updated_at": "2026-08-17T18:57:52+00:00"
  },
  "P9018": {
    "problem_number": 9018,
    "slug": "open-fc-8761cb98a5785f31fe22-erdos-428",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:13+00:00",
    "updated_at": "2026-08-17T19:45:14+00:00"
  },
  "P8298": {
    "problem_number": 8298,
    "slug": "open-fc-1e1d8389a3960b72e060-erdos-155",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:44+00:00",
    "updated_at": "2026-08-17T18:38:49+00:00"
  },
  "P3226": {
    "problem_number": 3226,
    "slug": "erdos-problem-155",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:54:59+00:00",
    "updated_at": "2026-08-12T05:55:02+00:00"
  },
  "P8270": {
    "problem_number": 8270,
    "slug": "open-fc-19b0fffe38f18b47c40c-erdos-949",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:02+00:00",
    "updated_at": "2026-08-17T18:38:04+00:00"
  },
  "P9644": {
    "problem_number": 9644,
    "slug": "open-fc-41c0deacafd175fde3f5-erdos-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:24+00:00",
    "updated_at": "2026-08-17T20:00:25+00:00"
  },
  "P2962": {
    "problem_number": 2962,
    "slug": "erdos-problem-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:28+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8512": {
    "problem_number": 8512,
    "slug": "open-fc-5ceec8375ecf5e9670a3-erdos-749",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:43+00:00",
    "updated_at": "2026-08-17T18:53:49+00:00"
  },
  "P8850": {
    "problem_number": 8850,
    "slug": "open-fc-adb5c85ae3d76e1d3211-erdos-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:19+00:00",
    "updated_at": "2026-08-17T19:26:32+00:00"
  },
  "P3014": {
    "problem_number": 3014,
    "slug": "erdos-problem-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:40+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P2964": {
    "problem_number": 2964,
    "slug": "erdos-problem-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:30+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8294": {
    "problem_number": 8294,
    "slug": "open-fc-1cec496c18c263f07898-erdos-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:33+00:00",
    "updated_at": "2026-08-17T18:38:39+00:00"
  },
  "P8536": {
    "problem_number": 8536,
    "slug": "open-fc-68e5e3f4bf192d45cfdf-erdos-11-variants-not-four-dvd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:21+00:00",
    "updated_at": "2026-08-17T18:54:22+00:00"
  },
  "P8434": {
    "problem_number": 8434,
    "slug": "open-fc-337ce3e405886edd785b-erdos-364-variants-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:05+00:00",
    "updated_at": "2026-08-17T18:52:05+00:00"
  },
  "P10028": {
    "problem_number": 10028,
    "slug": "open-fc-d02cf972c4f9c459e7e8-erdos-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:32+00:00",
    "updated_at": "2026-08-17T20:05:32+00:00"
  },
  "P2956": {
    "problem_number": 2956,
    "slug": "erdos-problem-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:13+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9050": {
    "problem_number": 9050,
    "slug": "open-fc-9e637509d2913fa08ad5-erdos-1-variants-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:14+00:00",
    "updated_at": "2026-08-17T19:46:16+00:00"
  },
  "P8468": {
    "problem_number": 8468,
    "slug": "open-fc-456c16b7ef170ee92f6d-erdos-52",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:13+00:00",
    "updated_at": "2026-08-17T18:52:14+00:00"
  },
  "P3002": {
    "problem_number": 3002,
    "slug": "erdos-problem-52",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:18+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P3174": {
    "problem_number": 3174,
    "slug": "erdos-problem-128",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:49:01+00:00",
    "updated_at": "2026-08-12T05:49:06+00:00"
  },
  "P9862": {
    "problem_number": 9862,
    "slug": "open-fc-5225e49b72b8fa0ec506-erdos-128",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:03+00:00",
    "updated_at": "2026-08-17T20:04:04+00:00"
  },
  "P9878": {
    "problem_number": 9878,
    "slug": "open-fc-5edecf4d593c1e1373e4-erdos-11-variants-two-pow-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:11+00:00",
    "updated_at": "2026-08-17T20:04:12+00:00"
  },
  "P8178": {
    "problem_number": 8178,
    "slug": "open-fc-0acbe6725f57a68b766e-erdos-74-variants-sqrt",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:23+00:00",
    "updated_at": "2026-08-17T18:36:26+00:00"
  },
  "P3012": {
    "problem_number": 3012,
    "slug": "erdos-problem-74",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:37+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P43": {
    "problem_number": 43,
    "slug": "erdos-hajnal-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T11:36:50+00:00"
  },
  "P6": {
    "problem_number": 6,
    "slug": "erdos-moser-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T11:37:21+00:00"
  },
  "P5": {
    "problem_number": 5,
    "slug": "erdos-straus-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:07:03+00:00"
  },
  "P9334": {
    "problem_number": 9334,
    "slug": "open-fc-d529399b001b77ef694a-erdos-385-variants-lb",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:58+00:00",
    "updated_at": "2026-08-17T19:50:58+00:00"
  },
  "P8962": {
    "problem_number": 8962,
    "slug": "open-fc-47046fc37868df514969-erdos-184",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:43:46+00:00",
    "updated_at": "2026-08-17T19:43:47+00:00"
  },
  "P8752": {
    "problem_number": 8752,
    "slug": "open-fc-5d10ce989a31577fa43f-erdos-596-variants-k4-k3-exceptional-iff",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:23+00:00",
    "updated_at": "2026-08-17T19:20:21+00:00"
  },
  "P9526": {
    "problem_number": 9526,
    "slug": "open-fc-acb75a9065ceea2627a4-erdos-918-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:38+00:00",
    "updated_at": "2026-08-17T19:54:39+00:00"
  },
  "P9868": {
    "problem_number": 9868,
    "slug": "open-fc-58d5457f544128e547c3-erdos-918-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:07+00:00",
    "updated_at": "2026-08-17T20:04:08+00:00"
  },
  "P8502": {
    "problem_number": 8502,
    "slug": "open-fc-580947ecdb258242e3f9-erdos-394-variants-hall-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:04+00:00",
    "updated_at": "2026-08-17T18:53:10+00:00"
  },
  "P8450": {
    "problem_number": 8450,
    "slug": "open-fc-3bdb652e4658a00e6e00-erdos-945-variants-constant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:09+00:00",
    "updated_at": "2026-08-17T18:52:09+00:00"
  },
  "P2976": {
    "problem_number": 2976,
    "slug": "erdos-problem-20",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:41+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8576": {
    "problem_number": 8576,
    "slug": "open-fc-7ea688f6968be0675c12-erdos-20",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:04+00:00",
    "updated_at": "2026-08-17T18:56:16+00:00"
  },
  "P9230": {
    "problem_number": 9230,
    "slug": "open-fc-7fefdadeb17a85a45b57-erdos-887-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:02+00:00",
    "updated_at": "2026-08-17T19:50:04+00:00"
  },
  "P9210": {
    "problem_number": 9210,
    "slug": "open-fc-62a87fbcda462835e30f-erdos-890-parts-a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:28+00:00",
    "updated_at": "2026-08-17T19:49:30+00:00"
  },
  "P8744": {
    "problem_number": 8744,
    "slug": "open-fc-4fd45ebb1389426543d2-erdos-szekeres-strengthening",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:37+00:00",
    "updated_at": "2026-08-17T19:12:51+00:00"
  },
  "P10194": {
    "problem_number": 10194,
    "slug": "open-fc-8ea8bba0afc476662ce3-error-term-improvement",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:42+00:00",
    "updated_at": "2026-08-18T02:51:42+00:00"
  },
  "P9482": {
    "problem_number": 9482,
    "slug": "open-fc-8ce9734b3989260b5d51-green-54",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:12+00:00",
    "updated_at": "2026-08-17T19:54:14+00:00"
  },
  "P10068": {
    "problem_number": 10068,
    "slug": "open-fc-f0918e8b808c2b6b3c37-eulers-sum-of-powers-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:08+00:00",
    "updated_at": "2026-08-17T20:06:09+00:00"
  },
  "P12245": {
    "problem_number": 12245,
    "slug": "even-numbers-paired-with-every-prime-above-their-midpoint",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:29:14+00:00",
    "updated_at": "2026-09-01T19:29:20+00:00"
  },
  "P12511": {
    "problem_number": 12511,
    "slug": "even-terms-in-a-prime-difference-avoiding-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:43:12+00:00",
    "updated_at": "2026-09-02T21:43:19+00:00"
  },
  "P11634": {
    "problem_number": 11634,
    "slug": "eventual-common-prime-factor-in-the-three-term-radical-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:41:31+00:00",
    "updated_at": "2026-08-30T04:41:38+00:00"
  },
  "P8554": {
    "problem_number": 8554,
    "slug": "open-fc-72287b29e7fddd6664c0-erdos-422-variants-eventually-const",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:39+00:00",
    "updated_at": "2026-08-17T18:54:41+00:00"
  },
  "P12301": {
    "problem_number": 12301,
    "slug": "eventual-cycling-under-a-piecewise-3-to-5-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:36:08+00:00",
    "updated_at": "2026-09-01T19:36:14+00:00"
  },
  "P2540": {
    "problem_number": 2540,
    "slug": "distinct-cycle-length-probability-decreasing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:21+00:00",
    "updated_at": "2026-07-29T20:55:33+00:00"
  },
  "P2820": {
    "problem_number": 2820,
    "slug": "circular-abelian-square-free-four-eventual",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:14+00:00",
    "updated_at": "2026-07-30T02:24:21+00:00"
  },
  "P9356": {
    "problem_number": 9356,
    "slug": "open-fc-e78a90f1b2e0e5976796-green-31-variants-lower-eventually",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:07+00:00",
    "updated_at": "2026-08-17T19:51:08+00:00"
  },
  "P11716": {
    "problem_number": 11716,
    "slug": "eventual-modular-periodicity-of-even-block-set-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:17:08+00:00",
    "updated_at": "2026-08-30T11:17:15+00:00"
  },
  "P11802": {
    "problem_number": 11802,
    "slug": "eventual-modular-periodicity-of-ordered-odd-block-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:45:32+00:00",
    "updated_at": "2026-08-30T12:45:41+00:00"
  },
  "P2538": {
    "problem_number": 2538,
    "slug": "signed-subset-sum-local-clt-monotone",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:20+00:00",
    "updated_at": "2026-07-29T20:56:33+00:00"
  },
  "P11598": {
    "problem_number": 11598,
    "slug": "eventual-periodicity-of-automorphism-iterates-of-cyclic-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:37:12+00:00",
    "updated_at": "2026-08-30T04:37:17+00:00"
  },
  "P8496": {
    "problem_number": 8496,
    "slug": "open-fc-53a03db0cfc162847a7a-erdos-342-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:38+00:00",
    "updated_at": "2026-08-17T18:52:44+00:00"
  },
  "P9908": {
    "problem_number": 9908,
    "slug": "open-fc-768ea8e31b87d78c27e4-erdos-341",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:27+00:00",
    "updated_at": "2026-08-17T20:04:29+00:00"
  },
  "P12609": {
    "problem_number": 12609,
    "slug": "eventual-periodicity-of-permutation-order-sums-modulo-m",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:57:01+00:00",
    "updated_at": "2026-09-02T21:57:08+00:00"
  },
  "P12477": {
    "problem_number": 12477,
    "slug": "eventual-prime-divisors-of-goldbach-record-centers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:39:51+00:00",
    "updated_at": "2026-09-02T21:39:59+00:00"
  },
  "P12093": {
    "problem_number": 12093,
    "slug": "eventual-scaling-of-greedy-carry-free-sequences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:10:14+00:00",
    "updated_at": "2026-09-01T19:10:20+00:00"
  },
  "P12109": {
    "problem_number": 12109,
    "slug": "eventual-strictness-in-the-no-three-in-line-grid-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:12:11+00:00",
    "updated_at": "2026-09-01T19:12:36+00:00"
  },
  "P2448": {
    "problem_number": 2448,
    "slug": "ternary-subset-polynomial-unimodality",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:56:48+00:00",
    "updated_at": "2026-08-01T23:50:19+00:00"
  },
  "P8930": {
    "problem_number": 8930,
    "slug": "open-fc-eb5a8d83e83dda4e9dc7-green-72-variants-eventually",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:47+00:00",
    "updated_at": "2026-08-17T19:40:48+00:00"
  },
  "P11656": {
    "problem_number": 11656,
    "slug": "eventual-zero-in-the-signed-digit-queue-process",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:03:29+00:00",
    "updated_at": "2026-08-30T11:03:36+00:00"
  },
  "P11889": {
    "problem_number": 11889,
    "slug": "every-exact-gap-length-in-the-range-of-sigma",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:18+00:00",
    "updated_at": "2026-08-30T16:20:24+00:00"
  },
  "P12283": {
    "problem_number": 12283,
    "slug": "every-prime-index-gap-between-consecutive-twin-prime-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:33:57+00:00",
    "updated_at": "2026-09-01T19:34:04+00:00"
  },
  "P4028": {
    "problem_number": 4028,
    "slug": "covering-array-can-3-16-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:16:36+00:00",
    "updated_at": "2026-08-16T01:59:44+00:00"
  },
  "P4030": {
    "problem_number": 4030,
    "slug": "covering-array-can-3-17-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:16:59+00:00",
    "updated_at": "2026-08-16T01:59:47+00:00"
  },
  "P4032": {
    "problem_number": 4032,
    "slug": "covering-array-can-3-18-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:17:21+00:00",
    "updated_at": "2026-08-16T01:59:49+00:00"
  },
  "P4034": {
    "problem_number": 4034,
    "slug": "covering-array-can-3-19-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:17:33+00:00",
    "updated_at": "2026-08-16T01:59:49+00:00"
  },
  "P4036": {
    "problem_number": 4036,
    "slug": "covering-array-can-3-20-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:17:47+00:00",
    "updated_at": "2026-08-16T01:59:50+00:00"
  },
  "P4038": {
    "problem_number": 4038,
    "slug": "covering-array-can-3-21-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:17:55+00:00",
    "updated_at": "2026-08-16T01:59:54+00:00"
  },
  "P4040": {
    "problem_number": 4040,
    "slug": "covering-array-can-3-22-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:04+00:00",
    "updated_at": "2026-08-16T01:59:58+00:00"
  },
  "P4042": {
    "problem_number": 4042,
    "slug": "covering-array-can-3-23-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:11+00:00",
    "updated_at": "2026-08-16T02:00:02+00:00"
  },
  "P4044": {
    "problem_number": 4044,
    "slug": "covering-array-can-3-24-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:34+00:00",
    "updated_at": "2026-08-16T02:00:07+00:00"
  },
  "P4046": {
    "problem_number": 4046,
    "slug": "covering-array-can-3-25-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:47+00:00",
    "updated_at": "2026-08-16T02:00:11+00:00"
  },
  "P4048": {
    "problem_number": 4048,
    "slug": "covering-array-can-3-26-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:53+00:00",
    "updated_at": "2026-08-16T02:00:14+00:00"
  },
  "P4050": {
    "problem_number": 4050,
    "slug": "covering-array-can-3-27-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:56+00:00",
    "updated_at": "2026-08-16T02:00:15+00:00"
  },
  "P4052": {
    "problem_number": 4052,
    "slug": "covering-array-can-3-28-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:18:57+00:00",
    "updated_at": "2026-08-16T02:00:15+00:00"
  },
  "P4054": {
    "problem_number": 4054,
    "slug": "covering-array-can-3-29-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:01+00:00",
    "updated_at": "2026-08-16T02:00:16+00:00"
  },
  "P4056": {
    "problem_number": 4056,
    "slug": "covering-array-can-3-30-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:02+00:00",
    "updated_at": "2026-08-16T02:00:22+00:00"
  },
  "P4058": {
    "problem_number": 4058,
    "slug": "covering-array-can-3-31-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:03+00:00",
    "updated_at": "2026-08-16T02:00:28+00:00"
  },
  "P4060": {
    "problem_number": 4060,
    "slug": "covering-array-can-3-32-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:05+00:00",
    "updated_at": "2026-08-16T02:00:32+00:00"
  },
  "P4062": {
    "problem_number": 4062,
    "slug": "covering-array-can-3-33-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:06+00:00",
    "updated_at": "2026-08-16T02:00:38+00:00"
  },
  "P4064": {
    "problem_number": 4064,
    "slug": "covering-array-can-3-34-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:09+00:00",
    "updated_at": "2026-08-16T02:00:41+00:00"
  },
  "P4066": {
    "problem_number": 4066,
    "slug": "covering-array-can-3-35-2-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:11+00:00",
    "updated_at": "2026-08-16T02:00:47+00:00"
  },
  "P4388": {
    "problem_number": 4388,
    "slug": "turan-number-ex-50-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:28+00:00",
    "updated_at": "2026-08-16T02:06:13+00:00"
  },
  "P4390": {
    "problem_number": 4390,
    "slug": "turan-number-ex-51-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:29+00:00",
    "updated_at": "2026-08-16T02:06:20+00:00"
  },
  "P4392": {
    "problem_number": 4392,
    "slug": "turan-number-ex-52-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:30+00:00",
    "updated_at": "2026-08-16T02:06:23+00:00"
  },
  "P4394": {
    "problem_number": 4394,
    "slug": "turan-number-ex-53-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:32+00:00",
    "updated_at": "2026-08-16T02:06:30+00:00"
  },
  "P4396": {
    "problem_number": 4396,
    "slug": "turan-number-ex-54-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:38+00:00",
    "updated_at": "2026-08-16T02:06:35+00:00"
  },
  "P4398": {
    "problem_number": 4398,
    "slug": "turan-number-ex-55-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:49+00:00",
    "updated_at": "2026-08-16T02:06:40+00:00"
  },
  "P4400": {
    "problem_number": 4400,
    "slug": "turan-number-ex-56-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:51+00:00",
    "updated_at": "2026-08-16T02:06:45+00:00"
  },
  "P4402": {
    "problem_number": 4402,
    "slug": "turan-number-ex-58-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:53+00:00",
    "updated_at": "2026-08-16T02:06:50+00:00"
  },
  "P4404": {
    "problem_number": 4404,
    "slug": "turan-number-ex-59-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:54+00:00",
    "updated_at": "2026-08-16T02:06:54+00:00"
  },
  "P4406": {
    "problem_number": 4406,
    "slug": "turan-number-ex-60-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:56+00:00",
    "updated_at": "2026-08-16T02:06:59+00:00"
  },
  "P4408": {
    "problem_number": 4408,
    "slug": "turan-number-ex-61-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:58+00:00",
    "updated_at": "2026-08-16T02:07:01+00:00"
  },
  "P4410": {
    "problem_number": 4410,
    "slug": "turan-number-ex-62-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:02+00:00",
    "updated_at": "2026-08-16T02:07:03+00:00"
  },
  "P4412": {
    "problem_number": 4412,
    "slug": "turan-number-ex-63-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:03+00:00",
    "updated_at": "2026-08-16T02:07:03+00:00"
  },
  "P4414": {
    "problem_number": 4414,
    "slug": "turan-number-ex-64-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:05+00:00",
    "updated_at": "2026-08-16T02:07:04+00:00"
  },
  "P4416": {
    "problem_number": 4416,
    "slug": "turan-number-ex-65-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:10+00:00",
    "updated_at": "2026-08-16T02:07:04+00:00"
  },
  "P4418": {
    "problem_number": 4418,
    "slug": "turan-number-ex-66-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:16+00:00",
    "updated_at": "2026-08-16T02:07:04+00:00"
  },
  "P4420": {
    "problem_number": 4420,
    "slug": "turan-number-ex-67-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:20+00:00",
    "updated_at": "2026-08-16T02:07:05+00:00"
  },
  "P4422": {
    "problem_number": 4422,
    "slug": "turan-number-ex-68-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:22+00:00",
    "updated_at": "2026-08-16T02:07:05+00:00"
  },
  "P4424": {
    "problem_number": 4424,
    "slug": "turan-number-ex-69-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:33+00:00",
    "updated_at": "2026-08-16T02:07:10+00:00"
  },
  "P4426": {
    "problem_number": 4426,
    "slug": "turan-number-ex-70-c4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:40+00:00",
    "updated_at": "2026-08-16T02:07:12+00:00"
  },
  "P3106": {
    "problem_number": 3106,
    "slug": "gaussian-interference-channel-capacity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:02+00:00",
    "updated_at": "2026-08-02T12:50:52+00:00"
  },
  "P3714": {
    "problem_number": 3714,
    "slug": "hidden-weighted-bit-eight-formula",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:36+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3668": {
    "problem_number": 3668,
    "slug": "petersen-antiferromagnetic-heisenberg-ground-polynomial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:17+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2584": {
    "problem_number": 2584,
    "slug": "hamiltonian-graph-probability-eight",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:36+00:00",
    "updated_at": "2026-08-01T23:29:29+00:00"
  },
  "P2700": {
    "problem_number": 2700,
    "slug": "ising-six-torus-heat-bath-gap",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:20+00:00",
    "updated_at": "2026-08-01T02:10:40+00:00"
  },
  "P3664": {
    "problem_number": 3664,
    "slug": "random-greedy-eight-grid-expectation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:14+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2550": {
    "problem_number": 2550,
    "slug": "dyadic-jensen-stability-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:25+00:00",
    "updated_at": "2026-08-01T02:06:59+00:00"
  },
  "P4348": {
    "problem_number": 4348,
    "slug": "kissing-number-dimension-25-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:34+00:00",
    "updated_at": "2026-08-16T02:02:40+00:00"
  },
  "P4350": {
    "problem_number": 4350,
    "slug": "kissing-number-dimension-26-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:36+00:00",
    "updated_at": "2026-08-16T02:02:40+00:00"
  },
  "P4352": {
    "problem_number": 4352,
    "slug": "kissing-number-dimension-27-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:38+00:00",
    "updated_at": "2026-08-16T02:02:40+00:00"
  },
  "P4354": {
    "problem_number": 4354,
    "slug": "kissing-number-dimension-28-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:44+00:00",
    "updated_at": "2026-08-16T02:02:40+00:00"
  },
  "P4356": {
    "problem_number": 4356,
    "slug": "kissing-number-dimension-29-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:51+00:00",
    "updated_at": "2026-08-16T02:02:42+00:00"
  },
  "P4358": {
    "problem_number": 4358,
    "slug": "kissing-number-dimension-30-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:34:53+00:00",
    "updated_at": "2026-08-16T02:02:44+00:00"
  },
  "P4360": {
    "problem_number": 4360,
    "slug": "kissing-number-dimension-31-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:35:05+00:00",
    "updated_at": "2026-08-16T02:02:44+00:00"
  },
  "P4362": {
    "problem_number": 4362,
    "slug": "kissing-number-dimension-32-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:35:06+00:00",
    "updated_at": "2026-08-16T02:02:46+00:00"
  },
  "P4364": {
    "problem_number": 4364,
    "slug": "kissing-number-dimension-33-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:35:10+00:00",
    "updated_at": "2026-08-16T02:02:47+00:00"
  },
  "P4366": {
    "problem_number": 4366,
    "slug": "kissing-number-dimension-34-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:35:18+00:00",
    "updated_at": "2026-08-16T02:02:47+00:00"
  },
  "P4368": {
    "problem_number": 4368,
    "slug": "kissing-number-dimension-35-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:35:44+00:00",
    "updated_at": "2026-08-16T02:02:48+00:00"
  },
  "P4370": {
    "problem_number": 4370,
    "slug": "kissing-number-dimension-36-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:36:15+00:00",
    "updated_at": "2026-08-16T02:02:52+00:00"
  },
  "P4372": {
    "problem_number": 4372,
    "slug": "kissing-number-dimension-37-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:36:33+00:00",
    "updated_at": "2026-08-16T02:02:55+00:00"
  },
  "P4374": {
    "problem_number": 4374,
    "slug": "kissing-number-dimension-38-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:36:57+00:00",
    "updated_at": "2026-08-16T02:02:56+00:00"
  },
  "P4376": {
    "problem_number": 4376,
    "slug": "kissing-number-dimension-39-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:14+00:00",
    "updated_at": "2026-08-16T02:02:57+00:00"
  },
  "P4378": {
    "problem_number": 4378,
    "slug": "kissing-number-dimension-40-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:17+00:00",
    "updated_at": "2026-08-16T02:02:58+00:00"
  },
  "P4380": {
    "problem_number": 4380,
    "slug": "kissing-number-dimension-41-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:19+00:00",
    "updated_at": "2026-08-16T02:02:59+00:00"
  },
  "P4382": {
    "problem_number": 4382,
    "slug": "kissing-number-dimension-42-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:20+00:00",
    "updated_at": "2026-08-16T02:02:59+00:00"
  },
  "P4384": {
    "problem_number": 4384,
    "slug": "kissing-number-dimension-43-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:22+00:00",
    "updated_at": "2026-08-16T02:03:01+00:00"
  },
  "P4386": {
    "problem_number": 4386,
    "slug": "kissing-number-dimension-44-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:37:25+00:00",
    "updated_at": "2026-08-16T02:03:02+00:00"
  },
  "P2796": {
    "problem_number": 2796,
    "slug": "mixed-dimension-subspace-code-f2-7-d4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:06+00:00",
    "updated_at": "2026-07-30T02:26:58+00:00"
  },
  "P4228": {
    "problem_number": 4228,
    "slug": "cubic-cage-girth-15-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:26+00:00",
    "updated_at": "2026-08-16T02:02:11+00:00"
  },
  "P4230": {
    "problem_number": 4230,
    "slug": "cubic-cage-girth-16-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:28+00:00",
    "updated_at": "2026-08-16T02:02:18+00:00"
  },
  "P4232": {
    "problem_number": 4232,
    "slug": "cubic-cage-girth-17-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:31+00:00",
    "updated_at": "2026-08-16T02:02:25+00:00"
  },
  "P4234": {
    "problem_number": 4234,
    "slug": "cubic-cage-girth-18-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:33+00:00",
    "updated_at": "2026-08-16T02:02:29+00:00"
  },
  "P4236": {
    "problem_number": 4236,
    "slug": "cubic-cage-girth-19-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:42+00:00",
    "updated_at": "2026-08-16T02:02:29+00:00"
  },
  "P4238": {
    "problem_number": 4238,
    "slug": "cubic-cage-girth-20-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:47+00:00",
    "updated_at": "2026-08-16T02:02:29+00:00"
  },
  "P4240": {
    "problem_number": 4240,
    "slug": "cubic-cage-girth-21-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:50+00:00",
    "updated_at": "2026-08-16T02:02:30+00:00"
  },
  "P4242": {
    "problem_number": 4242,
    "slug": "cubic-cage-girth-22-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:53+00:00",
    "updated_at": "2026-08-16T02:02:30+00:00"
  },
  "P4244": {
    "problem_number": 4244,
    "slug": "cubic-cage-girth-23-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:56+00:00",
    "updated_at": "2026-08-16T02:02:30+00:00"
  },
  "P4246": {
    "problem_number": 4246,
    "slug": "cubic-cage-girth-24-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:58+00:00",
    "updated_at": "2026-08-16T02:02:30+00:00"
  },
  "P4248": {
    "problem_number": 4248,
    "slug": "cubic-cage-girth-25-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:01+00:00",
    "updated_at": "2026-08-16T02:02:31+00:00"
  },
  "P4250": {
    "problem_number": 4250,
    "slug": "cubic-cage-girth-26-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:03+00:00",
    "updated_at": "2026-08-16T02:02:31+00:00"
  },
  "P4252": {
    "problem_number": 4252,
    "slug": "cubic-cage-girth-27-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:06+00:00",
    "updated_at": "2026-08-16T02:02:31+00:00"
  },
  "P4254": {
    "problem_number": 4254,
    "slug": "cubic-cage-girth-28-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:09+00:00",
    "updated_at": "2026-08-16T02:02:31+00:00"
  },
  "P4256": {
    "problem_number": 4256,
    "slug": "cubic-cage-girth-29-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:11+00:00",
    "updated_at": "2026-08-16T02:02:31+00:00"
  },
  "P4258": {
    "problem_number": 4258,
    "slug": "cubic-cage-girth-30-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:13+00:00",
    "updated_at": "2026-08-16T02:02:32+00:00"
  },
  "P4260": {
    "problem_number": 4260,
    "slug": "cubic-cage-girth-31-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:16+00:00",
    "updated_at": "2026-08-16T02:02:32+00:00"
  },
  "P4262": {
    "problem_number": 4262,
    "slug": "cubic-cage-girth-32-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:17+00:00",
    "updated_at": "2026-08-16T02:02:32+00:00"
  },
  "P4264": {
    "problem_number": 4264,
    "slug": "cubic-cage-girth-33-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:19+00:00",
    "updated_at": "2026-08-16T02:02:32+00:00"
  },
  "P4266": {
    "problem_number": 4266,
    "slug": "cubic-cage-girth-34-exact-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:30:22+00:00",
    "updated_at": "2026-08-16T02:02:32+00:00"
  },
  "P12089": {
    "problem_number": 12089,
    "slug": "exact-packing-formulas-for-two-one-transposition-codes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:09:45+00:00",
    "updated_at": "2026-09-01T19:09:50+00:00"
  },
  "P4148": {
    "problem_number": 4148,
    "slug": "ramsey-number-r-4-10-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:33+00:00",
    "updated_at": "2026-08-16T02:03:37+00:00"
  },
  "P4150": {
    "problem_number": 4150,
    "slug": "ramsey-number-r-4-11-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:39+00:00",
    "updated_at": "2026-08-16T02:03:41+00:00"
  },
  "P4152": {
    "problem_number": 4152,
    "slug": "ramsey-number-r-4-12-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:44+00:00",
    "updated_at": "2026-08-16T02:03:45+00:00"
  },
  "P4154": {
    "problem_number": 4154,
    "slug": "ramsey-number-r-4-13-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:47+00:00",
    "updated_at": "2026-08-16T02:03:49+00:00"
  },
  "P4156": {
    "problem_number": 4156,
    "slug": "ramsey-number-r-4-14-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:52+00:00",
    "updated_at": "2026-08-16T02:03:56+00:00"
  },
  "P4158": {
    "problem_number": 4158,
    "slug": "ramsey-number-r-4-15-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:23:55+00:00",
    "updated_at": "2026-08-16T02:04:05+00:00"
  },
  "P4160": {
    "problem_number": 4160,
    "slug": "ramsey-number-r-4-16-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:24:03+00:00",
    "updated_at": "2026-08-16T02:04:13+00:00"
  },
  "P4162": {
    "problem_number": 4162,
    "slug": "ramsey-number-r-4-17-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:24:11+00:00",
    "updated_at": "2026-08-16T02:04:17+00:00"
  },
  "P4164": {
    "problem_number": 4164,
    "slug": "ramsey-number-r-4-18-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:24:22+00:00",
    "updated_at": "2026-08-16T02:04:21+00:00"
  },
  "P4166": {
    "problem_number": 4166,
    "slug": "ramsey-number-r-4-19-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:24:40+00:00",
    "updated_at": "2026-08-16T02:04:29+00:00"
  },
  "P4168": {
    "problem_number": 4168,
    "slug": "ramsey-number-r-4-20-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:25:06+00:00",
    "updated_at": "2026-08-16T02:04:37+00:00"
  },
  "P4170": {
    "problem_number": 4170,
    "slug": "ramsey-number-r-4-21-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:25:29+00:00",
    "updated_at": "2026-08-16T02:04:43+00:00"
  },
  "P4172": {
    "problem_number": 4172,
    "slug": "ramsey-number-r-4-22-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:25:41+00:00",
    "updated_at": "2026-08-16T02:04:51+00:00"
  },
  "P4174": {
    "problem_number": 4174,
    "slug": "ramsey-number-r-4-23-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:25:58+00:00",
    "updated_at": "2026-08-16T02:04:58+00:00"
  },
  "P4176": {
    "problem_number": 4176,
    "slug": "ramsey-number-r-4-24-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:26:21+00:00",
    "updated_at": "2026-08-16T02:05:01+00:00"
  },
  "P4178": {
    "problem_number": 4178,
    "slug": "ramsey-number-r-4-25-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:26:54+00:00",
    "updated_at": "2026-08-16T02:05:08+00:00"
  },
  "P4180": {
    "problem_number": 4180,
    "slug": "ramsey-number-r-4-26-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:27:24+00:00",
    "updated_at": "2026-08-16T02:05:14+00:00"
  },
  "P4182": {
    "problem_number": 4182,
    "slug": "ramsey-number-r-4-27-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:27:47+00:00",
    "updated_at": "2026-08-16T02:05:23+00:00"
  },
  "P4184": {
    "problem_number": 4184,
    "slug": "ramsey-number-r-4-28-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:03+00:00",
    "updated_at": "2026-08-16T02:05:30+00:00"
  },
  "P4186": {
    "problem_number": 4186,
    "slug": "ramsey-number-r-4-29-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:07+00:00",
    "updated_at": "2026-08-16T02:05:32+00:00"
  },
  "P3690": {
    "problem_number": 3690,
    "slug": "random-greedy-matching-ten-grid-expectation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:14+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9202": {
    "problem_number": 9202,
    "slug": "open-fc-557bff9517ba1bbb66fc-rank-elkies28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:14+00:00",
    "updated_at": "2026-08-17T19:49:14+00:00"
  },
  "P9684": {
    "problem_number": 9684,
    "slug": "open-fc-807aff667af1a01d55fb-rank-elkiesklagsbrun29",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:27+00:00",
    "updated_at": "2026-08-17T20:01:30+00:00"
  },
  "P12281": {
    "problem_number": 12281,
    "slug": "exact-rounding-at-harmonic-number-thresholds",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:33:43+00:00",
    "updated_at": "2026-09-01T19:33:48+00:00"
  },
  "P11808": {
    "problem_number": 11808,
    "slug": "exact-self-ranks-in-integer-centrality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:46:13+00:00",
    "updated_at": "2026-08-30T12:47:00+00:00"
  },
  "P11688": {
    "problem_number": 11688,
    "slug": "exact-shell-staircase-for-connected-holes-in-the-trihexagonal-tiling",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:00+00:00",
    "updated_at": "2026-08-30T11:15:07+00:00"
  },
  "P4068": {
    "problem_number": 4068,
    "slug": "binary-code-a2-37-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:14+00:00",
    "updated_at": "2026-08-16T01:57:19+00:00"
  },
  "P4070": {
    "problem_number": 4070,
    "slug": "binary-code-a2-38-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:17+00:00",
    "updated_at": "2026-08-16T01:57:22+00:00"
  },
  "P4072": {
    "problem_number": 4072,
    "slug": "binary-code-a2-39-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:18+00:00",
    "updated_at": "2026-08-16T01:57:28+00:00"
  },
  "P4074": {
    "problem_number": 4074,
    "slug": "binary-code-a2-40-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:19+00:00",
    "updated_at": "2026-08-16T01:57:32+00:00"
  },
  "P4076": {
    "problem_number": 4076,
    "slug": "binary-code-a2-41-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:20+00:00",
    "updated_at": "2026-08-16T01:57:37+00:00"
  },
  "P4078": {
    "problem_number": 4078,
    "slug": "binary-code-a2-42-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:22+00:00",
    "updated_at": "2026-08-16T01:57:47+00:00"
  },
  "P4080": {
    "problem_number": 4080,
    "slug": "binary-code-a2-43-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:27+00:00",
    "updated_at": "2026-08-16T01:57:55+00:00"
  },
  "P4082": {
    "problem_number": 4082,
    "slug": "binary-code-a2-44-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:31+00:00",
    "updated_at": "2026-08-16T01:57:57+00:00"
  },
  "P4084": {
    "problem_number": 4084,
    "slug": "binary-code-a2-45-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:36+00:00",
    "updated_at": "2026-08-16T01:57:58+00:00"
  },
  "P4086": {
    "problem_number": 4086,
    "slug": "binary-code-a2-46-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:40+00:00",
    "updated_at": "2026-08-16T01:57:58+00:00"
  },
  "P4088": {
    "problem_number": 4088,
    "slug": "binary-code-a2-47-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:42+00:00",
    "updated_at": "2026-08-16T01:58:01+00:00"
  },
  "P4090": {
    "problem_number": 4090,
    "slug": "binary-code-a2-48-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:43+00:00",
    "updated_at": "2026-08-16T01:58:03+00:00"
  },
  "P4092": {
    "problem_number": 4092,
    "slug": "binary-code-a2-49-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:45+00:00",
    "updated_at": "2026-08-16T01:58:04+00:00"
  },
  "P4094": {
    "problem_number": 4094,
    "slug": "binary-code-a2-50-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:47+00:00",
    "updated_at": "2026-08-16T01:58:05+00:00"
  },
  "P4096": {
    "problem_number": 4096,
    "slug": "binary-code-a2-51-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:50+00:00",
    "updated_at": "2026-08-16T01:58:06+00:00"
  },
  "P4098": {
    "problem_number": 4098,
    "slug": "binary-code-a2-52-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:52+00:00",
    "updated_at": "2026-08-16T01:58:06+00:00"
  },
  "P4100": {
    "problem_number": 4100,
    "slug": "binary-code-a2-53-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:19:57+00:00",
    "updated_at": "2026-08-16T01:58:06+00:00"
  },
  "P4102": {
    "problem_number": 4102,
    "slug": "binary-code-a2-54-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:20:25+00:00",
    "updated_at": "2026-08-16T01:58:06+00:00"
  },
  "P4104": {
    "problem_number": 4104,
    "slug": "binary-code-a2-55-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:20:46+00:00",
    "updated_at": "2026-08-16T01:58:07+00:00"
  },
  "P4106": {
    "problem_number": 4106,
    "slug": "binary-code-a2-56-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:20:59+00:00",
    "updated_at": "2026-08-16T01:58:07+00:00"
  },
  "P2726": {
    "problem_number": 2726,
    "slug": "bootstrap-percolation-eight-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:32+00:00",
    "updated_at": "2026-08-01T02:03:31+00:00"
  },
  "P2798": {
    "problem_number": 2798,
    "slug": "heilbronn-square-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:07+00:00",
    "updated_at": "2026-07-30T02:25:47+00:00"
  },
  "P2686": {
    "problem_number": 2686,
    "slug": "four-cube-site-percolation-tunnel-probability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:13+00:00",
    "updated_at": "2026-08-01T02:08:01+00:00"
  },
  "P3948": {
    "problem_number": 3948,
    "slug": "binary-code-a-100-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:21+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5342": {
    "problem_number": 5342,
    "slug": "binary-constant-weight-code-a-100-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:00+00:00",
    "updated_at": "2026-08-16T08:22:02+00:00"
  },
  "P3950": {
    "problem_number": 3950,
    "slug": "binary-code-a-101-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:26+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5344": {
    "problem_number": 5344,
    "slug": "binary-constant-weight-code-a-101-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:04+00:00",
    "updated_at": "2026-08-16T08:22:04+00:00"
  },
  "P3952": {
    "problem_number": 3952,
    "slug": "binary-code-a-102-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:28+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5346": {
    "problem_number": 5346,
    "slug": "binary-constant-weight-code-a-102-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:05+00:00",
    "updated_at": "2026-08-16T08:22:05+00:00"
  },
  "P3954": {
    "problem_number": 3954,
    "slug": "binary-code-a-103-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:31+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5348": {
    "problem_number": 5348,
    "slug": "binary-constant-weight-code-a-103-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:06+00:00",
    "updated_at": "2026-08-16T08:22:10+00:00"
  },
  "P3956": {
    "problem_number": 3956,
    "slug": "binary-code-a-104-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:34+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5350": {
    "problem_number": 5350,
    "slug": "binary-constant-weight-code-a-104-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:12+00:00",
    "updated_at": "2026-08-16T08:22:13+00:00"
  },
  "P3958": {
    "problem_number": 3958,
    "slug": "binary-code-a-105-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:36+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5352": {
    "problem_number": 5352,
    "slug": "binary-constant-weight-code-a-105-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:13+00:00",
    "updated_at": "2026-08-16T08:22:15+00:00"
  },
  "P3960": {
    "problem_number": 3960,
    "slug": "binary-code-a-106-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:41+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5354": {
    "problem_number": 5354,
    "slug": "binary-constant-weight-code-a-106-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:17+00:00",
    "updated_at": "2026-08-16T08:22:19+00:00"
  },
  "P3962": {
    "problem_number": 3962,
    "slug": "binary-code-a-107-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:49+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5356": {
    "problem_number": 5356,
    "slug": "binary-constant-weight-code-a-107-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:20+00:00",
    "updated_at": "2026-08-16T08:22:21+00:00"
  },
  "P3964": {
    "problem_number": 3964,
    "slug": "binary-code-a-108-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:54+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5358": {
    "problem_number": 5358,
    "slug": "binary-constant-weight-code-a-108-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:22+00:00",
    "updated_at": "2026-08-16T08:22:25+00:00"
  },
  "P3966": {
    "problem_number": 3966,
    "slug": "binary-code-a-109-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:36:10+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5360": {
    "problem_number": 5360,
    "slug": "binary-constant-weight-code-a-109-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:27+00:00",
    "updated_at": "2026-08-16T08:22:30+00:00"
  },
  "P3968": {
    "problem_number": 3968,
    "slug": "binary-code-a-110-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:36:22+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5362": {
    "problem_number": 5362,
    "slug": "binary-constant-weight-code-a-110-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:30+00:00",
    "updated_at": "2026-08-16T08:22:32+00:00"
  },
  "P3970": {
    "problem_number": 3970,
    "slug": "binary-code-a-111-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:36:37+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5364": {
    "problem_number": 5364,
    "slug": "binary-constant-weight-code-a-111-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:34+00:00",
    "updated_at": "2026-08-16T08:22:34+00:00"
  },
  "P3972": {
    "problem_number": 3972,
    "slug": "binary-code-a-112-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:36:46+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5366": {
    "problem_number": 5366,
    "slug": "binary-constant-weight-code-a-112-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:35+00:00",
    "updated_at": "2026-08-16T08:22:36+00:00"
  },
  "P3974": {
    "problem_number": 3974,
    "slug": "binary-code-a-113-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:36:52+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5368": {
    "problem_number": 5368,
    "slug": "binary-constant-weight-code-a-113-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:37+00:00",
    "updated_at": "2026-08-16T08:22:40+00:00"
  },
  "P3976": {
    "problem_number": 3976,
    "slug": "binary-code-a-114-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:00+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5370": {
    "problem_number": 5370,
    "slug": "binary-constant-weight-code-a-114-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:40+00:00",
    "updated_at": "2026-08-16T08:22:41+00:00"
  },
  "P3978": {
    "problem_number": 3978,
    "slug": "binary-code-a-115-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:07+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5372": {
    "problem_number": 5372,
    "slug": "binary-constant-weight-code-a-115-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:41+00:00",
    "updated_at": "2026-08-16T08:22:41+00:00"
  },
  "P3980": {
    "problem_number": 3980,
    "slug": "binary-code-a-116-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:09+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5374": {
    "problem_number": 5374,
    "slug": "binary-constant-weight-code-a-116-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:42+00:00",
    "updated_at": "2026-08-16T08:22:43+00:00"
  },
  "P3982": {
    "problem_number": 3982,
    "slug": "binary-code-a-117-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:13+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5376": {
    "problem_number": 5376,
    "slug": "binary-constant-weight-code-a-117-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:44+00:00",
    "updated_at": "2026-08-16T08:22:45+00:00"
  },
  "P3984": {
    "problem_number": 3984,
    "slug": "binary-code-a-118-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:18+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5378": {
    "problem_number": 5378,
    "slug": "binary-constant-weight-code-a-118-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:46+00:00",
    "updated_at": "2026-08-16T08:22:47+00:00"
  },
  "P3986": {
    "problem_number": 3986,
    "slug": "binary-code-a-119-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:22+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5380": {
    "problem_number": 5380,
    "slug": "binary-constant-weight-code-a-119-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:48+00:00",
    "updated_at": "2026-08-16T08:22:49+00:00"
  },
  "P3988": {
    "problem_number": 3988,
    "slug": "binary-code-a-120-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:25+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5382": {
    "problem_number": 5382,
    "slug": "binary-constant-weight-code-a-120-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:51+00:00",
    "updated_at": "2026-08-16T08:22:55+00:00"
  },
  "P3990": {
    "problem_number": 3990,
    "slug": "binary-code-a-121-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5384": {
    "problem_number": 5384,
    "slug": "binary-constant-weight-code-a-121-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:56+00:00",
    "updated_at": "2026-08-16T08:22:57+00:00"
  },
  "P3992": {
    "problem_number": 3992,
    "slug": "binary-code-a-122-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:37:58+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5386": {
    "problem_number": 5386,
    "slug": "binary-constant-weight-code-a-122-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:57+00:00",
    "updated_at": "2026-08-16T08:22:58+00:00"
  },
  "P3994": {
    "problem_number": 3994,
    "slug": "binary-code-a-123-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:38:14+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5388": {
    "problem_number": 5388,
    "slug": "binary-constant-weight-code-a-123-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:22:59+00:00",
    "updated_at": "2026-08-16T08:23:02+00:00"
  },
  "P3996": {
    "problem_number": 3996,
    "slug": "binary-code-a-124-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:38:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5390": {
    "problem_number": 5390,
    "slug": "binary-constant-weight-code-a-124-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:03+00:00",
    "updated_at": "2026-08-16T08:23:03+00:00"
  },
  "P3998": {
    "problem_number": 3998,
    "slug": "binary-code-a-125-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:38:57+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5392": {
    "problem_number": 5392,
    "slug": "binary-constant-weight-code-a-125-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:04+00:00",
    "updated_at": "2026-08-16T08:23:04+00:00"
  },
  "P4000": {
    "problem_number": 4000,
    "slug": "binary-code-a-126-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:10+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5394": {
    "problem_number": 5394,
    "slug": "binary-constant-weight-code-a-126-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:06+00:00",
    "updated_at": "2026-08-16T08:23:09+00:00"
  },
  "P4002": {
    "problem_number": 4002,
    "slug": "binary-code-a-127-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:19+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5396": {
    "problem_number": 5396,
    "slug": "binary-constant-weight-code-a-127-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:09+00:00",
    "updated_at": "2026-08-16T08:23:10+00:00"
  },
  "P4004": {
    "problem_number": 4004,
    "slug": "binary-code-a-128-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:20+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5398": {
    "problem_number": 5398,
    "slug": "binary-constant-weight-code-a-128-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:11+00:00",
    "updated_at": "2026-08-16T08:23:13+00:00"
  },
  "P4006": {
    "problem_number": 4006,
    "slug": "binary-code-a-129-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:29+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5400": {
    "problem_number": 5400,
    "slug": "binary-constant-weight-code-a-129-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:18+00:00",
    "updated_at": "2026-08-16T08:23:21+00:00"
  },
  "P4008": {
    "problem_number": 4008,
    "slug": "binary-code-a-130-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:36+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5402": {
    "problem_number": 5402,
    "slug": "binary-constant-weight-code-a-130-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:22+00:00",
    "updated_at": "2026-08-16T08:23:27+00:00"
  },
  "P4010": {
    "problem_number": 4010,
    "slug": "binary-code-a-131-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:39:46+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5404": {
    "problem_number": 5404,
    "slug": "binary-constant-weight-code-a-131-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:28+00:00",
    "updated_at": "2026-08-16T08:23:30+00:00"
  },
  "P4012": {
    "problem_number": 4012,
    "slug": "binary-code-a-132-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:40:00+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5406": {
    "problem_number": 5406,
    "slug": "binary-constant-weight-code-a-132-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:33+00:00",
    "updated_at": "2026-08-16T08:23:35+00:00"
  },
  "P4014": {
    "problem_number": 4014,
    "slug": "binary-code-a-133-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:40:09+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5408": {
    "problem_number": 5408,
    "slug": "binary-constant-weight-code-a-133-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:38+00:00",
    "updated_at": "2026-08-16T08:23:42+00:00"
  },
  "P4016": {
    "problem_number": 4016,
    "slug": "binary-code-a-134-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:40:25+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5410": {
    "problem_number": 5410,
    "slug": "binary-constant-weight-code-a-134-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:43+00:00",
    "updated_at": "2026-08-16T08:23:47+00:00"
  },
  "P4018": {
    "problem_number": 4018,
    "slug": "binary-code-a-135-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:40:45+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5412": {
    "problem_number": 5412,
    "slug": "binary-constant-weight-code-a-135-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
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      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:50+00:00",
    "updated_at": "2026-08-16T08:23:52+00:00"
  },
  "P4020": {
    "problem_number": 4020,
    "slug": "binary-code-a-136-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:40:54+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5414": {
    "problem_number": 5414,
    "slug": "binary-constant-weight-code-a-136-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:55+00:00",
    "updated_at": "2026-08-16T08:23:56+00:00"
  },
  "P5416": {
    "problem_number": 5416,
    "slug": "binary-constant-weight-code-a-137-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:56+00:00",
    "updated_at": "2026-08-16T08:23:56+00:00"
  },
  "P5418": {
    "problem_number": 5418,
    "slug": "binary-constant-weight-code-a-138-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:57+00:00",
    "updated_at": "2026-08-16T08:23:58+00:00"
  },
  "P5420": {
    "problem_number": 5420,
    "slug": "binary-constant-weight-code-a-139-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:23:59+00:00",
    "updated_at": "2026-08-16T08:24:01+00:00"
  },
  "P5422": {
    "problem_number": 5422,
    "slug": "binary-constant-weight-code-a-140-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:24:01+00:00",
    "updated_at": "2026-08-16T08:24:02+00:00"
  },
  "P5424": {
    "problem_number": 5424,
    "slug": "binary-constant-weight-code-a-141-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:24:02+00:00",
    "updated_at": "2026-08-16T08:24:04+00:00"
  },
  "P5426": {
    "problem_number": 5426,
    "slug": "binary-constant-weight-code-a-142-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:07+00:00",
    "updated_at": "2026-08-16T08:24:12+00:00"
  },
  "P5428": {
    "problem_number": 5428,
    "slug": "binary-constant-weight-code-a-143-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
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      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:17+00:00",
    "updated_at": "2026-08-16T08:24:26+00:00"
  },
  "P5430": {
    "problem_number": 5430,
    "slug": "binary-constant-weight-code-a-144-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
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        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
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        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
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      "statement_format": "textbook_mathematics",
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      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:31+00:00",
    "updated_at": "2026-08-16T08:24:37+00:00"
  },
  "P5432": {
    "problem_number": 5432,
    "slug": "binary-constant-weight-code-a-145-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
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        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
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      "statement_format": "textbook_mathematics",
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      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:37+00:00",
    "updated_at": "2026-08-16T08:24:38+00:00"
  },
  "P5434": {
    "problem_number": 5434,
    "slug": "binary-constant-weight-code-a-146-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
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        "state": "open",
        "label": "Open",
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        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
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        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
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      "statement_format": "textbook_mathematics",
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      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:38+00:00",
    "updated_at": "2026-08-16T08:24:38+00:00"
  },
  "P5436": {
    "problem_number": 5436,
    "slug": "binary-constant-weight-code-a-147-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
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      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T08:24:38+00:00",
    "updated_at": "2026-08-16T08:24:40+00:00"
  },
  "P5438": {
    "problem_number": 5438,
    "slug": "binary-constant-weight-code-a-148-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
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        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
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        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
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      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
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    "created_at": "2026-08-16T08:24:41+00:00",
    "updated_at": "2026-08-16T08:24:47+00:00"
  },
  "P5440": {
    "problem_number": 5440,
    "slug": "binary-constant-weight-code-a-149-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
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        "verified": false,
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        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
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        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
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      "formal_correspondence": "not_applicable"
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    "updated_at": "2026-08-16T08:24:59+00:00"
  },
  "P5442": {
    "problem_number": 5442,
    "slug": "binary-constant-weight-code-a-150-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:25:04+00:00",
    "updated_at": "2026-08-16T08:25:14+00:00"
  },
  "P5444": {
    "problem_number": 5444,
    "slug": "binary-constant-weight-code-a-151-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:25:24+00:00",
    "updated_at": "2026-08-16T08:25:38+00:00"
  },
  "P5446": {
    "problem_number": 5446,
    "slug": "binary-constant-weight-code-a-152-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:25:41+00:00",
    "updated_at": "2026-08-16T08:25:43+00:00"
  },
  "P5448": {
    "problem_number": 5448,
    "slug": "binary-constant-weight-code-a-153-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:25:45+00:00",
    "updated_at": "2026-08-16T08:25:54+00:00"
  },
  "P5450": {
    "problem_number": 5450,
    "slug": "binary-constant-weight-code-a-154-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:25:59+00:00",
    "updated_at": "2026-08-16T08:26:09+00:00"
  },
  "P5452": {
    "problem_number": 5452,
    "slug": "binary-constant-weight-code-a-155-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:26:17+00:00",
    "updated_at": "2026-08-16T08:26:26+00:00"
  },
  "P5454": {
    "problem_number": 5454,
    "slug": "binary-constant-weight-code-a-156-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:26:28+00:00",
    "updated_at": "2026-08-16T08:26:34+00:00"
  },
  "P5456": {
    "problem_number": 5456,
    "slug": "binary-constant-weight-code-a-157-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:26:38+00:00",
    "updated_at": "2026-08-16T08:26:46+00:00"
  },
  "P5458": {
    "problem_number": 5458,
    "slug": "binary-constant-weight-code-a-158-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:26:55+00:00",
    "updated_at": "2026-08-16T08:27:01+00:00"
  },
  "P5460": {
    "problem_number": 5460,
    "slug": "binary-constant-weight-code-a-159-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:02+00:00",
    "updated_at": "2026-08-16T08:27:07+00:00"
  },
  "P5462": {
    "problem_number": 5462,
    "slug": "binary-constant-weight-code-a-160-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
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      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:10+00:00",
    "updated_at": "2026-08-16T08:27:15+00:00"
  },
  "P5464": {
    "problem_number": 5464,
    "slug": "binary-constant-weight-code-a-161-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:22+00:00",
    "updated_at": "2026-08-16T08:27:30+00:00"
  },
  "P5466": {
    "problem_number": 5466,
    "slug": "binary-constant-weight-code-a-162-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:33+00:00",
    "updated_at": "2026-08-16T08:27:36+00:00"
  },
  "P5468": {
    "problem_number": 5468,
    "slug": "binary-constant-weight-code-a-163-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:27:45+00:00",
    "updated_at": "2026-08-16T08:27:48+00:00"
  },
  "P4628": {
    "problem_number": 4628,
    "slug": "binary-constant-weight-code-a-24-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:21+00:00",
    "updated_at": "2026-08-16T05:37:23+00:00"
  },
  "P4630": {
    "problem_number": 4630,
    "slug": "binary-constant-weight-code-a-25-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:23+00:00",
    "updated_at": "2026-08-16T05:37:26+00:00"
  },
  "P4632": {
    "problem_number": 4632,
    "slug": "binary-constant-weight-code-a-26-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:27+00:00",
    "updated_at": "2026-08-16T05:37:27+00:00"
  },
  "P4634": {
    "problem_number": 4634,
    "slug": "binary-constant-weight-code-a-27-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:27+00:00",
    "updated_at": "2026-08-16T05:37:29+00:00"
  },
  "P4636": {
    "problem_number": 4636,
    "slug": "binary-constant-weight-code-a-28-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:29+00:00",
    "updated_at": "2026-08-16T05:37:29+00:00"
  },
  "P4638": {
    "problem_number": 4638,
    "slug": "binary-constant-weight-code-a-29-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:29+00:00",
    "updated_at": "2026-08-16T05:37:31+00:00"
  },
  "P4640": {
    "problem_number": 4640,
    "slug": "binary-constant-weight-code-a-30-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:32+00:00",
    "updated_at": "2026-08-16T05:37:33+00:00"
  },
  "P4642": {
    "problem_number": 4642,
    "slug": "binary-constant-weight-code-a-31-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:33+00:00",
    "updated_at": "2026-08-16T05:37:41+00:00"
  },
  "P4644": {
    "problem_number": 4644,
    "slug": "binary-constant-weight-code-a-32-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:41+00:00",
    "updated_at": "2026-08-16T05:37:41+00:00"
  },
  "P4646": {
    "problem_number": 4646,
    "slug": "binary-constant-weight-code-a-33-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:43+00:00",
    "updated_at": "2026-08-16T05:37:46+00:00"
  },
  "P4648": {
    "problem_number": 4648,
    "slug": "binary-constant-weight-code-a-34-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T05:37:46+00:00",
    "updated_at": "2026-08-16T05:37:48+00:00"
  },
  "P4650": {
    "problem_number": 4650,
    "slug": "binary-constant-weight-code-a-35-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T05:37:51+00:00",
    "updated_at": "2026-08-16T05:37:54+00:00"
  },
  "P4652": {
    "problem_number": 4652,
    "slug": "binary-constant-weight-code-a-36-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
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        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
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        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:57+00:00",
    "updated_at": "2026-08-16T05:37:57+00:00"
  },
  "P4654": {
    "problem_number": 4654,
    "slug": "binary-constant-weight-code-a-37-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:37:58+00:00",
    "updated_at": "2026-08-16T05:38:08+00:00"
  },
  "P4656": {
    "problem_number": 4656,
    "slug": "binary-constant-weight-code-a-38-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:12+00:00",
    "updated_at": "2026-08-16T05:38:14+00:00"
  },
  "P4658": {
    "problem_number": 4658,
    "slug": "binary-constant-weight-code-a-39-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:16+00:00",
    "updated_at": "2026-08-16T05:38:25+00:00"
  },
  "P4660": {
    "problem_number": 4660,
    "slug": "binary-constant-weight-code-a-40-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
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    "created_at": "2026-08-16T05:38:26+00:00",
    "updated_at": "2026-08-16T05:38:27+00:00"
  },
  "P4662": {
    "problem_number": 4662,
    "slug": "binary-constant-weight-code-a-41-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:28+00:00",
    "updated_at": "2026-08-16T05:38:29+00:00"
  },
  "P4664": {
    "problem_number": 4664,
    "slug": "binary-constant-weight-code-a-42-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:29+00:00",
    "updated_at": "2026-08-16T05:38:31+00:00"
  },
  "P4666": {
    "problem_number": 4666,
    "slug": "binary-constant-weight-code-a-43-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:31+00:00",
    "updated_at": "2026-08-16T05:38:31+00:00"
  },
  "P4668": {
    "problem_number": 4668,
    "slug": "binary-constant-weight-code-a-44-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:32+00:00",
    "updated_at": "2026-08-16T05:38:32+00:00"
  },
  "P4670": {
    "problem_number": 4670,
    "slug": "binary-constant-weight-code-a-45-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:36+00:00",
    "updated_at": "2026-08-16T05:38:38+00:00"
  },
  "P4672": {
    "problem_number": 4672,
    "slug": "binary-constant-weight-code-a-46-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:42+00:00",
    "updated_at": "2026-08-16T05:38:47+00:00"
  },
  "P4674": {
    "problem_number": 4674,
    "slug": "binary-constant-weight-code-a-47-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:38:49+00:00",
    "updated_at": "2026-08-16T05:39:02+00:00"
  },
  "P4676": {
    "problem_number": 4676,
    "slug": "binary-constant-weight-code-a-48-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:39:05+00:00",
    "updated_at": "2026-08-16T05:39:17+00:00"
  },
  "P4678": {
    "problem_number": 4678,
    "slug": "binary-constant-weight-code-a-49-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:39:24+00:00",
    "updated_at": "2026-08-16T05:39:33+00:00"
  },
  "P4680": {
    "problem_number": 4680,
    "slug": "binary-constant-weight-code-a-50-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:39:39+00:00",
    "updated_at": "2026-08-16T05:39:48+00:00"
  },
  "P4682": {
    "problem_number": 4682,
    "slug": "binary-constant-weight-code-a-51-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:39:50+00:00",
    "updated_at": "2026-08-16T05:39:55+00:00"
  },
  "P4684": {
    "problem_number": 4684,
    "slug": "binary-constant-weight-code-a-52-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:39:57+00:00",
    "updated_at": "2026-08-16T05:40:04+00:00"
  },
  "P4686": {
    "problem_number": 4686,
    "slug": "binary-constant-weight-code-a-53-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:05+00:00",
    "updated_at": "2026-08-16T05:40:08+00:00"
  },
  "P4688": {
    "problem_number": 4688,
    "slug": "binary-constant-weight-code-a-54-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:14+00:00",
    "updated_at": "2026-08-16T05:40:24+00:00"
  },
  "P4690": {
    "problem_number": 4690,
    "slug": "binary-constant-weight-code-a-55-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:30+00:00",
    "updated_at": "2026-08-16T05:40:38+00:00"
  },
  "P4692": {
    "problem_number": 4692,
    "slug": "binary-constant-weight-code-a-56-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:42+00:00",
    "updated_at": "2026-08-16T05:40:45+00:00"
  },
  "P4694": {
    "problem_number": 4694,
    "slug": "binary-constant-weight-code-a-57-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:45+00:00",
    "updated_at": "2026-08-16T05:40:45+00:00"
  },
  "P4696": {
    "problem_number": 4696,
    "slug": "binary-constant-weight-code-a-58-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:46+00:00",
    "updated_at": "2026-08-16T05:40:46+00:00"
  },
  "P4698": {
    "problem_number": 4698,
    "slug": "binary-constant-weight-code-a-59-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:47+00:00",
    "updated_at": "2026-08-16T05:40:48+00:00"
  },
  "P4700": {
    "problem_number": 4700,
    "slug": "binary-constant-weight-code-a-60-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:49+00:00",
    "updated_at": "2026-08-16T05:40:50+00:00"
  },
  "P4702": {
    "problem_number": 4702,
    "slug": "binary-constant-weight-code-a-61-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "version": "theoremdb-problem-display-v5",
      "status": "passed",
      "statement_format": "textbook_mathematics",
      "definitions_format": "typed_textbook_exposition",
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:51+00:00",
    "updated_at": "2026-08-16T05:40:54+00:00"
  },
  "P4704": {
    "problem_number": 4704,
    "slug": "binary-constant-weight-code-a-62-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:40:56+00:00",
    "updated_at": "2026-08-16T05:40:59+00:00"
  },
  "P4706": {
    "problem_number": 4706,
    "slug": "binary-constant-weight-code-a-63-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:41:00+00:00",
    "updated_at": "2026-08-16T05:41:01+00:00"
  },
  "P5010": {
    "problem_number": 5010,
    "slug": "binary-constant-weight-code-a-64-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:58:32+00:00",
    "updated_at": "2026-08-16T07:59:14+00:00"
  },
  "P5012": {
    "problem_number": 5012,
    "slug": "binary-constant-weight-code-a-65-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:59:21+00:00",
    "updated_at": "2026-08-16T07:59:37+00:00"
  },
  "P5014": {
    "problem_number": 5014,
    "slug": "binary-constant-weight-code-a-66-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:59:47+00:00",
    "updated_at": "2026-08-16T08:00:03+00:00"
  },
  "P5018": {
    "problem_number": 5018,
    "slug": "binary-constant-weight-code-a-67-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:00:11+00:00",
    "updated_at": "2026-08-16T08:00:14+00:00"
  },
  "P5020": {
    "problem_number": 5020,
    "slug": "binary-constant-weight-code-a-68-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:00:17+00:00",
    "updated_at": "2026-08-16T08:00:18+00:00"
  },
  "P5022": {
    "problem_number": 5022,
    "slug": "binary-constant-weight-code-a-69-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:00:18+00:00",
    "updated_at": "2026-08-16T08:20:06+00:00"
  },
  "P5282": {
    "problem_number": 5282,
    "slug": "binary-constant-weight-code-a-70-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:09+00:00",
    "updated_at": "2026-08-16T08:20:11+00:00"
  },
  "P5284": {
    "problem_number": 5284,
    "slug": "binary-constant-weight-code-a-71-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:11+00:00",
    "updated_at": "2026-08-16T08:20:15+00:00"
  },
  "P5286": {
    "problem_number": 5286,
    "slug": "binary-constant-weight-code-a-72-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:18+00:00",
    "updated_at": "2026-08-16T08:20:21+00:00"
  },
  "P5288": {
    "problem_number": 5288,
    "slug": "binary-constant-weight-code-a-73-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:25+00:00",
    "updated_at": "2026-08-16T08:20:32+00:00"
  },
  "P5290": {
    "problem_number": 5290,
    "slug": "binary-constant-weight-code-a-74-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:34+00:00",
    "updated_at": "2026-08-16T08:20:36+00:00"
  },
  "P5292": {
    "problem_number": 5292,
    "slug": "binary-constant-weight-code-a-75-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:40+00:00",
    "updated_at": "2026-08-16T08:20:42+00:00"
  },
  "P5294": {
    "problem_number": 5294,
    "slug": "binary-constant-weight-code-a-76-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:43+00:00",
    "updated_at": "2026-08-16T08:20:44+00:00"
  },
  "P5296": {
    "problem_number": 5296,
    "slug": "binary-constant-weight-code-a-77-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:47+00:00",
    "updated_at": "2026-08-16T08:20:51+00:00"
  },
  "P3904": {
    "problem_number": 3904,
    "slug": "binary-code-a-78-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:05+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5298": {
    "problem_number": 5298,
    "slug": "binary-constant-weight-code-a-78-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:20:54+00:00",
    "updated_at": "2026-08-16T08:21:00+00:00"
  },
  "P3906": {
    "problem_number": 3906,
    "slug": "binary-code-a-79-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:07+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5300": {
    "problem_number": 5300,
    "slug": "binary-constant-weight-code-a-79-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:01+00:00",
    "updated_at": "2026-08-16T08:21:01+00:00"
  },
  "P3908": {
    "problem_number": 3908,
    "slug": "binary-code-a-80-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:08+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5302": {
    "problem_number": 5302,
    "slug": "binary-constant-weight-code-a-80-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:03+00:00",
    "updated_at": "2026-08-16T08:21:08+00:00"
  },
  "P3910": {
    "problem_number": 3910,
    "slug": "binary-code-a-81-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:09+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5304": {
    "problem_number": 5304,
    "slug": "binary-constant-weight-code-a-81-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:08+00:00",
    "updated_at": "2026-08-16T08:21:09+00:00"
  },
  "P3912": {
    "problem_number": 3912,
    "slug": "binary-code-a-82-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:12+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5306": {
    "problem_number": 5306,
    "slug": "binary-constant-weight-code-a-82-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:10+00:00",
    "updated_at": "2026-08-16T08:21:10+00:00"
  },
  "P3914": {
    "problem_number": 3914,
    "slug": "binary-code-a-83-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:13+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5308": {
    "problem_number": 5308,
    "slug": "binary-constant-weight-code-a-83-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:10+00:00",
    "updated_at": "2026-08-16T08:21:12+00:00"
  },
  "P3916": {
    "problem_number": 3916,
    "slug": "binary-code-a-84-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:14+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5310": {
    "problem_number": 5310,
    "slug": "binary-constant-weight-code-a-84-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:14+00:00",
    "updated_at": "2026-08-16T08:21:16+00:00"
  },
  "P3918": {
    "problem_number": 3918,
    "slug": "binary-code-a-85-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:14+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5312": {
    "problem_number": 5312,
    "slug": "binary-constant-weight-code-a-85-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:17+00:00",
    "updated_at": "2026-08-16T08:21:21+00:00"
  },
  "P3920": {
    "problem_number": 3920,
    "slug": "binary-code-a-86-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:15+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5314": {
    "problem_number": 5314,
    "slug": "binary-constant-weight-code-a-86-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:22+00:00",
    "updated_at": "2026-08-16T08:21:23+00:00"
  },
  "P3922": {
    "problem_number": 3922,
    "slug": "binary-code-a-87-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:17+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5316": {
    "problem_number": 5316,
    "slug": "binary-constant-weight-code-a-87-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:24+00:00",
    "updated_at": "2026-08-16T08:21:24+00:00"
  },
  "P3924": {
    "problem_number": 3924,
    "slug": "binary-code-a-88-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:18+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5318": {
    "problem_number": 5318,
    "slug": "binary-constant-weight-code-a-88-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:26+00:00",
    "updated_at": "2026-08-16T08:21:32+00:00"
  },
  "P3926": {
    "problem_number": 3926,
    "slug": "binary-code-a-89-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:20+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5320": {
    "problem_number": 5320,
    "slug": "binary-constant-weight-code-a-89-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:32+00:00",
    "updated_at": "2026-08-16T08:21:34+00:00"
  },
  "P3928": {
    "problem_number": 3928,
    "slug": "binary-code-a-90-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:22+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5322": {
    "problem_number": 5322,
    "slug": "binary-constant-weight-code-a-90-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:35+00:00",
    "updated_at": "2026-08-16T08:21:36+00:00"
  },
  "P3930": {
    "problem_number": 3930,
    "slug": "binary-code-a-91-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:27+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5324": {
    "problem_number": 5324,
    "slug": "binary-constant-weight-code-a-91-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:37+00:00",
    "updated_at": "2026-08-16T08:21:40+00:00"
  },
  "P3932": {
    "problem_number": 3932,
    "slug": "binary-code-a-92-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:29+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5326": {
    "problem_number": 5326,
    "slug": "binary-constant-weight-code-a-92-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:41+00:00",
    "updated_at": "2026-08-16T08:21:42+00:00"
  },
  "P3934": {
    "problem_number": 3934,
    "slug": "binary-code-a-93-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:31+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5328": {
    "problem_number": 5328,
    "slug": "binary-constant-weight-code-a-93-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:43+00:00",
    "updated_at": "2026-08-16T08:21:43+00:00"
  },
  "P3936": {
    "problem_number": 3936,
    "slug": "binary-code-a-94-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:35+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5330": {
    "problem_number": 5330,
    "slug": "binary-constant-weight-code-a-94-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:43+00:00",
    "updated_at": "2026-08-16T08:21:47+00:00"
  },
  "P3938": {
    "problem_number": 3938,
    "slug": "binary-code-a-95-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:37+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5332": {
    "problem_number": 5332,
    "slug": "binary-constant-weight-code-a-95-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:47+00:00",
    "updated_at": "2026-08-16T08:21:48+00:00"
  },
  "P3940": {
    "problem_number": 3940,
    "slug": "binary-code-a-96-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:42+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5334": {
    "problem_number": 5334,
    "slug": "binary-constant-weight-code-a-96-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:48+00:00",
    "updated_at": "2026-08-16T08:21:50+00:00"
  },
  "P3942": {
    "problem_number": 3942,
    "slug": "binary-code-a-97-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:48+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5336": {
    "problem_number": 5336,
    "slug": "binary-constant-weight-code-a-97-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:52+00:00",
    "updated_at": "2026-08-16T08:21:55+00:00"
  },
  "P3944": {
    "problem_number": 3944,
    "slug": "binary-code-a-98-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:08+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5338": {
    "problem_number": 5338,
    "slug": "binary-constant-weight-code-a-98-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:55+00:00",
    "updated_at": "2026-08-16T08:21:58+00:00"
  },
  "P3946": {
    "problem_number": 3946,
    "slug": "binary-code-a-99-6-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:35:16+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P5340": {
    "problem_number": 5340,
    "slug": "binary-constant-weight-code-a-99-6-4-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:21:59+00:00",
    "updated_at": "2026-08-16T08:22:00+00:00"
  },
  "P2634": {
    "problem_number": 2634,
    "slug": "covering-array-3-15-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:53+00:00",
    "updated_at": "2026-08-01T02:04:35+00:00"
  },
  "P9664": {
    "problem_number": 9664,
    "slug": "open-fc-60ec977de5c5b4ae953a-blochconstant-exact-value",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:52+00:00",
    "updated_at": "2026-08-17T20:00:54+00:00"
  },
  "P8216": {
    "problem_number": 8216,
    "slug": "open-fc-10e7ee966e26da791c9d-landauconstant-exact-value",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:13+00:00",
    "updated_at": "2026-08-17T18:37:15+00:00"
  },
  "P12781": {
    "problem_number": 12781,
    "slug": "exceptions-to-a-mod-4-goldbach-representation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:56:41+00:00",
    "updated_at": "2026-09-02T22:57:14+00:00"
  },
  "P12419": {
    "problem_number": 12419,
    "slug": "exceptions-to-a-three-prime-quadratic-form",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:33:57+00:00",
    "updated_at": "2026-09-02T21:34:05+00:00"
  },
  "P12495": {
    "problem_number": 12495,
    "slug": "exceptions-to-four-nonnegative-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:41:38+00:00",
    "updated_at": "2026-09-02T21:41:46+00:00"
  },
  "P11997": {
    "problem_number": 11997,
    "slug": "exceptions-to-representation-by-three-polygonal-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:32:45+00:00",
    "updated_at": "2026-09-01T18:33:11+00:00"
  },
  "P12139": {
    "problem_number": 12139,
    "slug": "existence-and-finiteness-of-primitive-cycles-for-every-3x-k-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:16:16+00:00",
    "updated_at": "2026-09-01T19:16:21+00:00"
  },
  "P8382": {
    "problem_number": 8382,
    "slug": "open-fc-2726bd32bfd639ee4f01-navier-stokes-existence-and-smoothness-periodic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:51+00:00",
    "updated_at": "2026-08-17T18:48:54+00:00"
  },
  "P3092": {
    "problem_number": 3092,
    "slug": "diagonal-ramsey-exponential-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:59+00:00",
    "updated_at": "2026-08-02T12:48:44+00:00"
  },
  "P8794": {
    "problem_number": 8794,
    "slug": "open-fc-7fe4890b77df3f476d42-n-dim-euler-brick-existence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:21:22+00:00",
    "updated_at": "2026-08-17T19:21:29+00:00"
  },
  "P9596": {
    "problem_number": 9596,
    "slug": "open-fc-e4674342e2b40eb45fac-molsorder12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:31+00:00",
    "updated_at": "2026-08-17T19:56:33+00:00"
  },
  "P8230": {
    "problem_number": 8230,
    "slug": "open-fc-130230251b0994218cad-erdos-944-variants-dirac-conjecture-k-eq-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:24+00:00",
    "updated_at": "2026-08-17T18:37:26+00:00"
  },
  "P9100": {
    "problem_number": 9100,
    "slug": "open-fc-c51f56b246fce6e53471-green-41-variants-exists-better-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:34+00:00",
    "updated_at": "2026-08-17T19:47:35+00:00"
  },
  "P8846": {
    "problem_number": 8846,
    "slug": "open-fc-abbc23a2779e5bfb3831-erdos-276",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:00+00:00",
    "updated_at": "2026-08-17T19:26:09+00:00"
  },
  "P9976": {
    "problem_number": 9976,
    "slug": "open-fc-a9751504dcb7f5e667e1-erdos-234",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:08+00:00",
    "updated_at": "2026-08-17T20:05:09+00:00"
  },
  "P2612": {
    "problem_number": 2612,
    "slug": "costas-array-order-32",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:46+00:00",
    "updated_at": "2026-07-29T20:55:22+00:00"
  },
  "P9750": {
    "problem_number": 9750,
    "slug": "open-fc-b8976ac04e1777ad0647-erdos-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:18+00:00",
    "updated_at": "2026-08-17T20:02:19+00:00"
  },
  "P3314": {
    "problem_number": 3314,
    "slug": "erdos-problem-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:33+00:00",
    "updated_at": "2026-08-12T06:04:34+00:00"
  },
  "P9092": {
    "problem_number": 9092,
    "slug": "open-fc-c052e6c937e49980697e-taxicab-for-5-2-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:24+00:00",
    "updated_at": "2026-08-17T19:47:25+00:00"
  },
  "P8966": {
    "problem_number": 8966,
    "slug": "open-fc-5ad0ebd10e7f8c9a4415-finite-equation677-not-implies-equation255",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:43:55+00:00",
    "updated_at": "2026-08-17T19:43:56+00:00"
  },
  "P3560": {
    "problem_number": 3560,
    "slug": "non-sofic-groups-exist",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:51:03+00:00",
    "updated_at": "2026-08-18T06:09:34+00:00"
  },
  "P9914": {
    "problem_number": 9914,
    "slug": "open-fc-7d2f9a81730a61345fb3-four-dim-euler-brick-existence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:30+00:00",
    "updated_at": "2026-08-17T20:04:31+00:00"
  },
  "P8498": {
    "problem_number": 8498,
    "slug": "open-fc-5509304c497bcfe9d5d2-hadamardconjecture-variants-167",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:47+00:00",
    "updated_at": "2026-08-17T18:52:52+00:00"
  },
  "P8376": {
    "problem_number": 8376,
    "slug": "open-fc-25a07ccdb937e6611cc5-existsweaklyfirstcountablecompactbig",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:41+00:00",
    "updated_at": "2026-08-17T18:48:44+00:00"
  },
  "P8984": {
    "problem_number": 8984,
    "slug": "open-fc-6e34b2abdbaab677552e-hasg-singletons-lindelof-card",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:20+00:00",
    "updated_at": "2026-08-17T19:44:21+00:00"
  },
  "P8912": {
    "problem_number": 8912,
    "slug": "open-fc-dee1f94058f624e3a175-perfect-euler-brick-existence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:19+00:00",
    "updated_at": "2026-08-17T19:40:20+00:00"
  },
  "P10008": {
    "problem_number": 10008,
    "slug": "open-fc-c2e644ba900c117f4a0a-countablymonolithicspace-exists-nhds-generated-countable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:22+00:00",
    "updated_at": "2026-08-17T20:05:22+00:00"
  },
  "P8530": {
    "problem_number": 8530,
    "slug": "open-fc-66d9038153e6c2510e45-artin-primitive-roots-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:15+00:00",
    "updated_at": "2026-08-17T18:54:18+00:00"
  },
  "P8830": {
    "problem_number": 8830,
    "slug": "open-fc-a01c4e2b1b26b499877a-erdos-971",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:51+00:00",
    "updated_at": "2026-08-17T19:24:58+00:00"
  },
  "P8302": {
    "problem_number": 8302,
    "slug": "open-fc-1e5db26171391699c759-erdos-723-variants-eq-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:53+00:00",
    "updated_at": "2026-08-17T18:38:58+00:00"
  },
  "P8514": {
    "problem_number": 8514,
    "slug": "open-fc-5dcb86815aec6f3a9f6d-hassicpovm-56",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:52+00:00",
    "updated_at": "2026-08-17T18:53:57+00:00"
  },
  "P8474": {
    "problem_number": 8474,
    "slug": "open-fc-48097b4ef7db0326cb9d-hassicpovm-58",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:17+00:00",
    "updated_at": "2026-08-17T18:52:18+00:00"
  },
  "P8282": {
    "problem_number": 8282,
    "slug": "open-fc-1c2fbf08e060153ac309-hassicpovm-59",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:14+00:00",
    "updated_at": "2026-08-17T18:38:15+00:00"
  },
  "P9572": {
    "problem_number": 9572,
    "slug": "open-fc-cfb48e4647aeb81b6cf9-hassicpovm-60",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:42+00:00",
    "updated_at": "2026-08-17T19:55:44+00:00"
  },
  "P9618": {
    "problem_number": 9618,
    "slug": "open-fc-f3acde69f5121d26de4a-hassicpovm-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:15+00:00",
    "updated_at": "2026-08-17T19:57:16+00:00"
  },
  "P9894": {
    "problem_number": 9894,
    "slug": "open-fc-6ac5c49dd08bc3352a83-hassicpovm-68",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:20+00:00",
    "updated_at": "2026-08-17T20:04:21+00:00"
  },
  "P8202": {
    "problem_number": 8202,
    "slug": "open-fc-0dbc1d97baa72ae934a7-hassicpovm-69",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:01+00:00",
    "updated_at": "2026-08-17T18:37:03+00:00"
  },
  "P8864": {
    "problem_number": 8864,
    "slug": "open-fc-b90274e06cfefa3537e0-hassicpovm-70",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:31+00:00",
    "updated_at": "2026-08-17T19:35:36+00:00"
  },
  "P9312": {
    "problem_number": 9312,
    "slug": "open-fc-c43dba1836e0e24eea62-hassicpovm-71",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:50+00:00",
    "updated_at": "2026-08-17T19:50:50+00:00"
  },
  "P9932": {
    "problem_number": 9932,
    "slug": "open-fc-88488cc7d46eae6a8553-hassicpovm-72",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:39+00:00",
    "updated_at": "2026-08-17T20:04:39+00:00"
  },
  "P9866": {
    "problem_number": 9866,
    "slug": "open-fc-566a7e7e8d706739e844-hassicpovm-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:06+00:00",
    "updated_at": "2026-08-17T20:04:07+00:00"
  },
  "P8306": {
    "problem_number": 8306,
    "slug": "open-fc-1ebc5d0777f9cbd42d01-exists-k",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:03+00:00",
    "updated_at": "2026-08-17T18:39:17+00:00"
  },
  "P9610": {
    "problem_number": 9610,
    "slug": "open-fc-ef093c4b8ddb95b0ccdb-erdos-326",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:00+00:00",
    "updated_at": "2026-08-17T19:57:02+00:00"
  },
  "P10082": {
    "problem_number": 10082,
    "slug": "open-fc-f9683da3b58a78213a10-problem-10-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:18+00:00",
    "updated_at": "2026-08-17T20:06:19+00:00"
  },
  "P8104": {
    "problem_number": 8104,
    "slug": "open-fc-02da796435bb8559ed13-latinsquareorder11transversal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:42+00:00",
    "updated_at": "2026-08-17T18:34:42+00:00"
  },
  "P9024": {
    "problem_number": 9024,
    "slug": "open-fc-8c6873ccc430f1bff719-erdos-352",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:23+00:00",
    "updated_at": "2026-08-17T19:45:25+00:00"
  },
  "P8226": {
    "problem_number": 8226,
    "slug": "open-fc-12b8939ab3fdd24797af-erdos-97-variants-k-equidistant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:21+00:00",
    "updated_at": "2026-08-17T18:37:23+00:00"
  },
  "P9494": {
    "problem_number": 9494,
    "slug": "open-fc-966b60d27979be13cf64-erdos-312",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:25+00:00",
    "updated_at": "2026-08-17T19:54:25+00:00"
  },
  "P8758": {
    "problem_number": 8758,
    "slug": "open-fc-5c6434403678edfb7fb9-erdos-973",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:56+00:00",
    "updated_at": "2026-08-17T19:14:17+00:00"
  },
  "P9400": {
    "problem_number": 9400,
    "slug": "open-fc-4b1849be7380cbe82d96-erdos-354-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:18+00:00",
    "updated_at": "2026-08-17T19:52:20+00:00"
  },
  "P9916": {
    "problem_number": 9916,
    "slug": "open-fc-7e533b663dc9a5ab2192-erdos-520",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:31+00:00",
    "updated_at": "2026-08-17T20:04:32+00:00"
  },
  "P8146": {
    "problem_number": 8146,
    "slug": "open-fc-074618904bca45960c1a-exists-iswallsunsunprime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:16+00:00",
    "updated_at": "2026-08-17T18:35:18+00:00"
  },
  "P8372": {
    "problem_number": 8372,
    "slug": "open-fc-259f0cd1df79491942ce-exists-almost-perfect-not-power-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:59+00:00",
    "updated_at": "2026-08-17T18:48:41+00:00"
  },
  "P9560": {
    "problem_number": 9560,
    "slug": "open-fc-c6c3395c6260c720e7ec-ame-8-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:17+00:00",
    "updated_at": "2026-08-17T19:55:20+00:00"
  },
  "P8560": {
    "problem_number": 8560,
    "slug": "open-fc-746c0a4df6e5be00ef1d-ame-11-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:49+00:00",
    "updated_at": "2026-08-17T18:54:50+00:00"
  },
  "P8644": {
    "problem_number": 8644,
    "slug": "open-fc-4a11264014a5d35db3f5-ame-12-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:03+00:00",
    "updated_at": "2026-08-17T18:59:09+00:00"
  },
  "P8222": {
    "problem_number": 8222,
    "slug": "open-fc-128c7efa3f8907f4343a-ame-12-5-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:17+00:00",
    "updated_at": "2026-08-17T18:37:21+00:00"
  },
  "P8336": {
    "problem_number": 8336,
    "slug": "open-fc-21d77591d486508496f8-ame-12-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:03+00:00",
    "updated_at": "2026-08-17T18:40:04+00:00"
  },
  "P9380": {
    "problem_number": 9380,
    "slug": "open-fc-f6c7c055231f3d34c021-ame-8-4-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:17+00:00",
    "updated_at": "2026-08-17T19:51:17+00:00"
  },
  "P9716": {
    "problem_number": 9716,
    "slug": "open-fc-9d2e71d4d0389052f2a7-ame-8-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:02+00:00",
    "updated_at": "2026-08-17T20:02:03+00:00"
  },
  "P8798": {
    "problem_number": 8798,
    "slug": "open-fc-83ff60cf7f5662c25ab8-ame-11-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:21:49+00:00",
    "updated_at": "2026-08-17T19:21:59+00:00"
  },
  "P8286": {
    "problem_number": 8286,
    "slug": "open-fc-1c4c2c70d39352101b12-ame-11-3-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:17+00:00",
    "updated_at": "2026-08-17T18:38:18+00:00"
  },
  "P9450": {
    "problem_number": 9450,
    "slug": "open-fc-744a703a940ed0ac52e0-ame-9-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:42+00:00",
    "updated_at": "2026-08-17T19:53:45+00:00"
  },
  "P9056": {
    "problem_number": 9056,
    "slug": "open-fc-a26ce241ac0b0a085d7d-ame-7-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:25+00:00",
    "updated_at": "2026-08-17T19:46:27+00:00"
  },
  "P9424": {
    "problem_number": 9424,
    "slug": "open-fc-5fec90accd29e56d8031-ame-7-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:41+00:00",
    "updated_at": "2026-08-17T19:52:41+00:00"
  },
  "P8190": {
    "problem_number": 8190,
    "slug": "open-fc-0bf6353823bfbc4a2d59-ame-10-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:43+00:00",
    "updated_at": "2026-08-17T18:36:46+00:00"
  },
  "P10020": {
    "problem_number": 10020,
    "slug": "open-fc-c910f8757e7bd6460e32-ame-9-10-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:28+00:00",
    "updated_at": "2026-08-17T20:05:29+00:00"
  },
  "P10034": {
    "problem_number": 10034,
    "slug": "open-fc-d692ed9e03fe7026413e-ame-10-6-open",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:35+00:00",
    "updated_at": "2026-08-17T20:05:35+00:00"
  },
  "P8630": {
    "problem_number": 8630,
    "slug": "open-fc-42f5416314de8b9daee6-erdos-906",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:49+00:00",
    "updated_at": "2026-08-17T18:58:51+00:00"
  },
  "P8884": {
    "problem_number": 8884,
    "slug": "open-fc-c748732be57a64710171-beaver-math-olympiad-problem-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:22+00:00",
    "updated_at": "2026-08-17T19:36:25+00:00"
  },
  "P10012": {
    "problem_number": 10012,
    "slug": "open-fc-c45a6c2a5a5a96344c19-beaver-math-olympiad-problem-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:23+00:00",
    "updated_at": "2026-08-17T20:05:24+00:00"
  },
  "P9166": {
    "problem_number": 9166,
    "slug": "open-fc-f6c20fa04502afd97e41-infinite-club-exists",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:54+00:00",
    "updated_at": "2026-08-17T19:47:54+00:00"
  },
  "P9278": {
    "problem_number": 9278,
    "slug": "open-fc-aa960a9a26440816bf4b-erdos-51",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:34+00:00",
    "updated_at": "2026-08-17T19:50:35+00:00"
  },
  "P3000": {
    "problem_number": 3000,
    "slug": "erdos-problem-51",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:16+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9086": {
    "problem_number": 9086,
    "slug": "open-fc-bb52dd192019f1858c01-erdos-918-variants-all-subgraphs-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:15+00:00",
    "updated_at": "2026-08-17T19:47:17+00:00"
  },
  "P9402": {
    "problem_number": 9402,
    "slug": "open-fc-4f011c3a01eef4953ddd-erdos-44-variants-empty-start",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:21+00:00",
    "updated_at": "2026-08-17T19:52:22+00:00"
  },
  "P2996": {
    "problem_number": 2996,
    "slug": "erdos-problem-44",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:09+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P3218": {
    "problem_number": 3218,
    "slug": "erdos-problem-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:53:59+00:00",
    "updated_at": "2026-08-12T05:54:10+00:00"
  },
  "P8470": {
    "problem_number": 8470,
    "slug": "open-fc-46b9565e0d4f5a98890e-erdos-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:15+00:00",
    "updated_at": "2026-08-17T18:52:16+00:00"
  },
  "P9550": {
    "problem_number": 9550,
    "slug": "open-fc-c0b79c9c5012dae13082-erdos-39",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:07+00:00",
    "updated_at": "2026-08-17T19:55:09+00:00"
  },
  "P2990": {
    "problem_number": 2990,
    "slug": "erdos-problem-39",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:01+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P3332": {
    "problem_number": 3332,
    "slug": "erdos-problem-850",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:28+00:00",
    "updated_at": "2026-08-12T06:06:33+00:00"
  },
  "P8828": {
    "problem_number": 8828,
    "slug": "open-fc-99dbf30a40afb2551842-erdos-850",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:43+00:00",
    "updated_at": "2026-08-17T19:24:50+00:00"
  },
  "P8602": {
    "problem_number": 8602,
    "slug": "open-fc-36f4dc98847e13ce7111-erdos-141-variants-eleven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:09+00:00",
    "updated_at": "2026-08-17T18:57:21+00:00"
  },
  "P11602": {
    "problem_number": 11602,
    "slug": "existence-of-further-odd-terms-in-oeis-a347391",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:37:33+00:00",
    "updated_at": "2026-08-30T04:37:39+00:00"
  },
  "P8350": {
    "problem_number": 8350,
    "slug": "open-fc-22b1b2633d56ad546cbf-erdos-213",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:13+00:00",
    "updated_at": "2026-08-17T18:40:15+00:00"
  },
  "P8698": {
    "problem_number": 8698,
    "slug": "open-fc-3b1bede8fc88b0b10b87-green-50",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:28+00:00",
    "updated_at": "2026-08-17T19:05:45+00:00"
  },
  "P8908": {
    "problem_number": 8908,
    "slug": "open-fc-dae15489286ab4bc956b-erdos-786-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:13+00:00",
    "updated_at": "2026-08-17T19:40:14+00:00"
  },
  "P9646": {
    "problem_number": 9646,
    "slug": "open-fc-44cdc8603432a9b92199-green-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:25+00:00",
    "updated_at": "2026-08-17T20:00:27+00:00"
  },
  "P8732": {
    "problem_number": 8732,
    "slug": "open-fc-43061a91a3f429ef02e9-green-36",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:40+00:00",
    "updated_at": "2026-08-17T19:11:54+00:00"
  },
  "P8156": {
    "problem_number": 8156,
    "slug": "open-fc-085b51d71cae95b1be8f-erdos-770-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:24+00:00",
    "updated_at": "2026-08-17T18:35:28+00:00"
  },
  "P3300": {
    "problem_number": 3300,
    "slug": "erdos-problem-770",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:28+00:00",
    "updated_at": "2026-08-12T06:03:32+00:00"
  },
  "P9738": {
    "problem_number": 9738,
    "slug": "open-fc-ad8656a9fa179976ae61-green-33",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:11+00:00",
    "updated_at": "2026-08-17T20:02:12+00:00"
  },
  "P8616": {
    "problem_number": 8616,
    "slug": "open-fc-3f78d78465d84bf166e8-erdos-470-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:54+00:00",
    "updated_at": "2026-08-17T18:58:10+00:00"
  },
  "P3198": {
    "problem_number": 3198,
    "slug": "erdos-problem-470",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:51:27+00:00",
    "updated_at": "2026-08-12T05:51:39+00:00"
  },
  "P8158": {
    "problem_number": 8158,
    "slug": "open-fc-0876f586c7b29d700a77-exists-quasiperfect",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:30+00:00",
    "updated_at": "2026-08-17T18:35:33+00:00"
  },
  "P10076": {
    "problem_number": 10076,
    "slug": "open-fc-f4cc958d2e7d47a4dea8-relatively-prime-amicable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:15+00:00",
    "updated_at": "2026-08-17T20:06:16+00:00"
  },
  "P9688": {
    "problem_number": 9688,
    "slug": "open-fc-82bba48172dcf990dee6-sicpovms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:38+00:00",
    "updated_at": "2026-08-17T20:01:41+00:00"
  },
  "P8740": {
    "problem_number": 8740,
    "slug": "open-fc-4c033271b1ec182a229b-green-31-variants-zmod-p",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:21+00:00",
    "updated_at": "2026-08-17T19:19:39+00:00"
  },
  "P8760": {
    "problem_number": 8760,
    "slug": "open-fc-6b75fa3e0d44cf80e03a-erdos-939",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:14:09+00:00",
    "updated_at": "2026-08-17T19:20:56+00:00"
  },
  "P9430": {
    "problem_number": 9430,
    "slug": "open-fc-6625c30844e3a8962692-green-66",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:55+00:00",
    "updated_at": "2026-08-17T19:52:59+00:00"
  },
  "P8610": {
    "problem_number": 8610,
    "slug": "open-fc-3ab22843d50d2bfb8b5c-taxicab-for-5-2-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:39+00:00",
    "updated_at": "2026-08-17T18:57:48+00:00"
  },
  "P8822": {
    "problem_number": 8822,
    "slug": "open-fc-9cb9f915e6f239c535e7-voronovskaja-theorem-bezier-bernstein-operators-variants-eventually-smooth-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:31+00:00",
    "updated_at": "2026-08-17T19:24:38+00:00"
  },
  "P9632": {
    "problem_number": 9632,
    "slug": "open-fc-fe12ce564622d3ce70cf-erdos-417-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:44+00:00",
    "updated_at": "2026-08-17T19:57:46+00:00"
  },
  "P3248": {
    "problem_number": 3248,
    "slug": "erdos-problem-417",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:57:46+00:00",
    "updated_at": "2026-08-12T05:57:54+00:00"
  },
  "P3052": {
    "problem_number": 3052,
    "slug": "erdos-problem-145",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:24+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9996": {
    "problem_number": 9996,
    "slug": "open-fc-b8eff53cf092b2b2d8ba-erdos-145",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:17+00:00",
    "updated_at": "2026-08-17T20:05:17+00:00"
  },
  "P3210": {
    "problem_number": 3210,
    "slug": "erdos-problem-1074",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:47+00:00",
    "updated_at": "2026-08-12T05:52:50+00:00"
  },
  "P3260": {
    "problem_number": 3260,
    "slug": "erdos-problem-1192",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:48+00:00",
    "updated_at": "2026-08-12T05:58:52+00:00"
  },
  "P8764": {
    "problem_number": 8764,
    "slug": "open-fc-7265a4ede00688fbc48c-oddorderlatinsquaretransversal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:14:34+00:00",
    "updated_at": "2026-08-17T19:14:52+00:00"
  },
  "P10058": {
    "problem_number": 10058,
    "slug": "open-fc-e92c72fe37234d286455-erdos-918-variants-all-subgraphs-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:59+00:00",
    "updated_at": "2026-08-17T20:06:00+00:00"
  },
  "P8422": {
    "problem_number": 8422,
    "slug": "open-fc-2d04930371b02fc5468b-erdos-944",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:00+00:00",
    "updated_at": "2026-08-17T18:52:01+00:00"
  },
  "P3692": {
    "problem_number": 3692,
    "slug": "ust-twelve-grid-expected-leaves",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:27+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8448": {
    "problem_number": 8448,
    "slug": "open-fc-3a5c661ec6602835cbf9-green-14-variant-2r2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:09+00:00",
    "updated_at": "2026-08-17T18:52:09+00:00"
  },
  "P8950": {
    "problem_number": 8950,
    "slug": "open-fc-f8012a1d46cadfa2ad1c-large-steiner-systems",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:15+00:00",
    "updated_at": "2026-08-17T19:41:15+00:00"
  },
  "P8710": {
    "problem_number": 8710,
    "slug": "open-fc-3e6d0bf915c425adf9f8-erdos-357-parts-ii-bigo-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:06:35+00:00",
    "updated_at": "2026-08-17T19:10:09+00:00"
  },
  "P9810": {
    "problem_number": 9810,
    "slug": "open-fc-e7e82a05e6a3fb31c299-erdos-357-variants-monotone-parts-ii-bigo-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:52+00:00",
    "updated_at": "2026-08-17T20:02:53+00:00"
  },
  "P9058": {
    "problem_number": 9058,
    "slug": "open-fc-a479520541097896a400-erdos-357-parts-ii-littleo-version",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:29+00:00",
    "updated_at": "2026-08-17T19:46:30+00:00"
  },
  "P10072": {
    "problem_number": 10072,
    "slug": "open-fc-f27d06d8cffee1a7e50c-erdos-357-parts-ii-bigo-version-symm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:11+00:00",
    "updated_at": "2026-08-17T20:06:13+00:00"
  },
  "P8254": {
    "problem_number": 8254,
    "slug": "open-fc-16e8b0e4ec9a7fc77e13-erdos-683-variant-exp-sqrt",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:46+00:00",
    "updated_at": "2026-08-17T18:37:47+00:00"
  },
  "P12627": {
    "problem_number": 12627,
    "slug": "factorial-and-primorial-factors-of-lcm-staircase-terms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:59:35+00:00",
    "updated_at": "2026-09-02T22:00:06+00:00"
  },
  "P8826": {
    "problem_number": 8826,
    "slug": "open-fc-9e37f720bf41c0842177-mathoverflow-339137",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:40+00:00",
    "updated_at": "2026-08-17T19:24:48+00:00"
  },
  "P12455": {
    "problem_number": 12455,
    "slug": "factorization-map-trajectories",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:37:39+00:00",
    "updated_at": "2026-09-02T21:37:47+00:00"
  },
  "P3520": {
    "problem_number": 3520,
    "slug": "kourovka-21-130-factorizations-of-odd-order-abelian-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:11:35+00:00",
    "updated_at": "2026-08-12T08:11:39+00:00"
  },
  "P12": {
    "problem_number": 12,
    "slug": "falconer-distance-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:08:31+00:00"
  },
  "P3754": {
    "problem_number": 3754,
    "slug": "reversible-pyramid-eight-space-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:20+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11654": {
    "problem_number": 11654,
    "slug": "fate-of-the-a340008-trajectory-starting-at-397",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:03:18+00:00",
    "updated_at": "2026-08-30T11:03:26+00:00"
  },
  "P11106": {
    "problem_number": 11106,
    "slug": "fels-conjecture-numerical-semigroup-syzygy-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T07:34:28+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P8": {
    "problem_number": 8,
    "slug": "fermat-catalan-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:08:57+00:00"
  },
  "P3740": {
    "problem_number": 3740,
    "slug": "disjointness-six-protocol-leaves",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:50:46+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3772": {
    "problem_number": 3772,
    "slug": "outer-totalistic-count-observation-tests",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:52:50+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3610": {
    "problem_number": 3610,
    "slug": "sparse-ternary-double-error-checks",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:57+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12465": {
    "problem_number": 12465,
    "slug": "fibonomial-polynomial-factors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:38:39+00:00",
    "updated_at": "2026-09-02T21:38:50+00:00"
  },
  "P12135": {
    "problem_number": 12135,
    "slug": "final-digit-9-for-large-least-semiprimes-of-a-given-digit-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:15:46+00:00",
    "updated_at": "2026-09-01T19:15:52+00:00"
  },
  "P11374": {
    "problem_number": 11374,
    "slug": "recursion-for-rational-curves-on-a-cubic-surface",
    "resolution_state": "open",
    "solution_state": "submitted",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "candidate_resolution",
        "label": "Solution submitted",
        "tone": "candidate",
        "reason": "A complete answer is reported without an accepted resolution review.",
        "transitionRule": "A complete answer is reported without an accepted resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": {
          "id": null,
          "slug": "recursion-for-rational-curves-on-a-cubic-surface-source-audit-result-3f93c56a08d7b3bf-claim",
          "title": "Claim from Prove a Kontsevich-style recursion for H_d, the number of smooth rational curves of hyperplane degree d on a general cubic surface S in P^3 passing through d-1 general points, and resolve the inconsistency in the values (459, 936",
          "url": "/research/changes/?proposal_id=tdbrpp1%3Abbb960be2ea405bb315e9303b303b429",
          "proposalId": "tdbrpp1:bbb960be2ea405bb315e9303b303b429"
        }
      },
      "proofMessage": "A solution has been submitted and awaits independent review.",
      "summary": "Solution submitted. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:40:46+00:00",
    "updated_at": "2026-08-29T18:51:59+00:00"
  },
  "P12129": {
    "problem_number": 12129,
    "slug": "finite-cycles-for-the-rational-3x-1-map-with-odd-denominator",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:15:00+00:00",
    "updated_at": "2026-09-01T19:15:05+00:00"
  },
  "P3412": {
    "problem_number": 3412,
    "slug": "kourovka-21-36-finite-extensions-in-kropholler-s-hierarchy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:14+00:00",
    "updated_at": "2026-08-12T07:58:26+00:00"
  },
  "P3378": {
    "problem_number": 3378,
    "slug": "kourovka-21-16-finite-group-width-versus-finite-monoid-width",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:52:38+00:00",
    "updated_at": "2026-08-12T07:53:40+00:00"
  },
  "P3416": {
    "problem_number": 3416,
    "slug": "kourovka-21-38-finite-groups-with-prescribed-spread",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:33+00:00",
    "updated_at": "2026-08-12T07:58:36+00:00"
  },
  "P9978": {
    "problem_number": 9978,
    "slug": "open-fc-ab04f825f0a8e2a2a1d6-finite-equation677-implies-equation255",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:10+00:00",
    "updated_at": "2026-08-17T20:05:10+00:00"
  },
  "P11822": {
    "problem_number": 11822,
    "slug": "finite-occurrence-of-every-digit-two-count-in-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T13:01:39+00:00",
    "updated_at": "2026-08-30T13:03:48+00:00"
  },
  "P3502": {
    "problem_number": 3502,
    "slug": "kourovka-21-119-finite-index-kernels-with-prescribed-homomorphisms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:09:08+00:00",
    "updated_at": "2026-08-12T08:09:14+00:00"
  },
  "P3432": {
    "problem_number": 3432,
    "slug": "kourovka-21-47-finitely-presented-groups-isomorphic-to-a-proper-direct-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:01:30+00:00",
    "updated_at": "2026-08-12T08:01:41+00:00"
  },
  "P3512": {
    "problem_number": 3512,
    "slug": "kourovka-21-126-finitely-presented-subgroups-of-right-angled-artin-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:21+00:00",
    "updated_at": "2026-08-12T08:10:23+00:00"
  },
  "P10002": {
    "problem_number": 10002,
    "slug": "open-fc-bd8c52a4ad429303af0a-erdos-288-variants-k-intervals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:19+00:00",
    "updated_at": "2026-08-17T20:05:19+00:00"
  },
  "P8816": {
    "problem_number": 8816,
    "slug": "open-fc-96061be8b132e4155e64-erdos-288-variants-exists-k-gt-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:14+00:00",
    "updated_at": "2026-08-17T19:24:20+00:00"
  },
  "P9342": {
    "problem_number": 9342,
    "slug": "open-fc-dd24838cc5de3f7e1bba-erdos-373",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:02+00:00",
    "updated_at": "2026-08-17T19:51:02+00:00"
  },
  "P3326": {
    "problem_number": 3326,
    "slug": "erdos-problem-1108",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:09+00:00",
    "updated_at": "2026-08-12T06:06:12+00:00"
  },
  "P9186": {
    "problem_number": 9186,
    "slug": "open-fc-3c231103c71545ef3c89-abc-variants-quality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:04+00:00",
    "updated_at": "2026-08-17T19:49:04+00:00"
  },
  "P9512": {
    "problem_number": 9512,
    "slug": "open-fc-a1ffcf55b187446e1135-abc",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:33+00:00",
    "updated_at": "2026-08-17T19:54:33+00:00"
  },
  "P9070": {
    "problem_number": 9070,
    "slug": "open-fc-acf4c02e8112c29626d8-erdos-288",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:48+00:00",
    "updated_at": "2026-08-17T19:46:50+00:00"
  },
  "P10016": {
    "problem_number": 10016,
    "slug": "open-fc-c7160dd58d03fc90afa4-erdos-931",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:25+00:00",
    "updated_at": "2026-08-17T20:05:26+00:00"
  },
  "P10014": {
    "problem_number": 10014,
    "slug": "open-fc-c62f58844a24824ff9f2-erdos-406",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:24+00:00",
    "updated_at": "2026-08-17T20:05:24+00:00"
  },
  "P11582": {
    "problem_number": 11582,
    "slug": "finiteness-of-prime-or-semiprime-power-of-two-differences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:35:37+00:00",
    "updated_at": "2026-08-30T04:35:44+00:00"
  },
  "P8754": {
    "problem_number": 8754,
    "slug": "open-fc-58fd49d999b6368dee06-finite-twentyone-lt-finrank",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:33+00:00",
    "updated_at": "2026-08-17T19:13:48+00:00"
  },
  "P11574": {
    "problem_number": 11574,
    "slug": "finiteness-of-reverse-decay-series-ending-at-lead-209",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:34:35+00:00",
    "updated_at": "2026-08-30T04:34:46+00:00"
  },
  "P11786": {
    "problem_number": 11786,
    "slug": "finiteness-of-small-remainders-below-square-pyramidal-values",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:41:16+00:00",
    "updated_at": "2026-08-30T12:44:06+00:00"
  },
  "P8260": {
    "problem_number": 8260,
    "slug": "open-fc-1827ddc5582abac8fa82-erdos-889-variants-v1-eq-1-finite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:51+00:00",
    "updated_at": "2026-08-17T18:37:53+00:00"
  },
  "P8180": {
    "problem_number": 8180,
    "slug": "open-fc-0b558b4ca944d9cf56d3-erdos-931-variants-additional-condition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:27+00:00",
    "updated_at": "2026-08-17T18:36:30+00:00"
  },
  "P11570": {
    "problem_number": 11570,
    "slug": "finiteness-of-the-reverse-actinium-decay-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:33:59+00:00",
    "updated_at": "2026-08-30T04:34:11+00:00"
  },
  "P11572": {
    "problem_number": 11572,
    "slug": "finiteness-of-the-reverse-thorium-decay-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:34:20+00:00",
    "updated_at": "2026-08-30T04:34:29+00:00"
  },
  "P11566": {
    "problem_number": 11566,
    "slug": "finiteness-of-the-reverse-uranium-decay-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:33:19+00:00",
    "updated_at": "2026-08-30T04:33:31+00:00"
  },
  "P8366": {
    "problem_number": 8366,
    "slug": "open-fc-2526464824676cd11a3f-erdos-889-variants-v1-eq-1-finite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:27+00:00",
    "updated_at": "2026-08-17T18:40:39+00:00"
  },
  "P9986": {
    "problem_number": 9986,
    "slug": "open-fc-b054efed9bf3da66bc51-erdos-938",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:14+00:00",
    "updated_at": "2026-08-17T20:05:14+00:00"
  },
  "P3236": {
    "problem_number": 3236,
    "slug": "erdos-problem-938",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:56:06+00:00",
    "updated_at": "2026-08-12T05:56:23+00:00"
  },
  "P10070": {
    "problem_number": 10070,
    "slug": "open-fc-f1e2700f7fa44200600f-erdos-288-variants-i2-card-eq-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:09+00:00",
    "updated_at": "2026-08-17T20:06:11+00:00"
  },
  "P8692": {
    "problem_number": 8692,
    "slug": "open-fc-38b412313349aaca27ad-erdos-1052",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:02+00:00",
    "updated_at": "2026-08-17T19:52:06+00:00"
  },
  "P12527": {
    "problem_number": 12527,
    "slug": "firoozbakht-bounds-for-prime-gaps-of-eight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:44:49+00:00",
    "updated_at": "2026-09-02T21:45:01+00:00"
  },
  "P8408": {
    "problem_number": 8408,
    "slug": "open-fc-2b5c0f1a2b571f900e64-firoozbakht-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:50+00:00",
    "updated_at": "2026-08-17T18:49:56+00:00"
  },
  "P12479": {
    "problem_number": 12479,
    "slug": "first-appearances-of-prime-gaps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:04+00:00",
    "updated_at": "2026-09-02T21:40:16+00:00"
  },
  "P9578": {
    "problem_number": 9578,
    "slug": "open-fc-d5334f301e9ce03d1535-firstcountabletopology-of-countablymonolithicspace",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:54+00:00",
    "updated_at": "2026-08-17T19:55:56+00:00"
  },
  "P12053": {
    "problem_number": 12053,
    "slug": "first-multiple-hit-in-odd-digital-sums-of-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:57:55+00:00",
    "updated_at": "2026-09-01T18:58:06+00:00"
  },
  "P12525": {
    "problem_number": 12525,
    "slug": "first-nonintegral-terms-of-somos-sequences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:44:29+00:00",
    "updated_at": "2026-09-02T21:44:42+00:00"
  },
  "P3484": {
    "problem_number": 3484,
    "slug": "kourovka-21-106-first-order-descriptions-of-group-elements",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:53+00:00",
    "updated_at": "2026-08-12T08:06:56+00:00"
  },
  "P3364": {
    "problem_number": 3364,
    "slug": "kourovka-21-4-five-conjugates-in-groups-with-trivial-solvable-radical",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:42:19+00:00",
    "updated_at": "2026-08-12T07:42:52+00:00"
  },
  "P12427": {
    "problem_number": 12427,
    "slug": "five-connected-colored-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:34:44+00:00",
    "updated_at": "2026-09-02T21:34:56+00:00"
  },
  "P2874": {
    "problem_number": 2874,
    "slug": "triangle-free-degree-six-five-colouring",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:41:58+00:00",
    "updated_at": "2026-08-01T12:33:20+00:00"
  },
  "P2690": {
    "problem_number": 2690,
    "slug": "littlewood-32-minimum-peak",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:15+00:00",
    "updated_at": "2026-08-01T02:11:20+00:00"
  },
  "P3674": {
    "problem_number": 3674,
    "slug": "z37-nine-idempotent-min-sixth-moment",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:24+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3464": {
    "problem_number": 3464,
    "slug": "kourovka-21-85-flexible-permutation-stability-implies-permutation-stability",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:55+00:00",
    "updated_at": "2026-08-12T08:05:58+00:00"
  },
  "P2804": {
    "problem_number": 2804,
    "slug": "cyclic-polytope-c4-10-flip-diameter",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:09+00:00",
    "updated_at": "2026-08-01T23:23:57+00:00"
  },
  "P12739": {
    "problem_number": 12739,
    "slug": "for-n-2-is-the-least-prime-beginning-with-n-completed-by-a-smaller-suffix",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:37:22+00:00",
    "updated_at": "2026-09-02T22:37:59+00:00"
  },
  "P12063": {
    "problem_number": 12063,
    "slug": "four-divisibility-laws-for-a-sporadic-factorial-ratio",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:00:00+00:00",
    "updated_at": "2026-09-01T19:00:09+00:00"
  },
  "P4": {
    "problem_number": 4,
    "slug": "four-exponentials-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:09:29+00:00"
  },
  "P11843": {
    "problem_number": 11843,
    "slug": "four-positive-cubes-beyond-the-proposed-last-exception",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:29+00:00",
    "updated_at": "2026-08-30T16:14:33+00:00"
  },
  "P3080": {
    "problem_number": 3080,
    "slug": "c4-supersaturation-at-extremal-threshold",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:56+00:00",
    "updated_at": "2026-08-02T12:47:48+00:00"
  },
  "P12345": {
    "problem_number": 12345,
    "slug": "fourth-power-divisibility-in-weighted-ap-ry-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:41:22+00:00",
    "updated_at": "2026-09-01T19:41:29+00:00"
  },
  "P9476": {
    "problem_number": 9476,
    "slug": "open-fc-87ea96583ece2acdb6d9-fugledeconjecture-variants-dim-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:03+00:00",
    "updated_at": "2026-08-17T19:54:04+00:00"
  },
  "P8236": {
    "problem_number": 8236,
    "slug": "open-fc-14185c9627c0e4db5bb9-fugledeconjecture-variants-dim-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:29+00:00",
    "updated_at": "2026-08-17T18:37:34+00:00"
  },
  "P9222": {
    "problem_number": 9222,
    "slug": "open-fc-73e2a802660d315f995a-conjecture-1-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:43+00:00",
    "updated_at": "2026-08-17T19:49:44+00:00"
  },
  "P11648": {
    "problem_number": 11648,
    "slug": "further-composite-partial-sums-in-the-coprime-sum-product-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:48:57+00:00",
    "updated_at": "2026-08-30T04:49:47+00:00"
  },
  "P11883": {
    "problem_number": 11883,
    "slug": "further-fixed-points-in-a-coprime-greedy-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:19:45+00:00",
    "updated_at": "2026-08-30T16:19:51+00:00"
  },
  "P11955": {
    "problem_number": 11955,
    "slug": "further-fixed-points-in-the-guarded-gcd-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:37:14+00:00",
    "updated_at": "2026-08-30T16:39:34+00:00"
  },
  "P11636": {
    "problem_number": 11636,
    "slug": "further-nonstructural-zeros-in-the-neighbor-sum-spiral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:41:48+00:00",
    "updated_at": "2026-08-30T04:41:57+00:00"
  },
  "P11816": {
    "problem_number": 11816,
    "slug": "further-right-side-lines-in-the-greedy-square-spiral-packing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:55:06+00:00",
    "updated_at": "2026-08-30T12:57:14+00:00"
  },
  "P9822": {
    "problem_number": 9822,
    "slug": "open-fc-f07a736319ba95a7301e-conj-7-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:57+00:00",
    "updated_at": "2026-08-17T20:02:59+00:00"
  },
  "P3208": {
    "problem_number": 3208,
    "slug": "erdos-problem-208",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:38+00:00",
    "updated_at": "2026-08-12T05:52:42+00:00"
  },
  "P9514": {
    "problem_number": 9514,
    "slug": "open-fc-a2bb8aa2017cd2018dc8-erdos-208-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:34+00:00",
    "updated_at": "2026-08-17T19:54:35+00:00"
  },
  "P2900": {
    "problem_number": 2900,
    "slug": "frog-game-binary-tree-root",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:45:27+00:00",
    "updated_at": "2026-08-01T23:27:41+00:00"
  },
  "P12529": {
    "problem_number": 12529,
    "slug": "gauss-congruences-for-an-egj-transform",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:44:56+00:00",
    "updated_at": "2026-09-02T21:45:09+00:00"
  },
  "P11712": {
    "problem_number": 11712,
    "slug": "gauss-congruences-for-set-partitions-with-distinct-block-sizes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:51+00:00",
    "updated_at": "2026-08-30T11:16:58+00:00"
  },
  "P9790": {
    "problem_number": 9790,
    "slug": "open-fc-d817b42f8e4726ca818a-generalized-riemann-hypothesis",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:40+00:00",
    "updated_at": "2026-08-17T20:02:41+00:00"
  },
  "P3394": {
    "problem_number": 3394,
    "slug": "kourovka-21-26-generating-finite-groups-with-sylow-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:23+00:00",
    "updated_at": "2026-08-12T07:56:26+00:00"
  },
  "P3392": {
    "problem_number": 3392,
    "slug": "kourovka-21-25-generation-of-finite-simple-groups-by-two-sylow-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:14+00:00",
    "updated_at": "2026-08-12T07:56:19+00:00"
  },
  "P3428": {
    "problem_number": 3428,
    "slug": "kourovka-21-45-generator-rank-of-finitely-presented-infinite-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:00:04+00:00",
    "updated_at": "2026-08-12T08:00:25+00:00"
  },
  "P3110": {
    "problem_number": 3110,
    "slug": "generic-analytic-arnold-diffusion-apriori-stable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:02+00:00",
    "updated_at": "2026-08-02T12:51:23+00:00"
  },
  "P11798": {
    "problem_number": 11798,
    "slug": "geometric-means-of-consecutive-primes-lie-within-one-of-their-midpoint",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:45:09+00:00",
    "updated_at": "2026-08-30T12:45:18+00:00"
  },
  "P9648": {
    "problem_number": 9648,
    "slug": "open-fc-477dc04d6ccd2349961b-gilbreath-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:28+00:00",
    "updated_at": "2026-08-17T20:00:29+00:00"
  },
  "P8664": {
    "problem_number": 8664,
    "slug": "open-fc-2cbb852be7097883f4d3-agoh-giuga-variants-giuga",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:03:38+00:00",
    "updated_at": "2026-08-17T19:04:09+00:00"
  },
  "P12159": {
    "problem_number": 12159,
    "slug": "giuga-s-power-sum-test-for-primality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:18:45+00:00",
    "updated_at": "2026-09-01T19:18:51+00:00"
  },
  "P9310": {
    "problem_number": 9310,
    "slug": "open-fc-c3772a7845f38eaefb0a-navier-stokes-existence-and-smoothness-r3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:48+00:00",
    "updated_at": "2026-08-17T19:50:49+00:00"
  },
  "P11933": {
    "problem_number": 11933,
    "slug": "global-record-gaps-below-fifth-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:29:46+00:00",
    "updated_at": "2026-08-30T16:30:04+00:00"
  },
  "P3": {
    "problem_number": 3,
    "slug": "goldbach-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:10:17+00:00"
  },
  "P12505": {
    "problem_number": 12505,
    "slug": "goldbach-exceptions-and-composite-triples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:31+00:00",
    "updated_at": "2026-09-02T21:42:43+00:00"
  },
  "P12155": {
    "problem_number": 12155,
    "slug": "goldbach-pairs-as-distances-from-the-midpoint",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:18:15+00:00",
    "updated_at": "2026-09-01T19:18:21+00:00"
  },
  "P11875": {
    "problem_number": 11875,
    "slug": "goldbach-representations-by-two-isolated-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:39+00:00",
    "updated_at": "2026-08-30T16:16:44+00:00"
  },
  "P12177": {
    "problem_number": 12177,
    "slug": "goldbach-representations-with-a-very-small-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:20:57+00:00",
    "updated_at": "2026-09-01T19:21:03+00:00"
  },
  "P11782": {
    "problem_number": 11782,
    "slug": "goldbach-s-additive-conjecture-for-primes-k-squared-plus-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:37:06+00:00",
    "updated_at": "2026-08-30T12:38:56+00:00"
  },
  "P8442": {
    "problem_number": 8442,
    "slug": "open-fc-36d048655785dbecc93d-goldbach",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:07+00:00",
    "updated_at": "2026-08-17T18:52:07+00:00"
  },
  "P10118": {
    "problem_number": 10118,
    "slug": "open-fc-1bf257b2febe821336db-goormaghtigh-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:15+00:00",
    "updated_at": "2026-08-18T02:51:16+00:00"
  },
  "P8900": {
    "problem_number": 8900,
    "slug": "open-fc-d1b6ff4094e0c9803466-gottschalk-surjunctivity-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:08+00:00",
    "updated_at": "2026-08-17T19:40:09+00:00"
  },
  "P40": {
    "problem_number": 40,
    "slug": "graceful-tree-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:10:41+00:00"
  },
  "P9930": {
    "problem_number": 9930,
    "slug": "open-fc-8615a48ea203a0b4bd21-graceful-tree-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:38+00:00",
    "updated_at": "2026-08-17T20:04:39+00:00"
  },
  "P9298": {
    "problem_number": 9298,
    "slug": "open-fc-ba01cac287c666e928c6-erdos-10-variants-granville-soundararajan-odd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:43+00:00",
    "updated_at": "2026-08-17T19:50:43+00:00"
  },
  "P49": {
    "problem_number": 49,
    "slug": "graph-reconstruction-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:11:04+00:00"
  },
  "P9152": {
    "problem_number": 9152,
    "slug": "open-fc-ee9ad66d7abf38e30517-kurepa-conjecture-variants-gcd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:50+00:00",
    "updated_at": "2026-08-17T19:47:50+00:00"
  },
  "P9982": {
    "problem_number": 9982,
    "slug": "open-fc-acec418679c4e3547f8b-erdos-282-variants-graham",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:12+00:00",
    "updated_at": "2026-08-17T20:05:13+00:00"
  },
  "P10110": {
    "problem_number": 10110,
    "slug": "open-fc-13e5b93b7b21d8c414e4-green-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:12+00:00",
    "updated_at": "2026-08-18T02:51:13+00:00"
  },
  "P10206": {
    "problem_number": 10206,
    "slug": "open-fc-b69ea9e4d656d55d0564-green-21",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:46+00:00",
    "updated_at": "2026-08-18T02:51:46+00:00"
  },
  "P10140": {
    "problem_number": 10140,
    "slug": "open-fc-2f8edac1456d3ed30f65-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:22+00:00",
    "updated_at": "2026-08-18T02:51:22+00:00"
  },
  "P10132": {
    "problem_number": 10132,
    "slug": "open-fc-27805205f6eee01bfbdf-green-27-equivalent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:19+00:00",
    "updated_at": "2026-08-18T02:51:20+00:00"
  },
  "P10114": {
    "problem_number": 10114,
    "slug": "open-fc-1648fc4163ca197735fe-green-31-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:14+00:00",
    "updated_at": "2026-08-18T02:51:14+00:00"
  },
  "P10096": {
    "problem_number": 10096,
    "slug": "open-fc-0c9a3cb6af73436b9b80-green-31-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:08+00:00",
    "updated_at": "2026-08-18T02:51:08+00:00"
  },
  "P10102": {
    "problem_number": 10102,
    "slug": "open-fc-11ee385545e4133040aa-green-31-variants-abelian",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:10+00:00",
    "updated_at": "2026-08-18T02:51:10+00:00"
  },
  "P10108": {
    "problem_number": 10108,
    "slug": "open-fc-1343fcbbc5f6b47fec4f-green-31-variants-sidon-01n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:12+00:00",
    "updated_at": "2026-08-18T02:51:12+00:00"
  },
  "P10094": {
    "problem_number": 10094,
    "slug": "open-fc-05edee1d3158b8b498e8-green-46-improve-upper-conjectured",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:07+00:00",
    "updated_at": "2026-08-18T02:51:08+00:00"
  },
  "P10210": {
    "problem_number": 10210,
    "slug": "open-fc-b9e74f53862414a3863a-green-53",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:47+00:00",
    "updated_at": "2026-08-18T02:51:48+00:00"
  },
  "P10092": {
    "problem_number": 10092,
    "slug": "open-fc-01d3b5ddc0a230fe6a64-green-58",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:06+00:00",
    "updated_at": "2026-08-18T02:51:07+00:00"
  },
  "P10106": {
    "problem_number": 10106,
    "slug": "open-fc-12ca4f273f159ed391c4-green-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:11+00:00",
    "updated_at": "2026-08-18T02:51:12+00:00"
  },
  "P9456": {
    "problem_number": 9456,
    "slug": "open-fc-7a7aa6c800d1010c2d16-green-47",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:54+00:00",
    "updated_at": "2026-08-17T19:53:55+00:00"
  },
  "P9758": {
    "problem_number": 9758,
    "slug": "open-fc-be91202cc6bd3c068250-green-44",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:23+00:00",
    "updated_at": "2026-08-17T20:02:24+00:00"
  },
  "P2428": {
    "problem_number": 2428,
    "slug": "no-three-collinear-no-four-concyclic-grid",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-24T21:54:33+00:00",
    "updated_at": "2026-08-01T02:26:19+00:00"
  },
  "P8212": {
    "problem_number": 8212,
    "slug": "open-fc-0f9eb1283e24e35dc230-grimm-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:11+00:00",
    "updated_at": "2026-08-17T18:37:12+00:00"
  },
  "P3374": {
    "problem_number": 3374,
    "slug": "kourovka-21-11-groups-represented-by-nonprincipal-ultraproduct-images",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:48:46+00:00",
    "updated_at": "2026-08-12T07:50:38+00:00"
  },
  "P9442": {
    "problem_number": 9442,
    "slug": "open-fc-6e4eb9e3c995ebc0157e-erdos-695",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:25+00:00",
    "updated_at": "2026-08-17T19:53:28+00:00"
  },
  "P8392": {
    "problem_number": 8392,
    "slug": "open-fc-27d1b660d2eaee3343c1-erdos-138",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:10+00:00",
    "updated_at": "2026-08-17T18:49:12+00:00"
  },
  "P8540": {
    "problem_number": 8540,
    "slug": "open-fc-6a0440da285cf6254931-erdos-455",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:26+00:00",
    "updated_at": "2026-08-17T18:54:27+00:00"
  },
  "P8322": {
    "problem_number": 8322,
    "slug": "open-fc-1f86be59347502fc3bed-erdos-943",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:38+00:00",
    "updated_at": "2026-08-17T18:39:39+00:00"
  },
  "P8848": {
    "problem_number": 8848,
    "slug": "open-fc-acf340e5d2ed6481e742-erdos-893",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:13+00:00",
    "updated_at": "2026-08-17T19:26:27+00:00"
  },
  "P3294": {
    "problem_number": 3294,
    "slug": "erdos-problem-893",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:18+00:00",
    "updated_at": "2026-08-12T06:03:19+00:00"
  },
  "P8972": {
    "problem_number": 8972,
    "slug": "open-fc-6591321ee79510e24713-erdos-422-variants-growth-rate",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:03+00:00",
    "updated_at": "2026-08-17T19:44:05+00:00"
  },
  "P9008": {
    "problem_number": 9008,
    "slug": "open-fc-80eac407277108c9e831-erdos-812-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:52+00:00",
    "updated_at": "2026-08-17T19:44:54+00:00"
  },
  "P3228": {
    "problem_number": 3228,
    "slug": "erdos-problem-812",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:55:07+00:00",
    "updated_at": "2026-08-12T05:55:20+00:00"
  },
  "P22": {
    "problem_number": 22,
    "slug": "hadamard-matrix-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:11:26+00:00"
  },
  "P10036": {
    "problem_number": 10036,
    "slug": "open-fc-d8ba8234d573b635390a-hadamardconjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:35+00:00",
    "updated_at": "2026-08-17T20:05:36+00:00"
  },
  "P23": {
    "problem_number": 23,
    "slug": "hadwiger-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:11:51+00:00"
  },
  "P52": {
    "problem_number": 52,
    "slug": "hadwiger-nelson-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:12:17+00:00"
  },
  "P8614": {
    "problem_number": 8614,
    "slug": "open-fc-8521fc8254c4e1159263-hall-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:54+00:00",
    "updated_at": "2026-08-17T18:58:03+00:00"
  },
  "P12073": {
    "problem_number": 12073,
    "slug": "hamiltonian-cycles-in-densest-triangular-lattice-disks",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:12+00:00",
    "updated_at": "2026-09-01T19:08:17+00:00"
  },
  "P3696": {
    "problem_number": 3696,
    "slug": "hamilton-cycles-four-cubical-grid-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:53+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P10018": {
    "problem_number": 10018,
    "slug": "open-fc-c80ee52b80c5e5dd4912-conjecture198a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:26+00:00",
    "updated_at": "2026-08-17T20:05:27+00:00"
  },
  "P10762": {
    "problem_number": 10762,
    "slug": "unsolvedmath-0170-hamming-ball-covering-growth",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:07+00:00",
    "updated_at": "2026-08-18T02:55:07+00:00"
  },
  "P11678": {
    "problem_number": 11678,
    "slug": "harary-hill-crossing-number-conjecture-for-complete-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:06:37+00:00",
    "updated_at": "2026-08-30T16:34:58+00:00"
  },
  "P2594": {
    "problem_number": 2594,
    "slug": "hard-core-c4-strip-log-concavity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:39+00:00",
    "updated_at": "2026-08-01T02:09:32+00:00"
  },
  "P12181": {
    "problem_number": 12181,
    "slug": "harmonic-energy-minima-for-points-on-the-three-sphere",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:21:25+00:00",
    "updated_at": "2026-09-01T19:21:32+00:00"
  },
  "P9376": {
    "problem_number": 9376,
    "slug": "open-fc-f49698c011f925b61d98-harthshorne-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:15+00:00",
    "updated_at": "2026-08-17T19:51:16+00:00"
  },
  "P4024": {
    "problem_number": 4024,
    "slug": "heat-kernel-geometry-and-gromov-s-volume-growth-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T19:52:35+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9600": {
    "problem_number": 9600,
    "slug": "open-fc-e7ae7d5597f9ae9af459-erdos-233",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:40+00:00",
    "updated_at": "2026-08-17T19:56:43+00:00"
  },
  "P3290": {
    "problem_number": 3290,
    "slug": "erdos-problem-233",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:06+00:00",
    "updated_at": "2026-08-12T06:03:09+00:00"
  },
  "P11148": {
    "problem_number": 11148,
    "slug": "high-angular-momentum-doublet-splitting-elliptic-cone",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-20T17:16:13+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9": {
    "problem_number": 9,
    "slug": "hilberts-sixteenth-problem-second-part",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:12:38+00:00"
  },
  "P27": {
    "problem_number": 27,
    "slug": "hilberts-tenth-problem-over-the-rationals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:13:10+00:00"
  },
  "P7": {
    "problem_number": 7,
    "slug": "hodge-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:13:45+00:00"
  },
  "P2510": {
    "problem_number": 2510,
    "slug": "lee-rips-torus-7-homotopy",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:11+00:00",
    "updated_at": "2026-08-01T23:34:25+00:00"
  },
  "P3388": {
    "problem_number": 3388,
    "slug": "kourovka-21-22-hopficity-of-restricted-wreath-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:06+00:00",
    "updated_at": "2026-08-12T07:56:07+00:00"
  },
  "P3128": {
    "problem_number": 3128,
    "slug": "planar-convex-hot-spots",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:07+00:00",
    "updated_at": "2026-08-02T12:54:12+00:00"
  },
  "P11216": {
    "problem_number": 11216,
    "slug": "prime-without-prime-decimal-substring-asymptotics",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:53:15+00:00",
    "updated_at": "2026-08-29T18:49:18+00:00"
  },
  "P11098": {
    "problem_number": 11098,
    "slug": "imo-2026-problem-3-liu-bang-xiang-yu",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T07:10:07+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P2842": {
    "problem_number": 2842,
    "slug": "pierce-expansion-upper-exponent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:37:40+00:00",
    "updated_at": "2026-08-01T12:23:51+00:00"
  },
  "P9584": {
    "problem_number": 9584,
    "slug": "open-fc-dbb72abce3bc78610eaf-green-38-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:05+00:00",
    "updated_at": "2026-08-17T19:56:07+00:00"
  },
  "P3212": {
    "problem_number": 3212,
    "slug": "erdos-problem-160",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:54+00:00",
    "updated_at": "2026-08-12T05:52:58+00:00"
  },
  "P8194": {
    "problem_number": 8194,
    "slug": "open-fc-0ce3925c7df509d45da7-erdos-160-better-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:49+00:00",
    "updated_at": "2026-08-17T18:36:51+00:00"
  },
  "P8456": {
    "problem_number": 8456,
    "slug": "open-fc-3fcbc4d4d02e03f0f479-green-38-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:10+00:00",
    "updated_at": "2026-08-17T18:52:11+00:00"
  },
  "P8778": {
    "problem_number": 8778,
    "slug": "open-fc-46d979cd3b6dceac6b64-green-46-improve-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:19:23+00:00",
    "updated_at": "2026-08-17T19:19:31+00:00"
  },
  "P9870": {
    "problem_number": 9870,
    "slug": "open-fc-5a07c07dedbf00af968c-erdos-36-variants-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:09+00:00",
    "updated_at": "2026-08-17T20:04:09+00:00"
  },
  "P8886": {
    "problem_number": 8886,
    "slug": "open-fc-c814bd1ab85b78634707-erdos-36-variants-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:26+00:00",
    "updated_at": "2026-08-17T19:36:26+00:00"
  },
  "P8276": {
    "problem_number": 8276,
    "slug": "open-fc-1a4ae357c6c0c877fb62-mem-ico-c1a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:09+00:00",
    "updated_at": "2026-08-17T18:38:11+00:00"
  },
  "P4992": {
    "problem_number": 4992,
    "slug": "circulant-1009-4-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:13+00:00",
    "updated_at": "2026-08-16T07:49:17+00:00"
  },
  "P4994": {
    "problem_number": 4994,
    "slug": "circulant-1013-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:26+00:00",
    "updated_at": "2026-08-16T07:49:33+00:00"
  },
  "P4996": {
    "problem_number": 4996,
    "slug": "circulant-1019-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:35+00:00",
    "updated_at": "2026-08-16T07:49:37+00:00"
  },
  "P4998": {
    "problem_number": 4998,
    "slug": "circulant-1021-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:37+00:00",
    "updated_at": "2026-08-16T07:49:37+00:00"
  },
  "P5000": {
    "problem_number": 5000,
    "slug": "circulant-1031-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:40+00:00",
    "updated_at": "2026-08-16T07:49:49+00:00"
  },
  "P5002": {
    "problem_number": 5002,
    "slug": "circulant-1033-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:50+00:00",
    "updated_at": "2026-08-16T07:49:59+00:00"
  },
  "P5004": {
    "problem_number": 5004,
    "slug": "circulant-1039-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:50:01+00:00",
    "updated_at": "2026-08-16T07:50:01+00:00"
  },
  "P5006": {
    "problem_number": 5006,
    "slug": "circulant-1049-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:50:03+00:00",
    "updated_at": "2026-08-16T07:50:14+00:00"
  },
  "P5008": {
    "problem_number": 5008,
    "slug": "circulant-1051-12-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:50:20+00:00",
    "updated_at": "2026-08-16T07:50:24+00:00"
  },
  "P5016": {
    "problem_number": 5016,
    "slug": "circulant-1061-13-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:59:58+00:00",
    "updated_at": "2026-08-16T08:00:01+00:00"
  },
  "P5024": {
    "problem_number": 5024,
    "slug": "circulant-1063-14-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:02:48+00:00",
    "updated_at": "2026-08-16T08:02:53+00:00"
  },
  "P5026": {
    "problem_number": 5026,
    "slug": "circulant-1069-15-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:02:56+00:00",
    "updated_at": "2026-08-16T08:03:00+00:00"
  },
  "P5028": {
    "problem_number": 5028,
    "slug": "circulant-1087-16-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:05+00:00",
    "updated_at": "2026-08-16T08:03:09+00:00"
  },
  "P5030": {
    "problem_number": 5030,
    "slug": "circulant-1091-17-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:10+00:00",
    "updated_at": "2026-08-16T08:03:13+00:00"
  },
  "P5032": {
    "problem_number": 5032,
    "slug": "circulant-1093-18-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:14+00:00",
    "updated_at": "2026-08-16T08:03:15+00:00"
  },
  "P5034": {
    "problem_number": 5034,
    "slug": "circulant-1097-19-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:19+00:00",
    "updated_at": "2026-08-16T08:03:25+00:00"
  },
  "P5036": {
    "problem_number": 5036,
    "slug": "circulant-1103-20-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:25+00:00",
    "updated_at": "2026-08-16T08:03:27+00:00"
  },
  "P5038": {
    "problem_number": 5038,
    "slug": "circulant-1109-21-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:28+00:00",
    "updated_at": "2026-08-16T08:03:30+00:00"
  },
  "P5040": {
    "problem_number": 5040,
    "slug": "circulant-1117-22-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:30+00:00",
    "updated_at": "2026-08-16T08:03:33+00:00"
  },
  "P5042": {
    "problem_number": 5042,
    "slug": "circulant-1123-23-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:36+00:00",
    "updated_at": "2026-08-16T08:03:37+00:00"
  },
  "P5044": {
    "problem_number": 5044,
    "slug": "circulant-1129-24-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:38+00:00",
    "updated_at": "2026-08-16T08:03:39+00:00"
  },
  "P5046": {
    "problem_number": 5046,
    "slug": "circulant-1151-25-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:42+00:00",
    "updated_at": "2026-08-16T08:03:44+00:00"
  },
  "P5048": {
    "problem_number": 5048,
    "slug": "circulant-1153-26-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:44+00:00",
    "updated_at": "2026-08-16T08:03:45+00:00"
  },
  "P5050": {
    "problem_number": 5050,
    "slug": "circulant-1163-27-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:47+00:00",
    "updated_at": "2026-08-16T08:03:49+00:00"
  },
  "P5052": {
    "problem_number": 5052,
    "slug": "circulant-1171-28-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:50+00:00",
    "updated_at": "2026-08-16T08:03:52+00:00"
  },
  "P5054": {
    "problem_number": 5054,
    "slug": "circulant-1181-29-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:53+00:00",
    "updated_at": "2026-08-16T08:03:53+00:00"
  },
  "P5056": {
    "problem_number": 5056,
    "slug": "circulant-1187-30-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:54+00:00",
    "updated_at": "2026-08-16T08:03:57+00:00"
  },
  "P5058": {
    "problem_number": 5058,
    "slug": "circulant-1193-31-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:03:58+00:00",
    "updated_at": "2026-08-16T08:03:59+00:00"
  },
  "P5060": {
    "problem_number": 5060,
    "slug": "circulant-1201-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:04+00:00",
    "updated_at": "2026-08-16T08:04:08+00:00"
  },
  "P5062": {
    "problem_number": 5062,
    "slug": "circulant-1213-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:10+00:00",
    "updated_at": "2026-08-16T08:04:14+00:00"
  },
  "P5064": {
    "problem_number": 5064,
    "slug": "circulant-1217-4-independence-number",
    "resolution_state": "open",
    "solution_state": "submitted",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "candidate_resolution",
        "label": "Solution submitted",
        "tone": "candidate",
        "reason": "A complete answer is reported without an accepted resolution review.",
        "transitionRule": "A complete answer is reported without an accepted resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": {
          "id": null,
          "slug": "p5064-exact-independence-486",
          "title": "The independence number of C(1217; 1, 4) is 486",
          "url": "/research/changes/?proposal_id=tdbrpp1%3A3eca66fc7c6048c5b90d827935d1c46e",
          "proposalId": "tdbrpp1:3eca66fc7c6048c5b90d827935d1c46e"
        }
      },
      "proofMessage": "A solution has been submitted and awaits independent review.",
      "summary": "Solution submitted. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:17+00:00",
    "updated_at": "2026-08-16T08:04:24+00:00"
  },
  "P5066": {
    "problem_number": 5066,
    "slug": "circulant-1223-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:25+00:00",
    "updated_at": "2026-08-16T08:04:30+00:00"
  },
  "P5068": {
    "problem_number": 5068,
    "slug": "circulant-1229-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:31+00:00",
    "updated_at": "2026-08-16T08:04:37+00:00"
  },
  "P5070": {
    "problem_number": 5070,
    "slug": "circulant-1231-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:37+00:00",
    "updated_at": "2026-08-16T08:04:37+00:00"
  },
  "P5072": {
    "problem_number": 5072,
    "slug": "circulant-1237-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:38+00:00",
    "updated_at": "2026-08-16T08:04:38+00:00"
  },
  "P5074": {
    "problem_number": 5074,
    "slug": "circulant-1249-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:39+00:00",
    "updated_at": "2026-08-16T08:04:41+00:00"
  },
  "P5076": {
    "problem_number": 5076,
    "slug": "circulant-1259-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:41+00:00",
    "updated_at": "2026-08-16T08:04:45+00:00"
  },
  "P5078": {
    "problem_number": 5078,
    "slug": "circulant-1277-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T08:04:47+00:00",
    "updated_at": "2026-08-16T08:04:52+00:00"
  },
  "P4468": {
    "problem_number": 4468,
    "slug": "circulant-331-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:29:42+00:00",
    "updated_at": "2026-08-16T05:29:45+00:00"
  },
  "P4470": {
    "problem_number": 4470,
    "slug": "circulant-337-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:29:50+00:00",
    "updated_at": "2026-08-16T05:30:05+00:00"
  },
  "P4472": {
    "problem_number": 4472,
    "slug": "circulant-347-4-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:14+00:00",
    "updated_at": "2026-08-16T05:30:31+00:00"
  },
  "P4474": {
    "problem_number": 4474,
    "slug": "circulant-349-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:40+00:00",
    "updated_at": "2026-08-16T05:30:50+00:00"
  },
  "P4476": {
    "problem_number": 4476,
    "slug": "circulant-353-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:53+00:00",
    "updated_at": "2026-08-16T05:30:53+00:00"
  },
  "P4478": {
    "problem_number": 4478,
    "slug": "circulant-359-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:54+00:00",
    "updated_at": "2026-08-16T05:30:55+00:00"
  },
  "P4480": {
    "problem_number": 4480,
    "slug": "circulant-367-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:55+00:00",
    "updated_at": "2026-08-16T05:30:56+00:00"
  },
  "P4482": {
    "problem_number": 4482,
    "slug": "circulant-373-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:30:56+00:00",
    "updated_at": "2026-08-16T05:30:57+00:00"
  },
  "P4484": {
    "problem_number": 4484,
    "slug": "circulant-379-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:03+00:00",
    "updated_at": "2026-08-16T05:31:16+00:00"
  },
  "P4486": {
    "problem_number": 4486,
    "slug": "circulant-383-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:19+00:00",
    "updated_at": "2026-08-16T05:31:29+00:00"
  },
  "P4488": {
    "problem_number": 4488,
    "slug": "circulant-389-12-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:32+00:00",
    "updated_at": "2026-08-16T05:31:34+00:00"
  },
  "P4490": {
    "problem_number": 4490,
    "slug": "circulant-397-13-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:34+00:00",
    "updated_at": "2026-08-16T05:31:35+00:00"
  },
  "P4492": {
    "problem_number": 4492,
    "slug": "circulant-401-14-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:35+00:00",
    "updated_at": "2026-08-16T05:31:37+00:00"
  },
  "P4494": {
    "problem_number": 4494,
    "slug": "circulant-409-15-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:37+00:00",
    "updated_at": "2026-08-16T05:31:38+00:00"
  },
  "P4496": {
    "problem_number": 4496,
    "slug": "circulant-419-16-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:40+00:00",
    "updated_at": "2026-08-16T05:31:43+00:00"
  },
  "P4498": {
    "problem_number": 4498,
    "slug": "circulant-421-17-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:46+00:00",
    "updated_at": "2026-08-16T05:31:48+00:00"
  },
  "P4500": {
    "problem_number": 4500,
    "slug": "circulant-431-18-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:50+00:00",
    "updated_at": "2026-08-16T05:31:51+00:00"
  },
  "P4502": {
    "problem_number": 4502,
    "slug": "circulant-433-19-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:52+00:00",
    "updated_at": "2026-08-16T05:31:56+00:00"
  },
  "P4504": {
    "problem_number": 4504,
    "slug": "circulant-439-20-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:57+00:00",
    "updated_at": "2026-08-16T05:31:59+00:00"
  },
  "P4506": {
    "problem_number": 4506,
    "slug": "circulant-443-21-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:31:59+00:00",
    "updated_at": "2026-08-16T05:32:02+00:00"
  },
  "P4508": {
    "problem_number": 4508,
    "slug": "circulant-449-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:03+00:00",
    "updated_at": "2026-08-16T05:32:04+00:00"
  },
  "P4510": {
    "problem_number": 4510,
    "slug": "circulant-457-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:04+00:00",
    "updated_at": "2026-08-16T05:32:06+00:00"
  },
  "P4512": {
    "problem_number": 4512,
    "slug": "circulant-461-4-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:07+00:00",
    "updated_at": "2026-08-16T05:32:07+00:00"
  },
  "P4514": {
    "problem_number": 4514,
    "slug": "circulant-463-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:08+00:00",
    "updated_at": "2026-08-16T05:32:09+00:00"
  },
  "P4516": {
    "problem_number": 4516,
    "slug": "circulant-467-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:11+00:00",
    "updated_at": "2026-08-16T05:32:13+00:00"
  },
  "P4518": {
    "problem_number": 4518,
    "slug": "circulant-479-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:13+00:00",
    "updated_at": "2026-08-16T05:32:22+00:00"
  },
  "P4520": {
    "problem_number": 4520,
    "slug": "circulant-487-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:24+00:00",
    "updated_at": "2026-08-16T05:32:27+00:00"
  },
  "P4522": {
    "problem_number": 4522,
    "slug": "circulant-491-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:27+00:00",
    "updated_at": "2026-08-16T05:32:32+00:00"
  },
  "P4524": {
    "problem_number": 4524,
    "slug": "circulant-499-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:33+00:00",
    "updated_at": "2026-08-16T05:32:34+00:00"
  },
  "P4526": {
    "problem_number": 4526,
    "slug": "circulant-503-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:34+00:00",
    "updated_at": "2026-08-16T05:32:37+00:00"
  },
  "P4528": {
    "problem_number": 4528,
    "slug": "circulant-509-12-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:43+00:00",
    "updated_at": "2026-08-16T05:32:48+00:00"
  },
  "P4530": {
    "problem_number": 4530,
    "slug": "circulant-521-13-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:50+00:00",
    "updated_at": "2026-08-16T05:32:53+00:00"
  },
  "P4532": {
    "problem_number": 4532,
    "slug": "circulant-523-14-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:32:54+00:00",
    "updated_at": "2026-08-16T05:33:04+00:00"
  },
  "P4534": {
    "problem_number": 4534,
    "slug": "circulant-541-15-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:06+00:00",
    "updated_at": "2026-08-16T05:33:07+00:00"
  },
  "P4536": {
    "problem_number": 4536,
    "slug": "circulant-547-16-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:07+00:00",
    "updated_at": "2026-08-16T05:33:08+00:00"
  },
  "P4538": {
    "problem_number": 4538,
    "slug": "circulant-557-17-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:09+00:00",
    "updated_at": "2026-08-16T05:33:09+00:00"
  },
  "P4540": {
    "problem_number": 4540,
    "slug": "circulant-563-18-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:10+00:00",
    "updated_at": "2026-08-16T05:33:10+00:00"
  },
  "P4542": {
    "problem_number": 4542,
    "slug": "circulant-569-19-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:11+00:00",
    "updated_at": "2026-08-16T05:33:13+00:00"
  },
  "P4544": {
    "problem_number": 4544,
    "slug": "circulant-571-20-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:14+00:00",
    "updated_at": "2026-08-16T05:33:18+00:00"
  },
  "P4546": {
    "problem_number": 4546,
    "slug": "circulant-577-21-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T05:33:18+00:00",
    "updated_at": "2026-08-16T05:33:20+00:00"
  },
  "P4868": {
    "problem_number": 4868,
    "slug": "circulant-587-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:28:35+00:00",
    "updated_at": "2026-08-16T07:29:00+00:00"
  },
  "P4870": {
    "problem_number": 4870,
    "slug": "circulant-593-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:29:13+00:00",
    "updated_at": "2026-08-16T07:29:38+00:00"
  },
  "P4872": {
    "problem_number": 4872,
    "slug": "circulant-599-4-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:29:51+00:00",
    "updated_at": "2026-08-16T07:30:15+00:00"
  },
  "P4874": {
    "problem_number": 4874,
    "slug": "circulant-601-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:30:31+00:00",
    "updated_at": "2026-08-16T07:30:46+00:00"
  },
  "P4876": {
    "problem_number": 4876,
    "slug": "circulant-607-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:30:57+00:00",
    "updated_at": "2026-08-16T07:31:18+00:00"
  },
  "P4878": {
    "problem_number": 4878,
    "slug": "circulant-613-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:31:29+00:00",
    "updated_at": "2026-08-16T07:31:51+00:00"
  },
  "P4880": {
    "problem_number": 4880,
    "slug": "circulant-617-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:32:00+00:00",
    "updated_at": "2026-08-16T07:32:20+00:00"
  },
  "P4882": {
    "problem_number": 4882,
    "slug": "circulant-619-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:11+00:00",
    "updated_at": "2026-08-16T07:36:12+00:00"
  },
  "P4884": {
    "problem_number": 4884,
    "slug": "circulant-631-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:12+00:00",
    "updated_at": "2026-08-16T07:36:14+00:00"
  },
  "P4886": {
    "problem_number": 4886,
    "slug": "circulant-641-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:14+00:00",
    "updated_at": "2026-08-16T07:36:16+00:00"
  },
  "P4888": {
    "problem_number": 4888,
    "slug": "circulant-643-12-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:16+00:00",
    "updated_at": "2026-08-16T07:36:16+00:00"
  },
  "P4890": {
    "problem_number": 4890,
    "slug": "circulant-647-13-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:16+00:00",
    "updated_at": "2026-08-16T07:36:18+00:00"
  },
  "P4892": {
    "problem_number": 4892,
    "slug": "circulant-653-14-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:18+00:00",
    "updated_at": "2026-08-16T07:36:19+00:00"
  },
  "P4894": {
    "problem_number": 4894,
    "slug": "circulant-659-15-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:20+00:00",
    "updated_at": "2026-08-16T07:36:20+00:00"
  },
  "P4896": {
    "problem_number": 4896,
    "slug": "circulant-661-16-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:20+00:00",
    "updated_at": "2026-08-16T07:36:20+00:00"
  },
  "P4898": {
    "problem_number": 4898,
    "slug": "circulant-673-17-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:20+00:00",
    "updated_at": "2026-08-16T07:36:21+00:00"
  },
  "P4900": {
    "problem_number": 4900,
    "slug": "circulant-677-18-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:22+00:00",
    "updated_at": "2026-08-16T07:36:25+00:00"
  },
  "P4902": {
    "problem_number": 4902,
    "slug": "circulant-683-19-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:26+00:00",
    "updated_at": "2026-08-16T07:36:32+00:00"
  },
  "P4904": {
    "problem_number": 4904,
    "slug": "circulant-691-20-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:36+00:00",
    "updated_at": "2026-08-16T07:36:44+00:00"
  },
  "P4906": {
    "problem_number": 4906,
    "slug": "circulant-701-21-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:36:50+00:00",
    "updated_at": "2026-08-16T07:37:05+00:00"
  },
  "P4908": {
    "problem_number": 4908,
    "slug": "circulant-709-22-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:37:08+00:00",
    "updated_at": "2026-08-16T07:37:14+00:00"
  },
  "P4910": {
    "problem_number": 4910,
    "slug": "circulant-719-23-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:37:14+00:00",
    "updated_at": "2026-08-16T07:37:21+00:00"
  },
  "P4912": {
    "problem_number": 4912,
    "slug": "circulant-727-24-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:37:22+00:00",
    "updated_at": "2026-08-16T07:37:22+00:00"
  },
  "P4914": {
    "problem_number": 4914,
    "slug": "circulant-733-25-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:37:29+00:00",
    "updated_at": "2026-08-16T07:37:42+00:00"
  },
  "P4916": {
    "problem_number": 4916,
    "slug": "circulant-739-26-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:37:48+00:00",
    "updated_at": "2026-08-16T07:38:02+00:00"
  },
  "P4918": {
    "problem_number": 4918,
    "slug": "circulant-743-27-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:38:12+00:00",
    "updated_at": "2026-08-16T07:38:28+00:00"
  },
  "P4920": {
    "problem_number": 4920,
    "slug": "circulant-751-28-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:38:35+00:00",
    "updated_at": "2026-08-16T07:38:53+00:00"
  },
  "P4922": {
    "problem_number": 4922,
    "slug": "circulant-757-29-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:39:01+00:00",
    "updated_at": "2026-08-16T07:39:16+00:00"
  },
  "P4924": {
    "problem_number": 4924,
    "slug": "circulant-761-30-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:39:23+00:00",
    "updated_at": "2026-08-16T07:39:34+00:00"
  },
  "P4926": {
    "problem_number": 4926,
    "slug": "circulant-769-31-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:39:44+00:00",
    "updated_at": "2026-08-16T07:39:59+00:00"
  },
  "P4928": {
    "problem_number": 4928,
    "slug": "circulant-773-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:00+00:00",
    "updated_at": "2026-08-16T07:40:08+00:00"
  },
  "P4930": {
    "problem_number": 4930,
    "slug": "circulant-787-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:16+00:00",
    "updated_at": "2026-08-16T07:40:18+00:00"
  },
  "P4932": {
    "problem_number": 4932,
    "slug": "circulant-797-4-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:18+00:00",
    "updated_at": "2026-08-16T07:40:34+00:00"
  },
  "P4934": {
    "problem_number": 4934,
    "slug": "circulant-809-5-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:40+00:00",
    "updated_at": "2026-08-16T07:40:42+00:00"
  },
  "P4936": {
    "problem_number": 4936,
    "slug": "circulant-811-6-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:42+00:00",
    "updated_at": "2026-08-16T07:40:50+00:00"
  },
  "P4938": {
    "problem_number": 4938,
    "slug": "circulant-821-7-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:40:51+00:00",
    "updated_at": "2026-08-16T07:40:58+00:00"
  },
  "P4940": {
    "problem_number": 4940,
    "slug": "circulant-823-8-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:00+00:00",
    "updated_at": "2026-08-16T07:41:07+00:00"
  },
  "P4942": {
    "problem_number": 4942,
    "slug": "circulant-827-9-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:07+00:00",
    "updated_at": "2026-08-16T07:41:07+00:00"
  },
  "P4944": {
    "problem_number": 4944,
    "slug": "circulant-829-10-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:08+00:00",
    "updated_at": "2026-08-16T07:41:18+00:00"
  },
  "P4946": {
    "problem_number": 4946,
    "slug": "circulant-839-11-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:24+00:00",
    "updated_at": "2026-08-16T07:41:37+00:00"
  },
  "P4948": {
    "problem_number": 4948,
    "slug": "circulant-853-12-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:43+00:00",
    "updated_at": "2026-08-16T07:41:47+00:00"
  },
  "P4950": {
    "problem_number": 4950,
    "slug": "circulant-857-13-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:50+00:00",
    "updated_at": "2026-08-16T07:41:52+00:00"
  },
  "P4952": {
    "problem_number": 4952,
    "slug": "circulant-859-14-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:41:53+00:00",
    "updated_at": "2026-08-16T07:41:57+00:00"
  },
  "P4954": {
    "problem_number": 4954,
    "slug": "circulant-863-15-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:42:04+00:00",
    "updated_at": "2026-08-16T07:42:15+00:00"
  },
  "P4956": {
    "problem_number": 4956,
    "slug": "circulant-877-16-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:42:22+00:00",
    "updated_at": "2026-08-16T07:42:38+00:00"
  },
  "P4958": {
    "problem_number": 4958,
    "slug": "circulant-881-17-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:42:39+00:00",
    "updated_at": "2026-08-16T07:42:45+00:00"
  },
  "P4960": {
    "problem_number": 4960,
    "slug": "circulant-883-18-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:42:53+00:00",
    "updated_at": "2026-08-16T07:43:01+00:00"
  },
  "P4962": {
    "problem_number": 4962,
    "slug": "circulant-887-19-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:43:01+00:00",
    "updated_at": "2026-08-16T07:43:04+00:00"
  },
  "P4964": {
    "problem_number": 4964,
    "slug": "circulant-907-20-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:43:09+00:00",
    "updated_at": "2026-08-16T07:43:23+00:00"
  },
  "P4966": {
    "problem_number": 4966,
    "slug": "circulant-911-21-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:43:31+00:00",
    "updated_at": "2026-08-16T07:43:43+00:00"
  },
  "P4968": {
    "problem_number": 4968,
    "slug": "circulant-919-22-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:43:47+00:00",
    "updated_at": "2026-08-16T07:43:58+00:00"
  },
  "P4970": {
    "problem_number": 4970,
    "slug": "circulant-929-23-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:03+00:00",
    "updated_at": "2026-08-16T07:44:12+00:00"
  },
  "P4972": {
    "problem_number": 4972,
    "slug": "circulant-937-24-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:20+00:00",
    "updated_at": "2026-08-16T07:44:28+00:00"
  },
  "P4974": {
    "problem_number": 4974,
    "slug": "circulant-941-25-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:29+00:00",
    "updated_at": "2026-08-16T07:44:29+00:00"
  },
  "P4976": {
    "problem_number": 4976,
    "slug": "circulant-947-26-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:30+00:00",
    "updated_at": "2026-08-16T07:44:35+00:00"
  },
  "P4978": {
    "problem_number": 4978,
    "slug": "circulant-953-27-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:35+00:00",
    "updated_at": "2026-08-16T07:44:38+00:00"
  },
  "P4980": {
    "problem_number": 4980,
    "slug": "circulant-967-28-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:40+00:00",
    "updated_at": "2026-08-16T07:44:43+00:00"
  },
  "P4982": {
    "problem_number": 4982,
    "slug": "circulant-971-29-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:43+00:00",
    "updated_at": "2026-08-16T07:44:48+00:00"
  },
  "P4984": {
    "problem_number": 4984,
    "slug": "circulant-977-30-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:44:48+00:00",
    "updated_at": "2026-08-16T07:48:42+00:00"
  },
  "P4986": {
    "problem_number": 4986,
    "slug": "circulant-983-31-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:48:48+00:00",
    "updated_at": "2026-08-16T07:48:57+00:00"
  },
  "P4988": {
    "problem_number": 4988,
    "slug": "circulant-991-2-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:48:58+00:00",
    "updated_at": "2026-08-16T07:49:03+00:00"
  },
  "P4990": {
    "problem_number": 4990,
    "slug": "circulant-997-3-independence-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-16T07:49:04+00:00",
    "updated_at": "2026-08-16T07:49:12+00:00"
  },
  "P9700": {
    "problem_number": 9700,
    "slug": "open-fc-93e4b989cfc56b843cd3-independentdominationeven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:56+00:00",
    "updated_at": "2026-08-17T20:01:57+00:00"
  },
  "P8780": {
    "problem_number": 8780,
    "slug": "open-fc-52cc3f49f8a5562bd4fa-independentdominationodd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:19:43+00:00",
    "updated_at": "2026-08-17T19:19:53+00:00"
  },
  "P12429": {
    "problem_number": 12429,
    "slug": "indices-of-record-prime-gaps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:34:52+00:00",
    "updated_at": "2026-09-02T21:35:05+00:00"
  },
  "P10084": {
    "problem_number": 10084,
    "slug": "open-fc-fb454360cb305411310c-erdos-1038-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:19+00:00",
    "updated_at": "2026-08-17T20:06:21+00:00"
  },
  "P2824": {
    "problem_number": 2824,
    "slug": "additive-square-finite-alphabet",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:00+00:00",
    "updated_at": "2026-07-30T02:22:53+00:00"
  },
  "P3258": {
    "problem_number": 3258,
    "slug": "erdos-problem-1212",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:43+00:00",
    "updated_at": "2026-08-12T05:58:47+00:00"
  },
  "P8868": {
    "problem_number": 8868,
    "slug": "open-fc-bc9d3143c029b273dec4-erdos-141-variants-infinite-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:45+00:00",
    "updated_at": "2026-08-17T19:35:52+00:00"
  },
  "P11696": {
    "problem_number": 11696,
    "slug": "infinitely-many-attained-and-unattained-decimal-reversal-divisor-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:35+00:00",
    "updated_at": "2026-08-30T11:15:42+00:00"
  },
  "P8160": {
    "problem_number": 8160,
    "slug": "open-fc-090e29e92e5ac8616a96-erdos-413-variants-bigomega",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:34+00:00",
    "updated_at": "2026-08-17T18:35:35+00:00"
  },
  "P8472": {
    "problem_number": 8472,
    "slug": "open-fc-4738db39471c8205203a-erdos-386-variants-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:16+00:00",
    "updated_at": "2026-08-17T18:52:17+00:00"
  },
  "P9650": {
    "problem_number": 9650,
    "slug": "open-fc-4a32826c7006298006a5-erdos-386-variants-forall",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:30+00:00",
    "updated_at": "2026-08-17T20:00:31+00:00"
  },
  "P9606": {
    "problem_number": 9606,
    "slug": "open-fc-eb9202643695b16ae450-erdos-1003-variants-icc",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:53+00:00",
    "updated_at": "2026-08-17T19:56:55+00:00"
  },
  "P9030": {
    "problem_number": 9030,
    "slug": "open-fc-9136023083c220274bf2-erdos-913",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:34+00:00",
    "updated_at": "2026-08-17T19:45:37+00:00"
  },
  "P8440": {
    "problem_number": 8440,
    "slug": "open-fc-35bc43e06b9fff4a722d-erdos-141-variants-infinite-general-case",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:06+00:00",
    "updated_at": "2026-08-17T18:52:07+00:00"
  },
  "P12023": {
    "problem_number": 12023,
    "slug": "infinitely-many-consecutive-prime-hamming-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:51:58+00:00",
    "updated_at": "2026-09-01T18:52:09+00:00"
  },
  "P8766": {
    "problem_number": 8766,
    "slug": "open-fc-5f3ce0bcf88e4e923fed-erdos-939-variants-triples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:14:53+00:00",
    "updated_at": "2026-08-17T19:15:07+00:00"
  },
  "P9412": {
    "problem_number": 9412,
    "slug": "open-fc-5820b4f42ad5bafd86ec-erdos-968-variants-infinite-decreasingtriples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:29+00:00",
    "updated_at": "2026-08-17T19:52:30+00:00"
  },
  "P11887": {
    "problem_number": 11887,
    "slug": "infinitely-many-doubly-quadruplet-sophie-germain-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:08+00:00",
    "updated_at": "2026-08-30T16:20:14+00:00"
  },
  "P9370": {
    "problem_number": 9370,
    "slug": "open-fc-f187f25f0ff3da712c26-erdos-10-variants-grechuk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:13+00:00",
    "updated_at": "2026-08-17T19:51:13+00:00"
  },
  "P9340": {
    "problem_number": 9340,
    "slug": "open-fc-db9c7cc32a00170eeecd-infinitely-many-even-perfect",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:01+00:00",
    "updated_at": "2026-08-17T19:51:01+00:00"
  },
  "P8172": {
    "problem_number": 8172,
    "slug": "open-fc-0a103d7e6c800515ec29-erdos-349-variants-floor-3-halves-even",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:12+00:00",
    "updated_at": "2026-08-17T18:36:14+00:00"
  },
  "P11646": {
    "problem_number": 11646,
    "slug": "infinitely-many-exits-from-linear-stretches-of-a-josephus-permutation-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:46:55+00:00",
    "updated_at": "2026-08-30T04:48:04+00:00"
  },
  "P9276": {
    "problem_number": 9276,
    "slug": "open-fc-a8b8eb22cabffd348b6c-erdos-394-variants-factorial-gap-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:34+00:00",
    "updated_at": "2026-08-17T19:50:34+00:00"
  },
  "P11620": {
    "problem_number": 11620,
    "slug": "infinitely-many-fully-developed-prime-trajectories",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:39:41+00:00",
    "updated_at": "2026-08-30T04:39:47+00:00"
  },
  "P12077": {
    "problem_number": 12077,
    "slug": "infinitely-many-half-totients-for-infinitary-coprimality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:34+00:00",
    "updated_at": "2026-09-01T19:08:40+00:00"
  },
  "P12197": {
    "problem_number": 12197,
    "slug": "infinitely-many-happy-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:23:21+00:00",
    "updated_at": "2026-09-01T19:23:26+00:00"
  },
  "P8838": {
    "problem_number": 8838,
    "slug": "open-fc-a5fa3163c359c0fe7c40-erdos-968-variants-infinite-increasingtriples",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:24+00:00",
    "updated_at": "2026-08-17T19:25:38+00:00"
  },
  "P12039": {
    "problem_number": 12039,
    "slug": "infinitely-many-integers-prime-after-adjoining-13-on-either-side",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:55:09+00:00",
    "updated_at": "2026-09-01T18:55:19+00:00"
  },
  "P12119": {
    "problem_number": 12119,
    "slug": "infinitely-many-integers-prime-under-every-insertion-of-digit-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:13:49+00:00",
    "updated_at": "2026-09-01T19:13:55+00:00"
  },
  "P10056": {
    "problem_number": 10056,
    "slug": "open-fc-e7f256b8f642a34bd240-erdos-828",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:58+00:00",
    "updated_at": "2026-08-17T20:05:59+00:00"
  },
  "P8304": {
    "problem_number": 8304,
    "slug": "open-fc-1e81c1da5cb19b440b60-erdos-727-variants-k-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:59+00:00",
    "updated_at": "2026-08-17T18:39:09+00:00"
  },
  "P9574": {
    "problem_number": 9574,
    "slug": "open-fc-d15564cf82ab47c0a082-erdos-826",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:46+00:00",
    "updated_at": "2026-08-17T19:55:48+00:00"
  },
  "P11820": {
    "problem_number": 11820,
    "slug": "infinitely-many-linked-prime-pythagorean-triangles",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:59:23+00:00",
    "updated_at": "2026-08-30T13:01:28+00:00"
  },
  "P35": {
    "problem_number": 35,
    "slug": "infinitely-many-mersenne-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:14:26+00:00"
  },
  "P9748": {
    "problem_number": 9748,
    "slug": "open-fc-b6f19284fa1a932c0479-erdos-422",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:16+00:00",
    "updated_at": "2026-08-17T20:02:17+00:00"
  },
  "P11772": {
    "problem_number": 11772,
    "slug": "infinitely-many-near-cubes-that-are-sums-of-two-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:25:01+00:00",
    "updated_at": "2026-08-30T12:26:38+00:00"
  },
  "P9178": {
    "problem_number": 9178,
    "slug": "open-fc-2ecc01e670afba578823-erdos-647-variants-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:48:31+00:00",
    "updated_at": "2026-08-17T19:48:58+00:00"
  },
  "P2872": {
    "problem_number": 2872,
    "slug": "grahl-sequence-infinitely-many-ones",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:41:42+00:00",
    "updated_at": "2026-08-01T23:28:43+00:00"
  },
  "P9194": {
    "problem_number": 9194,
    "slug": "open-fc-488db4c46ec42603acd8-erdos-730",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:10+00:00",
    "updated_at": "2026-08-17T19:49:10+00:00"
  },
  "P8738": {
    "problem_number": 8738,
    "slug": "open-fc-50114fc1dfc766227a49-erdos-409-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:04+00:00",
    "updated_at": "2026-08-17T19:43:50+00:00"
  },
  "P11164": {
    "problem_number": 11164,
    "slug": "prime-coefficients-of-the-modular-j-function",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:14:23+00:00",
    "updated_at": "2026-08-29T18:48:31+00:00"
  },
  "P12121": {
    "problem_number": 12121,
    "slug": "infinitely-many-prime-concatenations-of-1-and-a-cube",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:14:03+00:00",
    "updated_at": "2026-09-01T19:14:09+00:00"
  },
  "P11845": {
    "problem_number": 11845,
    "slug": "infinitely-many-prime-sextuples-in-the-length-17-pattern",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:36+00:00",
    "updated_at": "2026-08-30T16:14:41+00:00"
  },
  "P12041": {
    "problem_number": 12041,
    "slug": "infinitely-many-primes-of-the-form-1-10n-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:55:41+00:00",
    "updated_at": "2026-09-01T18:55:52+00:00"
  },
  "P11592": {
    "problem_number": 11592,
    "slug": "infinitely-many-primes-of-the-form-n-squared-plus-169",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:36+00:00",
    "updated_at": "2026-08-30T04:36:41+00:00"
  },
  "P8704": {
    "problem_number": 8704,
    "slug": "open-fc-306c5eb102c885223b57-erdos-456-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:06:03+00:00",
    "updated_at": "2026-08-17T19:06:19+00:00"
  },
  "P3302": {
    "problem_number": 3302,
    "slug": "erdos-problem-1059",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:03:34+00:00",
    "updated_at": "2026-08-12T06:03:39+00:00"
  },
  "P11604": {
    "problem_number": 11604,
    "slug": "infinitely-many-primes-with-no-palindromic-base-representation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:37:45+00:00",
    "updated_at": "2026-08-30T04:37:51+00:00"
  },
  "P9778": {
    "problem_number": 9778,
    "slug": "open-fc-cdda1670dc1a35ec3c63-erdos-972",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:34+00:00",
    "updated_at": "2026-08-17T20:02:35+00:00"
  },
  "P9052": {
    "problem_number": 9052,
    "slug": "open-fc-a0456baff7dcf4bb3e6f-erdos-413-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:18+00:00",
    "updated_at": "2026-08-17T19:46:20+00:00"
  },
  "P12239": {
    "problem_number": 12239,
    "slug": "infinitely-many-returns-of-a-square-root-sign-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:28:30+00:00",
    "updated_at": "2026-09-01T19:28:36+00:00"
  },
  "P11824": {
    "problem_number": 11824,
    "slug": "infinitely-many-riesel-numbers-without-periodic-prime-covers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T13:03:57+00:00",
    "updated_at": "2026-08-30T13:05:53+00:00"
  },
  "P11893": {
    "problem_number": 11893,
    "slug": "infinitely-many-semiprimes-of-the-form-m-squared-plus-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:39+00:00",
    "updated_at": "2026-08-30T16:20:45+00:00"
  },
  "P11923": {
    "problem_number": 11923,
    "slug": "infinitely-many-shifted-primes-with-power-of-two-cofactors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:23:33+00:00",
    "updated_at": "2026-08-30T16:23:39+00:00"
  },
  "P11708": {
    "problem_number": 11708,
    "slug": "infinitely-many-simultaneous-zero-lines-in-the-prime-composite-array",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:33+00:00",
    "updated_at": "2026-08-30T11:16:41+00:00"
  },
  "P3320": {
    "problem_number": 3320,
    "slug": "erdos-problem-479",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:05:10+00:00",
    "updated_at": "2026-08-12T06:05:32+00:00"
  },
  "P9698": {
    "problem_number": 9698,
    "slug": "open-fc-9180e2125ccc50033e99-erdos-479",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:55+00:00",
    "updated_at": "2026-08-17T20:01:55+00:00"
  },
  "P8088": {
    "problem_number": 8088,
    "slug": "open-fc-011546103e140199fd46-erdos-313",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:37+00:00",
    "updated_at": "2026-08-17T18:34:38+00:00"
  },
  "P9590": {
    "problem_number": 9590,
    "slug": "open-fc-e162e9406faeaf968318-erdos-978-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:18+00:00",
    "updated_at": "2026-08-17T19:56:20+00:00"
  },
  "P12107": {
    "problem_number": 12107,
    "slug": "infinitely-many-ties-between-balanced-evil-and-odious-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:11:56+00:00",
    "updated_at": "2026-09-01T19:12:02+00:00"
  },
  "P12343": {
    "problem_number": 12343,
    "slug": "infinitely-many-twin-half-period-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:41:07+00:00",
    "updated_at": "2026-09-01T19:41:13+00:00"
  },
  "P11616": {
    "problem_number": 11616,
    "slug": "infinitely-many-twin-primes-sharing-primitive-root-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:39:08+00:00",
    "updated_at": "2026-08-30T04:39:14+00:00"
  },
  "P8994": {
    "problem_number": 8994,
    "slug": "open-fc-75cd2b51cbc96a1f0ae4-infinitely-many-amicable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:33+00:00",
    "updated_at": "2026-08-17T19:44:35+00:00"
  },
  "P8552": {
    "problem_number": 8552,
    "slug": "open-fc-71138207543a3d3fd8e0-erdos-830-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:37+00:00",
    "updated_at": "2026-08-17T18:54:38+00:00"
  },
  "P9204": {
    "problem_number": 9204,
    "slug": "open-fc-5961dcc2c25ab91fba95-balanced-primes-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:14+00:00",
    "updated_at": "2026-08-17T19:49:15+00:00"
  },
  "P9730": {
    "problem_number": 9730,
    "slug": "open-fc-a95bab5500dbe68bf622-balanced-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:08+00:00",
    "updated_at": "2026-08-17T20:02:08+00:00"
  },
  "P8720": {
    "problem_number": 8720,
    "slug": "open-fc-39be37ce5f59e4184062-erdos-413-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:10:53+00:00",
    "updated_at": "2026-08-17T19:11:01+00:00"
  },
  "P8978": {
    "problem_number": 8978,
    "slug": "open-fc-693be0117c9c3ae78bb6-infinitely-many-betrothed",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:12+00:00",
    "updated_at": "2026-08-17T19:44:14+00:00"
  },
  "P8210": {
    "problem_number": 8210,
    "slug": "open-fc-0ec81888af93709b84e2-erdos-376",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:09+00:00",
    "updated_at": "2026-08-17T18:37:10+00:00"
  },
  "P2972": {
    "problem_number": 2972,
    "slug": "erdos-problem-17",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:37+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8224": {
    "problem_number": 8224,
    "slug": "open-fc-129578a4e7423dc2c9c9-erdos-17",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:21+00:00",
    "updated_at": "2026-08-17T18:37:22+00:00"
  },
  "P9316": {
    "problem_number": 9316,
    "slug": "open-fc-c6b87b3e18c35b363169-infinite-fermat-composite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:51+00:00",
    "updated_at": "2026-08-17T19:50:51+00:00"
  },
  "P9042": {
    "problem_number": 9042,
    "slug": "open-fc-99df4b5cfd6d3a925fce-erdos-700-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:58+00:00",
    "updated_at": "2026-08-17T19:46:00+00:00"
  },
  "P8486": {
    "problem_number": 8486,
    "slug": "open-fc-4d5a7c4221fb3d592cdf-erdos-366-variants-three-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:24+00:00",
    "updated_at": "2026-08-17T18:52:25+00:00"
  },
  "P9360": {
    "problem_number": 9360,
    "slug": "open-fc-ea9ed1cb11573a5b0c75-erdos-218-variants-infinite-equal-prime-gap",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:09+00:00",
    "updated_at": "2026-08-17T19:51:10+00:00"
  },
  "P8506": {
    "problem_number": 8506,
    "slug": "open-fc-59f7f0847677548537a6-erdos-1003",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:20+00:00",
    "updated_at": "2026-08-17T18:53:26+00:00"
  },
  "P9164": {
    "problem_number": 9164,
    "slug": "open-fc-f57e73cf635a10b8783d-erdos-291-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:53+00:00",
    "updated_at": "2026-08-17T19:47:53+00:00"
  },
  "P9588": {
    "problem_number": 9588,
    "slug": "open-fc-dfc0fc91c6db5cee4d8c-infinite-cousin-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:13+00:00",
    "updated_at": "2026-08-17T19:56:16+00:00"
  },
  "P8402": {
    "problem_number": 8402,
    "slug": "open-fc-298fb272f265b6a8d1aa-infinite-fermat-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:29+00:00",
    "updated_at": "2026-08-17T18:49:31+00:00"
  },
  "P8646": {
    "problem_number": 8646,
    "slug": "open-fc-8c2a4ea4f0c52d5019fe-fib-primes-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:05+00:00",
    "updated_at": "2026-08-17T18:59:17+00:00"
  },
  "P8176": {
    "problem_number": 8176,
    "slug": "open-fc-0ac9c49fc6b07f50a361-erdos-770-variants-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:17+00:00",
    "updated_at": "2026-08-17T18:36:22+00:00"
  },
  "P8556": {
    "problem_number": 8556,
    "slug": "open-fc-729405f42b7bdffac257-infinitely-many-leinster-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:43+00:00",
    "updated_at": "2026-08-17T18:54:47+00:00"
  },
  "P9022": {
    "problem_number": 9022,
    "slug": "open-fc-89a5b51c62923f9ffbae-infinite-iswallsunsunprime-of-disc-eq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:20+00:00",
    "updated_at": "2026-08-17T19:45:21+00:00"
  },
  "P8188": {
    "problem_number": 8188,
    "slug": "open-fc-0bcf4acaa0b33c56ee14-infinitely-many-mersenne-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:40+00:00",
    "updated_at": "2026-08-17T18:36:43+00:00"
  },
  "P3336": {
    "problem_number": 3336,
    "slug": "erdos-problem-1142",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:42+00:00",
    "updated_at": "2026-08-12T06:06:43+00:00"
  },
  "P9766": {
    "problem_number": 9766,
    "slug": "open-fc-c44b426fbacf61414765-erdos-349-variants-floor-3-halves-odd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:27+00:00",
    "updated_at": "2026-08-17T20:02:27+00:00"
  },
  "P8538": {
    "problem_number": 8538,
    "slug": "open-fc-695ab4fc5dfa407b1f5f-infinitely-many-perfect",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:22+00:00",
    "updated_at": "2026-08-17T18:54:25+00:00"
  },
  "P8524": {
    "problem_number": 8524,
    "slug": "open-fc-63223435ca84d6145bbd-erdos-313-variants-primary-pseudoperfect-are-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:11+00:00",
    "updated_at": "2026-08-17T18:54:11+00:00"
  },
  "P9180": {
    "problem_number": 9180,
    "slug": "open-fc-32710222ae58aaa427e3-infinite-prime-euclid-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:00+00:00",
    "updated_at": "2026-08-17T19:49:02+00:00"
  },
  "P8618": {
    "problem_number": 8618,
    "slug": "open-fc-85f54a967d2e948e20f4-infinite-pellnumber-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:06+00:00",
    "updated_at": "2026-08-17T18:58:18+00:00"
  },
  "P9420": {
    "problem_number": 9420,
    "slug": "open-fc-5ddc63dcdd189266d84a-fib-primes-infinite-variant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:39+00:00",
    "updated_at": "2026-08-17T19:52:40+00:00"
  },
  "P8266": {
    "problem_number": 8266,
    "slug": "open-fc-18f90bb50894d75d6429-erdos-913-variants-infinite-many-8p-sq-add-one-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:57+00:00",
    "updated_at": "2026-08-17T18:38:00+00:00"
  },
  "P3204": {
    "problem_number": 3204,
    "slug": "erdos-problem-1055",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:24+00:00",
    "updated_at": "2026-08-12T05:52:29+00:00"
  },
  "P3240": {
    "problem_number": 3240,
    "slug": "erdos-problem-1065",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:56:59+00:00",
    "updated_at": "2026-08-12T05:57:07+00:00"
  },
  "P8882": {
    "problem_number": 8882,
    "slug": "open-fc-c636d95f73db9a060f0e-infinite-prime-sq-add-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:19+00:00",
    "updated_at": "2026-08-17T19:36:21+00:00"
  },
  "P8120": {
    "problem_number": 8120,
    "slug": "open-fc-040b106b2510db8dd6cb-conjecturea81091",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:49+00:00",
    "updated_at": "2026-08-17T18:34:50+00:00"
  },
  "P8168": {
    "problem_number": 8168,
    "slug": "open-fc-0973845f87147f75c2b9-erdos-383",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:01+00:00",
    "updated_at": "2026-08-17T18:36:09+00:00"
  },
  "P3230": {
    "problem_number": 3230,
    "slug": "erdos-problem-1072",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:55:27+00:00",
    "updated_at": "2026-08-12T05:55:31+00:00"
  },
  "P10050": {
    "problem_number": 10050,
    "slug": "open-fc-e3005f7609d76a90d1c6-erdos-470-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:50+00:00",
    "updated_at": "2026-08-17T20:05:51+00:00"
  },
  "P9796": {
    "problem_number": 9796,
    "slug": "open-fc-de5c767c0a523a091e03-class-number-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:44+00:00",
    "updated_at": "2026-08-17T20:02:44+00:00"
  },
  "P8410": {
    "problem_number": 8410,
    "slug": "open-fc-2b6cfc962827e3689588-regularprime-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:00+00:00",
    "updated_at": "2026-08-17T18:50:08+00:00"
  },
  "P9696": {
    "problem_number": 9696,
    "slug": "open-fc-8e7b728e2bc6519c6b2e-infinite-safe-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:52+00:00",
    "updated_at": "2026-08-17T20:01:53+00:00"
  },
  "P8788": {
    "problem_number": 8788,
    "slug": "open-fc-690922f4c27948df089d-infinite-sexy-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:20:44+00:00",
    "updated_at": "2026-08-17T19:20:51+00:00"
  },
  "P9652": {
    "problem_number": 9652,
    "slug": "open-fc-4caae3880f54bd99c022-erdos-939-variants-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:32+00:00",
    "updated_at": "2026-08-17T20:00:33+00:00"
  },
  "P9290": {
    "problem_number": 9290,
    "slug": "open-fc-b36a946982deb97f1cf9-erdos-342-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:39+00:00",
    "updated_at": "2026-08-17T19:50:40+00:00"
  },
  "P9692": {
    "problem_number": 9692,
    "slug": "open-fc-87f453181cdc7bedeaa9-infinite-iswallsunsunprime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:50+00:00",
    "updated_at": "2026-08-17T20:01:51+00:00"
  },
  "P8832": {
    "problem_number": 8832,
    "slug": "open-fc-a1408baa6eb26d9802ae-wolstenholme-prime-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:55+00:00",
    "updated_at": "2026-08-17T19:25:01+00:00"
  },
  "P9458": {
    "problem_number": 9458,
    "slug": "open-fc-7bdf85e3f9b6372d9c8b-infinitely-many-woodall-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:56+00:00",
    "updated_at": "2026-08-17T19:53:57+00:00"
  },
  "P8952": {
    "problem_number": 8952,
    "slug": "open-fc-f9f401f0180595cf53d1-inscribed-rectangle-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:15+00:00",
    "updated_at": "2026-08-17T19:41:16+00:00"
  },
  "P8786": {
    "problem_number": 8786,
    "slug": "open-fc-66f2df4917c02d8fda86-mathoverflow-17560",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:20:35+00:00",
    "updated_at": "2026-08-17T19:20:41+00:00"
  },
  "P12033": {
    "problem_number": 12033,
    "slug": "integer-fixed-points-of-finite-collatz-instruction-words",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:54:06+00:00",
    "updated_at": "2026-09-01T18:54:16+00:00"
  },
  "P11594": {
    "problem_number": 11594,
    "slug": "integer-proximity-of-riemann-zeta-zero-ordinates",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:47+00:00",
    "updated_at": "2026-08-30T04:36:53+00:00"
  },
  "P11963": {
    "problem_number": 11963,
    "slug": "integer-return-under-the-4-3-ceiling-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:53:39+00:00",
    "updated_at": "2026-08-31T03:53:42+00:00"
  },
  "P10236": {
    "problem_number": 10236,
    "slug": "open-fc-e1f0e6381fc089babc22-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:57+00:00",
    "updated_at": "2026-08-18T02:51:58+00:00"
  },
  "P10148": {
    "problem_number": 10148,
    "slug": "open-fc-3887cb8ae56ff927cead-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:25+00:00",
    "updated_at": "2026-08-18T02:51:25+00:00"
  },
  "P10232": {
    "problem_number": 10232,
    "slug": "open-fc-d77b78fff9ca9368fd63-conjecture1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:56+00:00",
    "updated_at": "2026-08-18T02:51:56+00:00"
  },
  "P10192": {
    "problem_number": 10192,
    "slug": "open-fc-8e420d37c8939d343647-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:41+00:00",
    "updated_at": "2026-08-18T02:51:41+00:00"
  },
  "P12103": {
    "problem_number": 12103,
    "slug": "integral-exponential-transforms-of-shanks-s-array",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:11:27+00:00",
    "updated_at": "2026-09-01T19:11:32+00:00"
  },
  "P12091": {
    "problem_number": 12091,
    "slug": "integral-factorial-roots-of-exponential-generating-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:09:56+00:00",
    "updated_at": "2026-09-01T19:10:02+00:00"
  },
  "P3454": {
    "problem_number": 3454,
    "slug": "kourovka-21-70-integral-poincare-duality-from-duality-over-every-field",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:28+00:00",
    "updated_at": "2026-08-12T08:05:33+00:00"
  },
  "P12141": {
    "problem_number": 12141,
    "slug": "integral-supercongruence-families-from-multinomial-exponentials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:16:30+00:00",
    "updated_at": "2026-09-01T19:16:36+00:00"
  },
  "P2816": {
    "problem_number": 2816,
    "slug": "hypercube-rips-scale-four-torsion-free",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:13+00:00",
    "updated_at": "2026-07-30T02:26:13+00:00"
  },
  "P2904": {
    "problem_number": 2904,
    "slug": "lloyd-polynomial-integral-root-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:45:59+00:00",
    "updated_at": "2026-08-01T23:35:42+00:00"
  },
  "P12337": {
    "problem_number": 12337,
    "slug": "integrality-in-an-implicitly-defined-exponential-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:40:23+00:00",
    "updated_at": "2026-09-01T19:40:29+00:00"
  },
  "P12587": {
    "problem_number": 12587,
    "slug": "integrality-of-a-half-index-factorial-ratio",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:53:06+00:00",
    "updated_at": "2026-09-02T21:53:12+00:00"
  },
  "P12595": {
    "problem_number": 12595,
    "slug": "interval-closure-of-subset-product-p-adic-fibers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:54:25+00:00",
    "updated_at": "2026-09-02T21:54:32+00:00"
  },
  "P37": {
    "problem_number": 37,
    "slug": "inverse-galois-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:14:55+00:00"
  },
  "P3384": {
    "problem_number": 3384,
    "slug": "kourovka-21-20-involution-free-groups-of-finite-morley-rank-acting-irreducibly",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:55:13+00:00",
    "updated_at": "2026-08-12T07:55:30+00:00"
  },
  "P11590": {
    "problem_number": 11590,
    "slug": "irrationality-and-continued-fraction-aperiodicity-of-e-to-the-e-to-the-e",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:25+00:00",
    "updated_at": "2026-08-30T04:36:31+00:00"
  },
  "P8896": {
    "problem_number": 8896,
    "slug": "open-fc-cf315208bfcfd800335f-irrational-e-to-e",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:07+00:00",
    "updated_at": "2026-08-17T19:40:07+00:00"
  },
  "P9840": {
    "problem_number": 9840,
    "slug": "open-fc-fcaa1d2f1ab87eecc29f-erdos-260",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:07+00:00",
    "updated_at": "2026-08-17T20:03:08+00:00"
  },
  "P9110": {
    "problem_number": 9110,
    "slug": "open-fc-cbb37f53e4a6974f09ce-erdos-264-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:39+00:00",
    "updated_at": "2026-08-17T19:47:39+00:00"
  },
  "P8674": {
    "problem_number": 8674,
    "slug": "open-fc-31eebd388ad0eb81ddfc-irrational-odd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:31+00:00",
    "updated_at": "2026-08-17T19:04:34+00:00"
  },
  "P8136": {
    "problem_number": 8136,
    "slug": "open-fc-0589c5cd515d9ea19f19-erdos-267-variants-generalisation-ratio-limit-to-infinity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:01+00:00",
    "updated_at": "2026-08-17T18:35:02+00:00"
  },
  "P9872": {
    "problem_number": 9872,
    "slug": "open-fc-5bbfc736d390fa3a010c-erdos-257",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:09+00:00",
    "updated_at": "2026-08-17T20:04:10+00:00"
  },
  "P9256": {
    "problem_number": 9256,
    "slug": "open-fc-99eba9dc5780a963620a-irrational-catalanconstant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:26+00:00",
    "updated_at": "2026-08-17T19:50:26+00:00"
  },
  "P9366": {
    "problem_number": 9366,
    "slug": "open-fc-eed74adfa71f82d4d64a-erdos-252-variants-k-ge-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:11+00:00",
    "updated_at": "2026-08-17T19:51:12+00:00"
  },
  "P8604": {
    "problem_number": 8604,
    "slug": "open-fc-830497f052014aca1716-erdos-252",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:11+00:00",
    "updated_at": "2026-08-17T18:57:24+00:00"
  },
  "P3324": {
    "problem_number": 3324,
    "slug": "erdos-problem-252",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:05:57+00:00",
    "updated_at": "2026-08-12T06:06:07+00:00"
  },
  "P9694": {
    "problem_number": 9694,
    "slug": "open-fc-8b70919460cb6f09555d-erdos-249",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:51+00:00",
    "updated_at": "2026-08-17T20:01:52+00:00"
  },
  "P9072": {
    "problem_number": 9072,
    "slug": "open-fc-af608ac5f6a554153c0c-irrational-eulermascheroniconstant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:51+00:00",
    "updated_at": "2026-08-17T19:46:53+00:00"
  },
  "P3008": {
    "problem_number": 3008,
    "slug": "erdos-problem-68",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:30+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9184": {
    "problem_number": 9184,
    "slug": "open-fc-38024d3830a4127544dc-erdos-68",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:03+00:00",
    "updated_at": "2026-08-17T19:49:04+00:00"
  },
  "P9452": {
    "problem_number": 9452,
    "slug": "open-fc-7626fc521b8150d9ffbf-pi-pow-pi-pow-pi-pow-pi-not-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:46+00:00",
    "updated_at": "2026-08-17T19:53:48+00:00"
  },
  "P8464": {
    "problem_number": 8464,
    "slug": "open-fc-42f1d1ee110baf1dbe37-erdos-1049",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:12+00:00",
    "updated_at": "2026-08-17T18:52:13+00:00"
  },
  "P9338": {
    "problem_number": 9338,
    "slug": "open-fc-d9aa3fa0c8a90f855d58-erdos-168-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:01+00:00",
    "updated_at": "2026-08-17T19:51:01+00:00"
  },
  "P8446": {
    "problem_number": 8446,
    "slug": "open-fc-39692c3a869e9aad0559-irrational-ln-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:08+00:00",
    "updated_at": "2026-08-17T18:52:08+00:00"
  },
  "P9046": {
    "problem_number": 9046,
    "slug": "open-fc-9bc58392551f7af94b3a-erdos-269-variants-irrational",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:07+00:00",
    "updated_at": "2026-08-17T19:46:08+00:00"
  },
  "P9576": {
    "problem_number": 9576,
    "slug": "open-fc-d2d3d07f8a51480e2d24-erdos-251",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:50+00:00",
    "updated_at": "2026-08-17T19:55:52+00:00"
  },
  "P8344": {
    "problem_number": 8344,
    "slug": "open-fc-22617958cf2123852ab5-irrational-e-times-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:08+00:00",
    "updated_at": "2026-08-17T18:40:10+00:00"
  },
  "P9602": {
    "problem_number": 9602,
    "slug": "open-fc-e8ca6ee2affd4f50bea4-irrational-eleven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:45+00:00",
    "updated_at": "2026-08-17T19:56:47+00:00"
  },
  "P8362": {
    "problem_number": 8362,
    "slug": "open-fc-244cd0f43c37f73de60a-irrational-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:22+00:00",
    "updated_at": "2026-08-17T18:40:23+00:00"
  },
  "P9614": {
    "problem_number": 9614,
    "slug": "open-fc-f1cf774c856e8c7410a0-irrational-seven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:08+00:00",
    "updated_at": "2026-08-17T19:57:10+00:00"
  },
  "P9216": {
    "problem_number": 9216,
    "slug": "open-fc-6aace6cf8f615ff744a4-irrational-nine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:37+00:00",
    "updated_at": "2026-08-17T19:49:37+00:00"
  },
  "P8906": {
    "problem_number": 8906,
    "slug": "open-fc-d8f1660ff7dbff078fdb-erdos-263-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:11+00:00",
    "updated_at": "2026-08-17T19:40:11+00:00"
  },
  "P8564": {
    "problem_number": 8564,
    "slug": "open-fc-76bdde5c7c8e7e823078-irrational-e-plus-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:55+00:00",
    "updated_at": "2026-08-17T18:54:59+00:00"
  },
  "P9922": {
    "problem_number": 9922,
    "slug": "open-fc-821bb4aae2ee90497ec2-irrational-pi-to-e",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:34+00:00",
    "updated_at": "2026-08-17T20:04:34+00:00"
  },
  "P8400": {
    "problem_number": 8400,
    "slug": "open-fc-28f7219c4e8c152a5a16-irrational-pi-to-pi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:25+00:00",
    "updated_at": "2026-08-17T18:49:28+00:00"
  },
  "P9498": {
    "problem_number": 9498,
    "slug": "open-fc-994eecf96a8644e778a7-cuboidtwo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:27+00:00",
    "updated_at": "2026-08-17T19:54:27+00:00"
  },
  "P9014": {
    "problem_number": 9014,
    "slug": "open-fc-8423a1c4ddd284cf2103-cuboidthree",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:04+00:00",
    "updated_at": "2026-08-17T19:45:06+00:00"
  },
  "P2846": {
    "problem_number": 2846,
    "slug": "random-littlewood-irreducibility-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:38:11+00:00",
    "updated_at": "2026-08-01T12:26:54+00:00"
  },
  "P3382": {
    "problem_number": 3382,
    "slug": "kourovka-21-19-irreducible-actions-on-simple-groups-of-finite-morley-rank",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:55:04+00:00",
    "updated_at": "2026-08-12T07:55:11+00:00"
  },
  "P3386": {
    "problem_number": 3386,
    "slug": "kourovka-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:55:46+00:00",
    "updated_at": "2026-08-12T07:56:05+00:00"
  },
  "P12565": {
    "problem_number": 12565,
    "slug": "irreducible-characteristic-polynomials-of-skew-band-matrices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:49:27+00:00",
    "updated_at": "2026-09-02T22:24:41+00:00"
  },
  "P12647": {
    "problem_number": 12647,
    "slug": "is-1-eventually-the-most-frequent-prime-midpoint-offset",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:41+00:00",
    "updated_at": "2026-09-02T22:07:46+00:00"
  },
  "P12701": {
    "problem_number": 12701,
    "slug": "is-10-d-d-10-the-largest-d-digit-power-difference-for-every-d-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:21:23+00:00",
    "updated_at": "2026-09-02T22:21:55+00:00"
  },
  "P11168": {
    "problem_number": 11168,
    "slug": "oeis-a051952-130-largest-three-positive-squares-exception",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:21:10+00:00",
    "updated_at": "2026-08-29T18:48:36+00:00"
  },
  "P12005": {
    "problem_number": 12005,
    "slug": "is-26471-the-last-exception-to-a-2-b-3-c-4-d-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:37:45+00:00",
    "updated_at": "2026-09-01T18:38:21+00:00"
  },
  "P11368": {
    "problem_number": 11368,
    "slug": "riesel-status-of-two-to-128-minus-two-to-18-minus-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:39:37+00:00",
    "updated_at": "2026-08-29T18:51:55+00:00"
  },
  "P11298": {
    "problem_number": 11298,
    "slug": "power-of-two-minus-every-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:23:27+00:00",
    "updated_at": "2026-08-29T18:50:44+00:00"
  },
  "P11370": {
    "problem_number": 11370,
    "slug": "three-five-exponential-square-minus-one-divisibility",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:40:00+00:00",
    "updated_at": "2026-08-29T18:51:56+00:00"
  },
  "P11943": {
    "problem_number": 11943,
    "slug": "is-3291-the-longest-nonzero-run-in-the-reset-process",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:31:56+00:00",
    "updated_at": "2026-08-30T16:32:20+00:00"
  },
  "P11410": {
    "problem_number": 11410,
    "slug": "associative-order-seven-magic-square-water-retention",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:50:58+00:00",
    "updated_at": "2026-08-29T18:52:38+00:00"
  },
  "P11534": {
    "problem_number": 11534,
    "slug": "nested-gcd-sequence-omits-only-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:51:59+00:00",
    "updated_at": "2026-08-29T18:54:22+00:00"
  },
  "P11202": {
    "problem_number": 11202,
    "slug": "minimum-gap-even-base-two-pseudoprimes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:50:00+00:00",
    "updated_at": "2026-08-29T18:49:06+00:00"
  },
  "P11308": {
    "problem_number": 11308,
    "slug": "is-564-a-sociable-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:13:59+00:00",
    "updated_at": "2026-08-29T18:50:56+00:00"
  },
  "P11770": {
    "problem_number": 11770,
    "slug": "is-6-a-difference-of-two-perfect-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:24:37+00:00",
    "updated_at": "2026-08-30T12:24:53+00:00"
  },
  "P12001": {
    "problem_number": 12001,
    "slug": "is-78557-the-smallest-sierpinski-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:33:48+00:00",
    "updated_at": "2026-09-01T18:34:09+00:00"
  },
  "P11206": {
    "problem_number": 11206,
    "slug": "largest-zero-free-decimal-power-of-two-exponent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:51:00+00:00",
    "updated_at": "2026-08-29T18:49:09+00:00"
  },
  "P12775": {
    "problem_number": 12775,
    "slug": "is-a-fibonacci-product-a-perfect-power-only-at-3-6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:53:21+00:00",
    "updated_at": "2026-09-02T22:53:58+00:00"
  },
  "P11288": {
    "problem_number": 11288,
    "slug": "prime-two-power-exponent-sum-of-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:20:31+00:00",
    "updated_at": "2026-08-29T18:50:34+00:00"
  },
  "P11238": {
    "problem_number": 11238,
    "slug": "irrationality-and-nonquadraticity-of-e-to-e",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:01:43+00:00",
    "updated_at": "2026-08-29T18:49:41+00:00"
  },
  "P11999": {
    "problem_number": 11999,
    "slug": "is-euler-s-constant-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:33:30+00:00",
    "updated_at": "2026-09-01T18:33:53+00:00"
  },
  "P11250": {
    "problem_number": 11250,
    "slug": "squared-factorial-least-prime-gap-always-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:05:07+00:00",
    "updated_at": "2026-08-29T18:49:55+00:00"
  },
  "P11240": {
    "problem_number": 11240,
    "slug": "nonunitary-perfect-number-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:02:07+00:00",
    "updated_at": "2026-08-29T18:49:44+00:00"
  },
  "P11550": {
    "problem_number": 11550,
    "slug": "triangular-product-least-prime-offset-always-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:02:23+00:00",
    "updated_at": "2026-08-29T18:54:33+00:00"
  },
  "P11272": {
    "problem_number": 11272,
    "slug": "universal-compositeness-consecutive-products-plus-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:12:33+00:00",
    "updated_at": "2026-08-29T18:50:18+00:00"
  },
  "P3112": {
    "problem_number": 3112,
    "slug": "graph-isomorphism-in-p",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:03+00:00",
    "updated_at": "2026-08-02T12:51:40+00:00"
  },
  "P3090": {
    "problem_number": 3090,
    "slug": "deterministic-logspace-versus-nondeterministic-logspace",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:58+00:00",
    "updated_at": "2026-08-02T12:48:27+00:00"
  },
  "P11338": {
    "problem_number": 11338,
    "slug": "squarefreeness-of-n-times-factorial-plus-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:27:45+00:00",
    "updated_at": "2026-08-29T18:51:29+00:00"
  },
  "P12259": {
    "problem_number": 12259,
    "slug": "is-one-the-only-square-passing-a-shifted-prime-divisor-test",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:31:00+00:00",
    "updated_at": "2026-09-01T19:31:05+00:00"
  },
  "P3078": {
    "problem_number": 3078,
    "slug": "bpp-equals-p",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:55+00:00",
    "updated_at": "2026-08-02T12:47:43+00:00"
  },
  "P11264": {
    "problem_number": 11264,
    "slug": "boundedness-of-seven-free-fibonacci-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:08:59+00:00",
    "updated_at": "2026-08-29T18:50:11+00:00"
  },
  "P11434": {
    "problem_number": 11434,
    "slug": "a278813-boundary-constant-transcendence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:58:39+00:00",
    "updated_at": "2026-08-29T18:52:55+00:00"
  },
  "P11310": {
    "problem_number": 11310,
    "slug": "aliquot-orbit-276-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:14:28+00:00",
    "updated_at": "2026-08-29T18:50:59+00:00"
  },
  "P11542": {
    "problem_number": 11542,
    "slug": "factorial-final-digit-balanced-bases-sufficiency",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:57:04+00:00",
    "updated_at": "2026-08-29T18:54:28+00:00"
  },
  "P11300": {
    "problem_number": 11300,
    "slug": "classification-of-the-double-mersenne-number-at-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:24:44+00:00",
    "updated_at": "2026-08-29T18:50:47+00:00"
  },
  "P12737": {
    "problem_number": 12737,
    "slug": "is-the-eta-sequence-the-continued-fraction-of-the-wythoff-orbit-supremum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:36:23+00:00",
    "updated_at": "2026-09-02T22:37:04+00:00"
  },
  "P11200": {
    "problem_number": 11200,
    "slug": "feigenbaum-delta-transcendence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:49:32+00:00",
    "updated_at": "2026-08-29T18:49:02+00:00"
  },
  "P11192": {
    "problem_number": 11192,
    "slug": "compositeness-of-fermat-number-f-65536",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:47:47+00:00",
    "updated_at": "2026-08-29T18:48:55+00:00"
  },
  "P11632": {
    "problem_number": 11632,
    "slug": "is-the-gap-free-prime-frequency-sequence-a-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:41:14+00:00",
    "updated_at": "2026-08-30T04:41:25+00:00"
  },
  "P11494": {
    "problem_number": 11494,
    "slug": "greatest-prime-factor-orbit-unboundedness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:26:45+00:00",
    "updated_at": "2026-08-29T18:53:52+00:00"
  },
  "P11496": {
    "problem_number": 11496,
    "slug": "greedy-prime-compatibility-infinitude",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:27:14+00:00",
    "updated_at": "2026-08-29T18:53:53+00:00"
  },
  "P11468": {
    "problem_number": 11468,
    "slug": "greedy-unused-square-gap-strict-increase",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:13:02+00:00",
    "updated_at": "2026-08-29T18:53:33+00:00"
  },
  "P11556": {
    "problem_number": 11556,
    "slug": "octal-game-007-eventual-periodicity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:04:30+00:00",
    "updated_at": "2026-08-29T18:54:38+00:00"
  },
  "P11538": {
    "problem_number": 11538,
    "slug": "guarded-greedy-gcd-sequence-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:54:57+00:00",
    "updated_at": "2026-08-29T18:54:24+00:00"
  },
  "P11362": {
    "problem_number": 11362,
    "slug": "height-four-power-tower-root-two-rationality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:38:27+00:00",
    "updated_at": "2026-08-29T18:51:50+00:00"
  },
  "P11486": {
    "problem_number": 11486,
    "slug": "isolated-term-prime-power-in-four-term-gcd-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:21:44+00:00",
    "updated_at": "2026-08-29T18:53:46+00:00"
  },
  "P11318": {
    "problem_number": 11318,
    "slug": "prime-composite-rank-permutation-orbit-ten-infinite",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:19:50+00:00",
    "updated_at": "2026-08-29T18:51:07+00:00"
  },
  "P11282": {
    "problem_number": 11282,
    "slug": "prime-position-digit-selection-from-e-arithmetic-nature",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:17:26+00:00",
    "updated_at": "2026-08-29T18:50:28+00:00"
  },
  "P11314": {
    "problem_number": 11314,
    "slug": "optional-letter-nfa-recursive-transition-optimality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:17:07+00:00",
    "updated_at": "2026-08-29T18:51:03+00:00"
  },
  "P11396": {
    "problem_number": 11396,
    "slug": "semiprime-partial-sum-greedy-sequence-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:46:59+00:00",
    "updated_at": "2026-08-29T18:52:23+00:00"
  },
  "P12373": {
    "problem_number": 12373,
    "slug": "is-the-square-root-of-two-normal-in-base-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:44:53+00:00",
    "updated_at": "2026-09-01T19:44:59+00:00"
  },
  "P11470": {
    "problem_number": 11470,
    "slug": "transcendence-square-factorial-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:13:28+00:00",
    "updated_at": "2026-08-29T18:53:35+00:00"
  },
  "P11518": {
    "problem_number": 11518,
    "slug": "irrationality-of-the-stribolic-constant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:43:23+00:00",
    "updated_at": "2026-08-29T18:54:10+00:00"
  },
  "P11458": {
    "problem_number": 11458,
    "slug": "d-finiteness-of-three-dimensional-kreweras-excursions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:08:05+00:00",
    "updated_at": "2026-08-29T18:53:23+00:00"
  },
  "P11416": {
    "problem_number": 11416,
    "slug": "two-fake-coins-information-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:53:07+00:00",
    "updated_at": "2026-08-29T18:52:42+00:00"
  },
  "P11228": {
    "problem_number": 11228,
    "slug": "two-generator-free-burnside-group-exponent-five-finiteness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:57:40+00:00",
    "updated_at": "2026-08-29T18:49:31+00:00"
  },
  "P11182": {
    "problem_number": 11182,
    "slug": "prime-between-consecutive-triangular-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:45:40+00:00",
    "updated_at": "2026-08-29T18:48:46+00:00"
  },
  "P3144": {
    "problem_number": 3144,
    "slug": "truly-subcubic-apsp",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:10+00:00",
    "updated_at": "2026-08-02T12:56:51+00:00"
  },
  "P11334": {
    "problem_number": 11334,
    "slug": "another-smarandache-friendly-prime-pair",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:25:48+00:00",
    "updated_at": "2026-08-29T18:51:25+00:00"
  },
  "P11226": {
    "problem_number": 11226,
    "slug": "reciprocal-binomial-numerator-large-square-prime-divisor",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:57:10+00:00",
    "updated_at": "2026-08-29T18:49:29+00:00"
  },
  "P3146": {
    "problem_number": 3146,
    "slug": "vp-versus-vnp",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:11+00:00",
    "updated_at": "2026-08-02T12:57:13+00:00"
  },
  "P3254": {
    "problem_number": 3254,
    "slug": "erdos-problem-409",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:23+00:00",
    "updated_at": "2026-08-12T05:58:33+00:00"
  },
  "P8384": {
    "problem_number": 8384,
    "slug": "open-fc-274d60f5906bc18a696d-erdos-409-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:56+00:00",
    "updated_at": "2026-08-17T18:48:58+00:00"
  },
  "P12205": {
    "problem_number": 12205,
    "slug": "joining-the-four-digit-sum-trajectories",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:24:20+00:00",
    "updated_at": "2026-09-01T19:24:26+00:00"
  },
  "P3504": {
    "problem_number": 3504,
    "slug": "kourovka-21-121-jordan-properties-at-a-fixed-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:09:26+00:00",
    "updated_at": "2026-08-12T08:09:46+00:00"
  },
  "P30": {
    "problem_number": 30,
    "slug": "kakeya-conjecture-in-dimensions-at-least-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:15:22+00:00"
  },
  "P50": {
    "problem_number": 50,
    "slug": "kaplansky-zero-divisor-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:15:45+00:00"
  },
  "P8386": {
    "problem_number": 8386,
    "slug": "open-fc-276a5b1c78b5bba206ac-idempotent-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:59+00:00",
    "updated_at": "2026-08-17T18:49:02+00:00"
  },
  "P2862": {
    "problem_number": 2862,
    "slug": "kaplansky-sixth-semisimple-hopf",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:40:20+00:00",
    "updated_at": "2026-08-01T23:31:19+00:00"
  },
  "P8806": {
    "problem_number": 8806,
    "slug": "open-fc-8d647eba0a480665d725-zero-divisor-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:22:50+00:00",
    "updated_at": "2026-08-17T19:22:59+00:00"
  },
  "P3114": {
    "problem_number": 3114,
    "slug": "kashaev-volume-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:03+00:00",
    "updated_at": "2026-08-02T12:51:56+00:00"
  },
  "P10866": {
    "problem_number": 10866,
    "slug": "unsolvedmath-2671-kirby-problem-1-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:31+00:00",
    "updated_at": "2026-08-18T02:58:34+00:00"
  },
  "P10906": {
    "problem_number": 10906,
    "slug": "unsolvedmath-2672-kirby-problem-1-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:18+00:00",
    "updated_at": "2026-08-18T02:59:20+00:00"
  },
  "P10822": {
    "problem_number": 10822,
    "slug": "unsolvedmath-2674-kirby-problem-1-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:02+00:00",
    "updated_at": "2026-08-18T02:56:07+00:00"
  },
  "P11058": {
    "problem_number": 11058,
    "slug": "unsolvedmath-2675-kirby-problem-1-16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:15+00:00",
    "updated_at": "2026-08-18T03:02:17+00:00"
  },
  "P10784": {
    "problem_number": 10784,
    "slug": "unsolvedmath-2677-kirby-problem-1-18",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:13+00:00",
    "updated_at": "2026-08-18T02:55:14+00:00"
  },
  "P11004": {
    "problem_number": 11004,
    "slug": "unsolvedmath-2678-kirby-problem-1-19",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:13+00:00",
    "updated_at": "2026-08-18T03:01:15+00:00"
  },
  "P11028": {
    "problem_number": 11028,
    "slug": "unsolvedmath-2661-kirby-problem-1-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:41+00:00",
    "updated_at": "2026-08-18T03:01:41+00:00"
  },
  "P10898": {
    "problem_number": 10898,
    "slug": "unsolvedmath-2679-kirby-problem-1-20",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:09+00:00",
    "updated_at": "2026-08-18T02:59:10+00:00"
  },
  "P10826": {
    "problem_number": 10826,
    "slug": "unsolvedmath-2680-kirby-problem-1-21",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:15+00:00",
    "updated_at": "2026-08-18T02:56:20+00:00"
  },
  "P10914": {
    "problem_number": 10914,
    "slug": "unsolvedmath-2684-kirby-problem-1-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:29+00:00",
    "updated_at": "2026-08-18T02:59:31+00:00"
  },
  "P11018": {
    "problem_number": 11018,
    "slug": "unsolvedmath-2685-kirby-problem-1-26",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:29+00:00",
    "updated_at": "2026-08-18T03:01:31+00:00"
  },
  "P11038": {
    "problem_number": 11038,
    "slug": "unsolvedmath-2687-kirby-problem-1-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:55+00:00",
    "updated_at": "2026-08-18T03:01:56+00:00"
  },
  "P10970": {
    "problem_number": 10970,
    "slug": "unsolvedmath-2688-kirby-problem-1-29",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:33+00:00",
    "updated_at": "2026-08-18T03:00:34+00:00"
  },
  "P10910": {
    "problem_number": 10910,
    "slug": "unsolvedmath-2691-kirby-problem-1-32",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:24+00:00",
    "updated_at": "2026-08-18T02:59:26+00:00"
  },
  "P10918": {
    "problem_number": 10918,
    "slug": "unsolvedmath-2696-kirby-problem-1-37",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:33+00:00",
    "updated_at": "2026-08-18T02:59:35+00:00"
  },
  "P10886": {
    "problem_number": 10886,
    "slug": "unsolvedmath-2697-kirby-problem-1-38",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:56+00:00",
    "updated_at": "2026-08-18T02:58:58+00:00"
  },
  "P10790": {
    "problem_number": 10790,
    "slug": "unsolvedmath-2699-kirby-problem-1-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:15+00:00",
    "updated_at": "2026-08-18T02:55:16+00:00"
  },
  "P10978": {
    "problem_number": 10978,
    "slug": "unsolvedmath-2700-kirby-problem-1-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:42+00:00",
    "updated_at": "2026-08-18T03:00:43+00:00"
  },
  "P10956": {
    "problem_number": 10956,
    "slug": "unsolvedmath-2704-kirby-problem-1-45",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:16+00:00",
    "updated_at": "2026-08-18T03:00:17+00:00"
  },
  "P10874": {
    "problem_number": 10874,
    "slug": "unsolvedmath-2706-kirby-problem-1-47",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:46+00:00",
    "updated_at": "2026-08-18T02:58:47+00:00"
  },
  "P10988": {
    "problem_number": 10988,
    "slug": "unsolvedmath-2707-kirby-problem-1-48",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:55+00:00",
    "updated_at": "2026-08-18T03:00:57+00:00"
  },
  "P10924": {
    "problem_number": 10924,
    "slug": "unsolvedmath-2708-kirby-problem-1-49",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:40+00:00",
    "updated_at": "2026-08-18T02:59:42+00:00"
  },
  "P10954": {
    "problem_number": 10954,
    "slug": "unsolvedmath-2664-kirby-problem-1-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:13+00:00",
    "updated_at": "2026-08-18T03:00:15+00:00"
  },
  "P10980": {
    "problem_number": 10980,
    "slug": "unsolvedmath-2713-kirby-problem-1-54",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:44+00:00",
    "updated_at": "2026-08-18T03:00:46+00:00"
  },
  "P10934": {
    "problem_number": 10934,
    "slug": "unsolvedmath-2714-kirby-problem-1-55",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:51+00:00",
    "updated_at": "2026-08-18T02:59:53+00:00"
  },
  "P10878": {
    "problem_number": 10878,
    "slug": "unsolvedmath-2717-kirby-problem-1-58",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:48+00:00",
    "updated_at": "2026-08-18T02:58:49+00:00"
  },
  "P10922": {
    "problem_number": 10922,
    "slug": "unsolvedmath-2718-kirby-problem-1-59",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:38+00:00",
    "updated_at": "2026-08-18T02:59:39+00:00"
  },
  "P10802": {
    "problem_number": 10802,
    "slug": "unsolvedmath-2720-kirby-problem-1-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:19+00:00",
    "updated_at": "2026-08-18T02:55:19+00:00"
  },
  "P10958": {
    "problem_number": 10958,
    "slug": "unsolvedmath-2723-kirby-problem-1-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:18+00:00",
    "updated_at": "2026-08-18T03:00:20+00:00"
  },
  "P11000": {
    "problem_number": 11000,
    "slug": "unsolvedmath-2724-kirby-problem-1-65",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:09+00:00",
    "updated_at": "2026-08-18T03:01:09+00:00"
  },
  "P11072": {
    "problem_number": 11072,
    "slug": "unsolvedmath-2725-kirby-problem-1-66",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:30+00:00",
    "updated_at": "2026-08-18T03:02:31+00:00"
  },
  "P11016": {
    "problem_number": 11016,
    "slug": "unsolvedmath-2666-kirby-problem-1-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:27+00:00",
    "updated_at": "2026-08-18T03:01:28+00:00"
  },
  "P11032": {
    "problem_number": 11032,
    "slug": "unsolvedmath-2729-kirby-problem-1-70",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:45+00:00",
    "updated_at": "2026-08-18T03:01:47+00:00"
  },
  "P10976": {
    "problem_number": 10976,
    "slug": "unsolvedmath-2733-kirby-problem-1-74",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:40+00:00",
    "updated_at": "2026-08-18T03:00:41+00:00"
  },
  "P11064": {
    "problem_number": 11064,
    "slug": "unsolvedmath-2734-kirby-problem-1-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:22+00:00",
    "updated_at": "2026-08-18T03:02:24+00:00"
  },
  "P10974": {
    "problem_number": 10974,
    "slug": "unsolvedmath-2737-kirby-problem-1-78",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:38+00:00",
    "updated_at": "2026-08-18T03:00:39+00:00"
  },
  "P10948": {
    "problem_number": 10948,
    "slug": "unsolvedmath-2744-kirby-problem-1-85",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:07+00:00",
    "updated_at": "2026-08-18T03:00:08+00:00"
  },
  "P10968": {
    "problem_number": 10968,
    "slug": "unsolvedmath-2748-kirby-problem-1-89",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:31+00:00",
    "updated_at": "2026-08-18T03:00:32+00:00"
  },
  "P11052": {
    "problem_number": 11052,
    "slug": "unsolvedmath-2760-kirby-problem-2-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:08+00:00",
    "updated_at": "2026-08-18T03:02:10+00:00"
  },
  "P10854": {
    "problem_number": 10854,
    "slug": "unsolvedmath-2762-kirby-problem-2-14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:52+00:00",
    "updated_at": "2026-08-18T02:57:57+00:00"
  },
  "P11080": {
    "problem_number": 11080,
    "slug": "unsolvedmath-2773-kirby-problem-2-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:39+00:00",
    "updated_at": "2026-08-18T03:02:41+00:00"
  },
  "P10938": {
    "problem_number": 10938,
    "slug": "unsolvedmath-2774-kirby-problem-2-26",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:56+00:00",
    "updated_at": "2026-08-18T02:59:57+00:00"
  },
  "P11060": {
    "problem_number": 11060,
    "slug": "unsolvedmath-2776-kirby-problem-2-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:17+00:00",
    "updated_at": "2026-08-18T03:02:19+00:00"
  },
  "P11040": {
    "problem_number": 11040,
    "slug": "unsolvedmath-2752-kirby-problem-2-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:57+00:00",
    "updated_at": "2026-08-18T03:01:58+00:00"
  },
  "P10796": {
    "problem_number": 10796,
    "slug": "unsolvedmath-2788-kirby-problem-2-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:17+00:00",
    "updated_at": "2026-08-18T02:55:18+00:00"
  },
  "P10776": {
    "problem_number": 10776,
    "slug": "unsolvedmath-2791-kirby-problem-2-43",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:11+00:00",
    "updated_at": "2026-08-18T02:55:11+00:00"
  },
  "P11074": {
    "problem_number": 11074,
    "slug": "unsolvedmath-2792-kirby-problem-2-44",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:32+00:00",
    "updated_at": "2026-08-18T03:02:34+00:00"
  },
  "P11088": {
    "problem_number": 11088,
    "slug": "unsolvedmath-2794-kirby-problem-2-46",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:03:17+00:00",
    "updated_at": "2026-08-18T03:03:27+00:00"
  },
  "P10768": {
    "problem_number": 10768,
    "slug": "unsolvedmath-2795-kirby-problem-2-47",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:08+00:00",
    "updated_at": "2026-08-18T02:55:09+00:00"
  },
  "P10838": {
    "problem_number": 10838,
    "slug": "unsolvedmath-2796-kirby-problem-2-48",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:57+00:00",
    "updated_at": "2026-08-18T02:57:01+00:00"
  },
  "P11022": {
    "problem_number": 11022,
    "slug": "unsolvedmath-2797-kirby-problem-2-49",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:34+00:00",
    "updated_at": "2026-08-18T03:01:36+00:00"
  },
  "P10862": {
    "problem_number": 10862,
    "slug": "unsolvedmath-2798-kirby-problem-2-50",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:19+00:00",
    "updated_at": "2026-08-18T02:58:23+00:00"
  },
  "P10932": {
    "problem_number": 10932,
    "slug": "unsolvedmath-2754-kirby-problem-2-6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:49+00:00",
    "updated_at": "2026-08-18T02:59:50+00:00"
  },
  "P10946": {
    "problem_number": 10946,
    "slug": "unsolvedmath-2799-kirby-problem-3-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:04+00:00",
    "updated_at": "2026-08-18T03:00:06+00:00"
  },
  "P10908": {
    "problem_number": 10908,
    "slug": "unsolvedmath-2810-kirby-problem-3-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:21+00:00",
    "updated_at": "2026-08-18T02:59:23+00:00"
  },
  "P10990": {
    "problem_number": 10990,
    "slug": "unsolvedmath-2811-kirby-problem-3-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:58+00:00",
    "updated_at": "2026-08-18T03:00:59+00:00"
  },
  "P10916": {
    "problem_number": 10916,
    "slug": "unsolvedmath-2813-kirby-problem-3-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:32+00:00",
    "updated_at": "2026-08-18T02:59:33+00:00"
  },
  "P10944": {
    "problem_number": 10944,
    "slug": "unsolvedmath-2817-kirby-problem-3-19",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:03+00:00",
    "updated_at": "2026-08-18T03:00:04+00:00"
  },
  "P11070": {
    "problem_number": 11070,
    "slug": "unsolvedmath-2822-kirby-problem-3-24",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:29+00:00",
    "updated_at": "2026-08-18T03:02:30+00:00"
  },
  "P11062": {
    "problem_number": 11062,
    "slug": "unsolvedmath-2824-kirby-problem-3-26",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:19+00:00",
    "updated_at": "2026-08-18T03:02:21+00:00"
  },
  "P10950": {
    "problem_number": 10950,
    "slug": "unsolvedmath-2827-kirby-problem-3-29",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:09+00:00",
    "updated_at": "2026-08-18T03:00:10+00:00"
  },
  "P10882": {
    "problem_number": 10882,
    "slug": "unsolvedmath-2833-kirby-problem-3-35",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:52+00:00",
    "updated_at": "2026-08-18T02:58:53+00:00"
  },
  "P10960": {
    "problem_number": 10960,
    "slug": "unsolvedmath-2837-kirby-problem-3-39",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:20+00:00",
    "updated_at": "2026-08-18T03:00:22+00:00"
  },
  "P10936": {
    "problem_number": 10936,
    "slug": "unsolvedmath-2802-kirby-problem-3-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:54+00:00",
    "updated_at": "2026-08-18T02:59:55+00:00"
  },
  "P11044": {
    "problem_number": 11044,
    "slug": "unsolvedmath-2852-kirby-problem-3-54",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:01+00:00",
    "updated_at": "2026-08-18T03:02:03+00:00"
  },
  "P11086": {
    "problem_number": 11086,
    "slug": "unsolvedmath-2853-kirby-problem-3-55",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:03:03+00:00",
    "updated_at": "2026-08-18T03:03:12+00:00"
  },
  "P10964": {
    "problem_number": 10964,
    "slug": "unsolvedmath-2854-kirby-problem-3-56",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:26+00:00",
    "updated_at": "2026-08-18T03:00:28+00:00"
  },
  "P11012": {
    "problem_number": 11012,
    "slug": "unsolvedmath-2804-kirby-problem-3-6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:22+00:00",
    "updated_at": "2026-08-18T03:01:22+00:00"
  },
  "P10984": {
    "problem_number": 10984,
    "slug": "unsolvedmath-2860-kirby-problem-3-62",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:49+00:00",
    "updated_at": "2026-08-18T03:00:52+00:00"
  },
  "P11024": {
    "problem_number": 11024,
    "slug": "unsolvedmath-2862-kirby-problem-3-64",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:37+00:00",
    "updated_at": "2026-08-18T03:01:38+00:00"
  },
  "P11020": {
    "problem_number": 11020,
    "slug": "unsolvedmath-2863-kirby-problem-3-65",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:31+00:00",
    "updated_at": "2026-08-18T03:01:33+00:00"
  },
  "P10926": {
    "problem_number": 10926,
    "slug": "unsolvedmath-2864-kirby-problem-3-66",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:42+00:00",
    "updated_at": "2026-08-18T02:59:44+00:00"
  },
  "P10928": {
    "problem_number": 10928,
    "slug": "unsolvedmath-2867-kirby-problem-3-69",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:45+00:00",
    "updated_at": "2026-08-18T02:59:46+00:00"
  },
  "P11042": {
    "problem_number": 11042,
    "slug": "unsolvedmath-2869-kirby-problem-3-71",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:59+00:00",
    "updated_at": "2026-08-18T03:02:01+00:00"
  },
  "P10920": {
    "problem_number": 10920,
    "slug": "unsolvedmath-2872-kirby-problem-3-74",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:36+00:00",
    "updated_at": "2026-08-18T02:59:37+00:00"
  },
  "P10902": {
    "problem_number": 10902,
    "slug": "unsolvedmath-2873-kirby-problem-3-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:13+00:00",
    "updated_at": "2026-08-18T02:59:15+00:00"
  },
  "P11082": {
    "problem_number": 11082,
    "slug": "unsolvedmath-2886-kirby-problem-4-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:42+00:00",
    "updated_at": "2026-08-18T03:02:46+00:00"
  },
  "P11046": {
    "problem_number": 11046,
    "slug": "unsolvedmath-2976-kirby-problem-4-100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:03+00:00",
    "updated_at": "2026-08-18T03:02:04+00:00"
  },
  "P10940": {
    "problem_number": 10940,
    "slug": "unsolvedmath-2978-kirby-problem-4-102",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:58+00:00",
    "updated_at": "2026-08-18T02:59:59+00:00"
  },
  "P11066": {
    "problem_number": 11066,
    "slug": "unsolvedmath-2980-kirby-problem-4-104",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:25+00:00",
    "updated_at": "2026-08-18T03:02:26+00:00"
  },
  "P10894": {
    "problem_number": 10894,
    "slug": "unsolvedmath-2983-kirby-problem-4-107",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:05+00:00",
    "updated_at": "2026-08-18T02:59:05+00:00"
  },
  "P10808": {
    "problem_number": 10808,
    "slug": "unsolvedmath-2984-kirby-problem-4-108",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:21+00:00",
    "updated_at": "2026-08-18T02:55:21+00:00"
  },
  "P10930": {
    "problem_number": 10930,
    "slug": "unsolvedmath-2887-kirby-problem-4-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:47+00:00",
    "updated_at": "2026-08-18T02:59:48+00:00"
  },
  "P10996": {
    "problem_number": 10996,
    "slug": "unsolvedmath-2990-kirby-problem-4-114",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:04+00:00",
    "updated_at": "2026-08-18T03:01:06+00:00"
  },
  "P10814": {
    "problem_number": 10814,
    "slug": "unsolvedmath-2888-kirby-problem-4-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:35+00:00",
    "updated_at": "2026-08-18T02:55:40+00:00"
  },
  "P10904": {
    "problem_number": 10904,
    "slug": "unsolvedmath-3004-kirby-problem-4-128",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:16+00:00",
    "updated_at": "2026-08-18T02:59:18+00:00"
  },
  "P10900": {
    "problem_number": 10900,
    "slug": "unsolvedmath-3005-kirby-problem-4-129",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:11+00:00",
    "updated_at": "2026-08-18T02:59:13+00:00"
  },
  "P10890": {
    "problem_number": 10890,
    "slug": "unsolvedmath-3007-kirby-problem-4-131",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:00+00:00",
    "updated_at": "2026-08-18T02:59:02+00:00"
  },
  "P11034": {
    "problem_number": 11034,
    "slug": "unsolvedmath-2890-kirby-problem-4-14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:49+00:00",
    "updated_at": "2026-08-18T03:01:51+00:00"
  },
  "P10982": {
    "problem_number": 10982,
    "slug": "unsolvedmath-2898-kirby-problem-4-22",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:47+00:00",
    "updated_at": "2026-08-18T03:00:48+00:00"
  },
  "P11014": {
    "problem_number": 11014,
    "slug": "unsolvedmath-2900-kirby-problem-4-24",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:24+00:00",
    "updated_at": "2026-08-18T03:01:26+00:00"
  },
  "P10818": {
    "problem_number": 10818,
    "slug": "unsolvedmath-2904-kirby-problem-4-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:49+00:00",
    "updated_at": "2026-08-18T02:55:52+00:00"
  },
  "P11078": {
    "problem_number": 11078,
    "slug": "unsolvedmath-2905-kirby-problem-4-29",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:37+00:00",
    "updated_at": "2026-08-18T03:02:39+00:00"
  },
  "P10992": {
    "problem_number": 10992,
    "slug": "unsolvedmath-2879-kirby-problem-4-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:00+00:00",
    "updated_at": "2026-08-18T03:01:01+00:00"
  },
  "P10962": {
    "problem_number": 10962,
    "slug": "unsolvedmath-2909-kirby-problem-4-33",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:24+00:00",
    "updated_at": "2026-08-18T03:00:26+00:00"
  },
  "P11054": {
    "problem_number": 11054,
    "slug": "unsolvedmath-2911-kirby-problem-4-35",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:12+00:00",
    "updated_at": "2026-08-18T03:02:13+00:00"
  },
  "P11006": {
    "problem_number": 11006,
    "slug": "unsolvedmath-2915-kirby-problem-4-39",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:15+00:00",
    "updated_at": "2026-08-18T03:01:17+00:00"
  },
  "P11026": {
    "problem_number": 11026,
    "slug": "unsolvedmath-2917-kirby-problem-4-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:38+00:00",
    "updated_at": "2026-08-18T03:01:40+00:00"
  },
  "P10972": {
    "problem_number": 10972,
    "slug": "unsolvedmath-2918-kirby-problem-4-42",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:35+00:00",
    "updated_at": "2026-08-18T03:00:37+00:00"
  },
  "P11030": {
    "problem_number": 11030,
    "slug": "unsolvedmath-2919-kirby-problem-4-43",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:42+00:00",
    "updated_at": "2026-08-18T03:01:43+00:00"
  },
  "P10842": {
    "problem_number": 10842,
    "slug": "unsolvedmath-2920-kirby-problem-4-44",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:10+00:00",
    "updated_at": "2026-08-18T02:57:15+00:00"
  },
  "P10850": {
    "problem_number": 10850,
    "slug": "unsolvedmath-2921-kirby-problem-4-45",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:38+00:00",
    "updated_at": "2026-08-18T02:57:42+00:00"
  },
  "P10994": {
    "problem_number": 10994,
    "slug": "unsolvedmath-2928-kirby-problem-4-52",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:02+00:00",
    "updated_at": "2026-08-18T03:01:04+00:00"
  },
  "P10896": {
    "problem_number": 10896,
    "slug": "unsolvedmath-2930-kirby-problem-4-54",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:06+00:00",
    "updated_at": "2026-08-18T02:59:08+00:00"
  },
  "P10952": {
    "problem_number": 10952,
    "slug": "unsolvedmath-2934-kirby-problem-4-58",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:11+00:00",
    "updated_at": "2026-08-18T03:00:12+00:00"
  },
  "P10846": {
    "problem_number": 10846,
    "slug": "unsolvedmath-2936-kirby-problem-4-60",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:23+00:00",
    "updated_at": "2026-08-18T02:57:29+00:00"
  },
  "P10912": {
    "problem_number": 10912,
    "slug": "unsolvedmath-2939-kirby-problem-4-63",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:27+00:00",
    "updated_at": "2026-08-18T02:59:28+00:00"
  },
  "P10834": {
    "problem_number": 10834,
    "slug": "unsolvedmath-2941-kirby-problem-4-65",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:43+00:00",
    "updated_at": "2026-08-18T02:56:47+00:00"
  },
  "P11056": {
    "problem_number": 11056,
    "slug": "unsolvedmath-2883-kirby-problem-4-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:13+00:00",
    "updated_at": "2026-08-18T03:02:14+00:00"
  },
  "P11090": {
    "problem_number": 11090,
    "slug": "unsolvedmath-2947-kirby-problem-4-71",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:03:31+00:00",
    "updated_at": "2026-08-18T03:03:38+00:00"
  },
  "P10942": {
    "problem_number": 10942,
    "slug": "unsolvedmath-2951-kirby-problem-4-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:00+00:00",
    "updated_at": "2026-08-18T03:00:02+00:00"
  },
  "P11076": {
    "problem_number": 11076,
    "slug": "unsolvedmath-2952-kirby-problem-4-76",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:34+00:00",
    "updated_at": "2026-08-18T03:02:36+00:00"
  },
  "P11050": {
    "problem_number": 11050,
    "slug": "unsolvedmath-2953-kirby-problem-4-77",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:06+00:00",
    "updated_at": "2026-08-18T03:02:08+00:00"
  },
  "P10986": {
    "problem_number": 10986,
    "slug": "unsolvedmath-2955-kirby-problem-4-79",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:53+00:00",
    "updated_at": "2026-08-18T03:00:55+00:00"
  },
  "P10998": {
    "problem_number": 10998,
    "slug": "unsolvedmath-2884-kirby-problem-4-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:07+00:00",
    "updated_at": "2026-08-18T03:01:08+00:00"
  },
  "P11048": {
    "problem_number": 11048,
    "slug": "unsolvedmath-2956-kirby-problem-4-80",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:05+00:00",
    "updated_at": "2026-08-18T03:02:06+00:00"
  },
  "P11002": {
    "problem_number": 11002,
    "slug": "unsolvedmath-2958-kirby-problem-4-82",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:10+00:00",
    "updated_at": "2026-08-18T03:01:12+00:00"
  },
  "P10966": {
    "problem_number": 10966,
    "slug": "unsolvedmath-2964-kirby-problem-4-88",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:00:28+00:00",
    "updated_at": "2026-08-18T03:00:30+00:00"
  },
  "P11084": {
    "problem_number": 11084,
    "slug": "unsolvedmath-2966-kirby-problem-4-90",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:50+00:00",
    "updated_at": "2026-08-18T03:02:59+00:00"
  },
  "P11010": {
    "problem_number": 11010,
    "slug": "unsolvedmath-2972-kirby-problem-4-96",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:19+00:00",
    "updated_at": "2026-08-18T03:01:21+00:00"
  },
  "P11036": {
    "problem_number": 11036,
    "slug": "unsolvedmath-2975-kirby-problem-4-99",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:53+00:00",
    "updated_at": "2026-08-18T03:01:54+00:00"
  },
  "P11008": {
    "problem_number": 11008,
    "slug": "unsolvedmath-3020-kirby-problem-5-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:01:17+00:00",
    "updated_at": "2026-08-18T03:01:19+00:00"
  },
  "P10830": {
    "problem_number": 10830,
    "slug": "unsolvedmath-3023-kirby-problem-5-16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:29+00:00",
    "updated_at": "2026-08-18T02:56:34+00:00"
  },
  "P10870": {
    "problem_number": 10870,
    "slug": "unsolvedmath-3009-kirby-problem-5-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:40+00:00",
    "updated_at": "2026-08-18T02:58:43+00:00"
  },
  "P11068": {
    "problem_number": 11068,
    "slug": "unsolvedmath-3010-kirby-problem-5-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T03:02:26+00:00",
    "updated_at": "2026-08-18T03:02:28+00:00"
  },
  "P10858": {
    "problem_number": 10858,
    "slug": "unsolvedmath-3013-kirby-problem-5-6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:07+00:00",
    "updated_at": "2026-08-18T02:58:11+00:00"
  },
  "P10844": {
    "problem_number": 10844,
    "slug": "unsolvedmath-2609-kourovka-notebook-problem-21-100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:17+00:00",
    "updated_at": "2026-08-18T02:57:22+00:00"
  },
  "P10876": {
    "problem_number": 10876,
    "slug": "unsolvedmath-2611-kourovka-notebook-problem-21-102",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:47+00:00",
    "updated_at": "2026-08-18T02:58:48+00:00"
  },
  "P10816": {
    "problem_number": 10816,
    "slug": "unsolvedmath-2613-kourovka-notebook-problem-21-104",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:42+00:00",
    "updated_at": "2026-08-18T02:55:47+00:00"
  },
  "P10832": {
    "problem_number": 10832,
    "slug": "unsolvedmath-2619-kourovka-notebook-problem-21-110",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:36+00:00",
    "updated_at": "2026-08-18T02:56:40+00:00"
  },
  "P10786": {
    "problem_number": 10786,
    "slug": "unsolvedmath-2622-kourovka-notebook-problem-21-113",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:14+00:00",
    "updated_at": "2026-08-18T02:55:14+00:00"
  },
  "P10840": {
    "problem_number": 10840,
    "slug": "unsolvedmath-2643-kourovka-notebook-problem-21-134",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:03+00:00",
    "updated_at": "2026-08-18T02:57:08+00:00"
  },
  "P10856": {
    "problem_number": 10856,
    "slug": "unsolvedmath-2651-kourovka-notebook-problem-21-142",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:59+00:00",
    "updated_at": "2026-08-18T02:58:04+00:00"
  },
  "P10810": {
    "problem_number": 10810,
    "slug": "unsolvedmath-2561-kourovka-notebook-problem-21-52",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:22+00:00",
    "updated_at": "2026-08-18T02:55:26+00:00"
  },
  "P10824": {
    "problem_number": 10824,
    "slug": "unsolvedmath-2562-kourovka-notebook-problem-21-53",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:09+00:00",
    "updated_at": "2026-08-18T02:56:13+00:00"
  },
  "P10892": {
    "problem_number": 10892,
    "slug": "unsolvedmath-2564-kourovka-notebook-problem-21-55",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:59:03+00:00",
    "updated_at": "2026-08-18T02:59:04+00:00"
  },
  "P10836": {
    "problem_number": 10836,
    "slug": "unsolvedmath-2565-kourovka-notebook-problem-21-56",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:49+00:00",
    "updated_at": "2026-08-18T02:56:54+00:00"
  },
  "P10864": {
    "problem_number": 10864,
    "slug": "unsolvedmath-2566-kourovka-notebook-problem-21-57",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:26+00:00",
    "updated_at": "2026-08-18T02:58:29+00:00"
  },
  "P10820": {
    "problem_number": 10820,
    "slug": "unsolvedmath-2569-kourovka-notebook-problem-21-60",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:55+00:00",
    "updated_at": "2026-08-18T02:56:00+00:00"
  },
  "P10848": {
    "problem_number": 10848,
    "slug": "unsolvedmath-2572-kourovka-notebook-problem-21-63",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:31+00:00",
    "updated_at": "2026-08-18T02:57:36+00:00"
  },
  "P10888": {
    "problem_number": 10888,
    "slug": "unsolvedmath-2576-kourovka-notebook-problem-21-67",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:58+00:00",
    "updated_at": "2026-08-18T02:59:00+00:00"
  },
  "P10828": {
    "problem_number": 10828,
    "slug": "unsolvedmath-2580-kourovka-notebook-problem-21-71",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:56:22+00:00",
    "updated_at": "2026-08-18T02:56:27+00:00"
  },
  "P10884": {
    "problem_number": 10884,
    "slug": "unsolvedmath-2583-kourovka-notebook-problem-21-74",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:54+00:00",
    "updated_at": "2026-08-18T02:58:55+00:00"
  },
  "P10868": {
    "problem_number": 10868,
    "slug": "unsolvedmath-2584-kourovka-notebook-problem-21-75",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:35+00:00",
    "updated_at": "2026-08-18T02:58:38+00:00"
  },
  "P10804": {
    "problem_number": 10804,
    "slug": "unsolvedmath-2585-kourovka-notebook-problem-21-76",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:20+00:00",
    "updated_at": "2026-08-18T02:55:20+00:00"
  },
  "P10770": {
    "problem_number": 10770,
    "slug": "unsolvedmath-2586-kourovka-notebook-problem-21-77",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:09+00:00",
    "updated_at": "2026-08-18T02:55:09+00:00"
  },
  "P10852": {
    "problem_number": 10852,
    "slug": "unsolvedmath-2587-kourovka-notebook-problem-21-78",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:57:45+00:00",
    "updated_at": "2026-08-18T02:57:49+00:00"
  },
  "P10798": {
    "problem_number": 10798,
    "slug": "unsolvedmath-2588-kourovka-notebook-problem-21-79",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:18+00:00",
    "updated_at": "2026-08-18T02:55:18+00:00"
  },
  "P10860": {
    "problem_number": 10860,
    "slug": "unsolvedmath-2590-kourovka-notebook-problem-21-81",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:14+00:00",
    "updated_at": "2026-08-18T02:58:17+00:00"
  },
  "P10792": {
    "problem_number": 10792,
    "slug": "unsolvedmath-2593-kourovka-notebook-problem-21-84",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:16+00:00",
    "updated_at": "2026-08-18T02:55:16+00:00"
  },
  "P10872": {
    "problem_number": 10872,
    "slug": "unsolvedmath-2602-kourovka-notebook-problem-21-93",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:44+00:00",
    "updated_at": "2026-08-18T02:58:45+00:00"
  },
  "P10778": {
    "problem_number": 10778,
    "slug": "unsolvedmath-2603-kourovka-notebook-problem-21-94",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:12+00:00",
    "updated_at": "2026-08-18T02:55:12+00:00"
  },
  "P10880": {
    "problem_number": 10880,
    "slug": "unsolvedmath-2608-kourovka-notebook-problem-21-99",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:58:49+00:00",
    "updated_at": "2026-08-18T02:58:50+00:00"
  },
  "P10170": {
    "problem_number": 10170,
    "slug": "open-fc-52a710de6da9b8759d52-kourovka-1-40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:33+00:00",
    "updated_at": "2026-08-18T02:51:33+00:00"
  },
  "P8714": {
    "problem_number": 8714,
    "slug": "open-fc-412d3184b27a90102ec6-kurepa-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:10:23+00:00",
    "updated_at": "2026-08-17T19:10:35+00:00"
  },
  "P3376": {
    "problem_number": 3376,
    "slug": "kourovka-21-13-large-free-abelian-duals-of-subgroups-of-integer-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:51:06+00:00",
    "updated_at": "2026-08-12T07:52:22+00:00"
  },
  "P9034": {
    "problem_number": 9034,
    "slug": "open-fc-94c7f24dfffa0f5920d9-green-32",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:42+00:00",
    "updated_at": "2026-08-17T19:45:45+00:00"
  },
  "P3276": {
    "problem_number": 3276,
    "slug": "erdos-problem-1139",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:00:33+00:00",
    "updated_at": "2026-08-12T06:00:56+00:00"
  },
  "P3626": {
    "problem_number": 3626,
    "slug": "ternary-balanced-shift-code-eighteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:14+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3576": {
    "problem_number": 3576,
    "slug": "complement-closed-code-20-10-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:13:45+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P3752": {
    "problem_number": 3752,
    "slug": "three-sat-twelve-solution-diameter",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:19+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2632": {
    "problem_number": 2632,
    "slug": "cyclic-315-packing-31",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:52+00:00",
    "updated_at": "2026-08-01T02:05:24+00:00"
  },
  "P3578": {
    "problem_number": 3578,
    "slug": "cyclic-sidon-set-z256",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:15:28+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P2694": {
    "problem_number": 2694,
    "slug": "six-dice-cyclic-margin",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:17+00:00",
    "updated_at": "2026-08-01T02:26:44+00:00"
  },
  "P12551": {
    "problem_number": 12551,
    "slug": "largest-discriminants-of-a-given-class-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:47:57+00:00",
    "updated_at": "2026-09-02T21:48:04+00:00"
  },
  "P2680": {
    "problem_number": 2680,
    "slug": "triangular-lattice-15-equilateral-free",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:11+00:00",
    "updated_at": "2026-08-01T02:26:49+00:00"
  },
  "P2724": {
    "problem_number": 2724,
    "slug": "grid-cover-time-four-by-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:31+00:00",
    "updated_at": "2026-08-01T02:08:46+00:00"
  },
  "P2708": {
    "problem_number": 2708,
    "slug": "hamming-rips-twenty-beta-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:23+00:00",
    "updated_at": "2026-08-01T02:09:07+00:00"
  },
  "P3648": {
    "problem_number": 3648,
    "slug": "twenty-voxel-maximum-first-betti",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:02+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2684": {
    "problem_number": 2684,
    "slug": "complete-skeleton-eleven-torsion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:12+00:00",
    "updated_at": "2026-08-01T02:04:16+00:00"
  },
  "P3646": {
    "problem_number": 3646,
    "slug": "five-distance-subset-ten-grid",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:59+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2622": {
    "problem_number": 2622,
    "slug": "z101-four-ap-free",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:49+00:00",
    "updated_at": "2026-08-01T02:26:59+00:00"
  },
  "P3634": {
    "problem_number": 3634,
    "slug": "max-six-generator-frobenius-fifty",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:36+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3624": {
    "problem_number": 3624,
    "slug": "sum-two-squares-gap-trillion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:13+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2646": {
    "problem_number": 2646,
    "slug": "max-girth-sl2-101-generators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:58+00:00",
    "updated_at": "2026-08-01T02:25:58+00:00"
  },
  "P9516": {
    "problem_number": 9516,
    "slug": "open-fc-a50e0999c3f84307dfce-erdos-195",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:35+00:00",
    "updated_at": "2026-08-17T19:54:35+00:00"
  },
  "P12123": {
    "problem_number": 12123,
    "slug": "largest-half-gap-exception-among-n-ramanujan-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:14:17+00:00",
    "updated_at": "2026-09-01T19:14:23+00:00"
  },
  "P3614": {
    "problem_number": 3614,
    "slug": "binary-row-three-matrix-order-mod16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:01+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9414": {
    "problem_number": 9414,
    "slug": "open-fc-59aefa3b87483ab5169d-erdos-406-variants-one-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:30+00:00",
    "updated_at": "2026-08-17T19:52:30+00:00"
  },
  "P3768": {
    "problem_number": 3768,
    "slug": "mealy-eight-preset-distinguishing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:52:20+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12589": {
    "problem_number": 12589,
    "slug": "largest-prime-factors-of-shifted-left-factorials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:53:17+00:00",
    "updated_at": "2026-09-02T21:53:24+00:00"
  },
  "P9300": {
    "problem_number": 9300,
    "slug": "open-fc-bb7c9a0130d3c75507db-green-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:43+00:00",
    "updated_at": "2026-08-17T19:50:44+00:00"
  },
  "P9354": {
    "problem_number": 9354,
    "slug": "open-fc-e698ac11ebb1903290ce-green-5-variants-sl-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:06+00:00",
    "updated_at": "2026-08-17T19:51:07+00:00"
  },
  "P3632": {
    "problem_number": 3632,
    "slug": "sqrt-period-record-trillion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:25+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2670": {
    "problem_number": 2670,
    "slug": "rainbow-squarefree-gap-1e12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:07+00:00",
    "updated_at": "2026-08-01T23:44:37+00:00"
  },
  "P3628": {
    "problem_number": 3628,
    "slug": "permutation-matrix-rank-code-eleven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:17+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3724": {
    "problem_number": 3724,
    "slug": "three-letter-defect-one-reset-sixteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:48+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3580": {
    "problem_number": 3580,
    "slug": "rotation-invariant-cap-f3-seven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:17:34+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P3592": {
    "problem_number": 3592,
    "slug": "distinct-pairwise-gcds-fifty",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:43+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3586": {
    "problem_number": 3586,
    "slug": "squarefree-pair-sum-clique-200",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:20:43+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P2604": {
    "problem_number": 2604,
    "slug": "graph-metric-subtour-gap-eight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:43+00:00",
    "updated_at": "2026-08-01T23:29:06+00:00"
  },
  "P3574": {
    "problem_number": 3574,
    "slug": "quadratic-residue-sum-free-1009",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:12:19+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P3588": {
    "problem_number": 3588,
    "slug": "symmetric-binary-rank-code-six-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:39+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12095": {
    "problem_number": 12095,
    "slug": "last-consecutive-prime-pair-in-a-squarefree-yellowstone-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:10:29+00:00",
    "updated_at": "2026-09-01T19:10:34+00:00"
  },
  "P12623": {
    "problem_number": 12623,
    "slug": "last-digits-of-numbers-whose-cubes-concatenate-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:59:12+00:00",
    "updated_at": "2026-09-02T21:59:19+00:00"
  },
  "P12201": {
    "problem_number": 12201,
    "slug": "last-occurrences-of-prime-counts-in-triangular-intervals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:23:50+00:00",
    "updated_at": "2026-09-01T19:23:55+00:00"
  },
  "P2570": {
    "problem_number": 2570,
    "slug": "connectivity-decision-tree-six-leaves",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:32+00:00",
    "updated_at": "2026-08-01T23:22:41+00:00"
  },
  "P11156": {
    "problem_number": 11156,
    "slug": "leakage-safe-revalidation-covariate-augmented-earthquake-point-process-forecasts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-23T07:24:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3738": {
    "problem_number": 3738,
    "slug": "rook-shrikhande-fo-rank",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:50:40+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12601": {
    "problem_number": 12601,
    "slug": "least-prime-factors-of-odd-catalan-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:55:33+00:00",
    "updated_at": "2026-09-02T21:55:40+00:00"
  },
  "P12543": {
    "problem_number": 12543,
    "slug": "least-primes-with-a-prescribed-greatest-factor",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:46:25+00:00",
    "updated_at": "2026-09-02T21:46:32+00:00"
  },
  "P11857": {
    "problem_number": 11857,
    "slug": "least-primes-with-a-prescribed-number-of-digit-3s",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:15:26+00:00",
    "updated_at": "2026-08-30T16:15:30+00:00"
  },
  "P9010": {
    "problem_number": 9010,
    "slug": "open-fc-8248726f10157f2d999b-least-three-square-packing-in-circle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:56+00:00",
    "updated_at": "2026-08-17T19:44:58+00:00"
  },
  "P9834": {
    "problem_number": 9834,
    "slug": "open-fc-f7760b25ce0563897572-least-seventeen-square-packing-in-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:01+00:00",
    "updated_at": "2026-08-17T20:03:02+00:00"
  },
  "P10004": {
    "problem_number": 10004,
    "slug": "open-fc-bf1dfe04a22901950ecb-least-eleven-square-packing-in-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:20+00:00",
    "updated_at": "2026-08-17T20:05:20+00:00"
  },
  "P9270": {
    "problem_number": 9270,
    "slug": "open-fc-a2777d81df12e41b6b4d-least-twenty-one-circle-packing-in-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:31+00:00",
    "updated_at": "2026-08-17T19:50:31+00:00"
  },
  "P2436": {
    "problem_number": 2436,
    "slug": "primitive-degree61-trinomial-multiple",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:56:44+00:00",
    "updated_at": "2026-08-01T02:26:24+00:00"
  },
  "P2822": {
    "problem_number": 2822,
    "slug": "abelian-square-free-uniform-morphism-minimum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:04:59+00:00",
    "updated_at": "2026-08-01T11:30:29+00:00"
  },
  "P3460": {
    "problem_number": 3460,
    "slug": "kourovka-21-80-left-orderable-groups-with-one-nontrivial-conjugacy-class",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:47+00:00",
    "updated_at": "2026-08-12T08:05:48+00:00"
  },
  "P25": {
    "problem_number": 25,
    "slug": "legendres-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:16:09+00:00"
  },
  "P9408": {
    "problem_number": 9408,
    "slug": "open-fc-5420b1767f14d85cbebf-legendre-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:27+00:00",
    "updated_at": "2026-08-17T19:52:27+00:00"
  },
  "P9942": {
    "problem_number": 9942,
    "slug": "open-fc-90f783d9aef5a3027376-lehmer-ramanujan-tau",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:46+00:00",
    "updated_at": "2026-08-17T20:04:46+00:00"
  },
  "P9598": {
    "problem_number": 9598,
    "slug": "open-fc-e6b3831044a094cdc185-erdos-828-variants-lehmer-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:35+00:00",
    "updated_at": "2026-08-17T19:56:38+00:00"
  },
  "P9500": {
    "problem_number": 9500,
    "slug": "open-fc-9a05850b0c7e31b2e688-lehmer-mahler-measure-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:28+00:00",
    "updated_at": "2026-08-17T19:54:29+00:00"
  },
  "P34": {
    "problem_number": 34,
    "slug": "lehmers-mahler-measure-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:16:32+00:00"
  },
  "P9364": {
    "problem_number": 9364,
    "slug": "open-fc-eda3e59e204174def210-lehmer-mahler-measure-problem-variants-best",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:10+00:00",
    "updated_at": "2026-08-17T19:51:11+00:00"
  },
  "P9988": {
    "problem_number": 9988,
    "slug": "open-fc-b2b743c85d9351764132-lehmer-totient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:14+00:00",
    "updated_at": "2026-08-17T20:05:14+00:00"
  },
  "P9078": {
    "problem_number": 9078,
    "slug": "open-fc-b46c687302735702de37-lemoine-conjecture-extension",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:02+00:00",
    "updated_at": "2026-08-17T19:47:04+00:00"
  },
  "P9612": {
    "problem_number": 9612,
    "slug": "open-fc-f079ab6ed7f2d86ea5b1-lemoine-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:04+00:00",
    "updated_at": "2026-08-17T19:57:06+00:00"
  },
  "P8334": {
    "problem_number": 8334,
    "slug": "open-fc-21bae9106eff2917f180-erdos-770-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:02+00:00",
    "updated_at": "2026-08-17T18:40:03+00:00"
  },
  "P8186": {
    "problem_number": 8186,
    "slug": "open-fc-0b9233a28c5835751ba8-erdos-346",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:37+00:00",
    "updated_at": "2026-08-17T18:36:38+00:00"
  },
  "P9506": {
    "problem_number": 9506,
    "slug": "open-fc-9d01b510ae703daba992-erdos-168-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:31+00:00",
    "updated_at": "2026-08-17T19:54:31+00:00"
  },
  "P3272": {
    "problem_number": 3272,
    "slug": "erdos-problem-168",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:00:02+00:00",
    "updated_at": "2026-08-12T06:00:03+00:00"
  },
  "P10078": {
    "problem_number": 10078,
    "slug": "open-fc-f65eddcc8cf9892c193a-erdos-647-variants-lim",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:16+00:00",
    "updated_at": "2026-08-17T20:06:17+00:00"
  },
  "P8164": {
    "problem_number": 8164,
    "slug": "open-fc-0944feb807d0ea8b80b4-erdos-417-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:52+00:00",
    "updated_at": "2026-08-17T18:35:56+00:00"
  },
  "P12553": {
    "problem_number": 12553,
    "slug": "limit-points-of-factorial-product-imbalances",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:48:10+00:00",
    "updated_at": "2026-09-02T21:48:16+00:00"
  },
  "P2898": {
    "problem_number": 2898,
    "slug": "platonic-graph-line-cover-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:45:12+00:00",
    "updated_at": "2026-08-01T12:24:36+00:00"
  },
  "P11580": {
    "problem_number": 11580,
    "slug": "linear-complexity-of-binary-sierpinski-triangle-rows",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:35:22+00:00",
    "updated_at": "2026-08-30T04:35:30+00:00"
  },
  "P3420": {
    "problem_number": 3420,
    "slug": "kourovka-21-40-linear-groups-with-finitely-many-automorphism-orbits",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:51+00:00",
    "updated_at": "2026-08-12T07:59:01+00:00"
  },
  "P9028": {
    "problem_number": 9028,
    "slug": "open-fc-8f41ec199209c3008a0e-conjecture-4-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:31+00:00",
    "updated_at": "2026-08-17T19:45:33+00:00"
  },
  "P8920": {
    "problem_number": 8920,
    "slug": "open-fc-e3360095ad58114723c3-conjecture-4-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:33+00:00",
    "updated_at": "2026-08-17T19:40:35+00:00"
  },
  "P8898": {
    "problem_number": 8898,
    "slug": "open-fc-d0b1efe401100ecd5f61-erdos-872-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:07+00:00",
    "updated_at": "2026-08-17T19:40:08+00:00"
  },
  "P11674": {
    "problem_number": 11674,
    "slug": "linear-recurrence-for-the-pisot-sequence-l-8-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:29+00:00",
    "updated_at": "2026-08-30T11:06:24+00:00"
  },
  "P9762": {
    "problem_number": 9762,
    "slug": "open-fc-c2a96d5a598069a37c3d-erdos-96",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:26+00:00",
    "updated_at": "2026-08-17T20:02:27+00:00"
  },
  "P3024": {
    "problem_number": 3024,
    "slug": "erdos-problem-96",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:53+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8924": {
    "problem_number": 8924,
    "slug": "open-fc-e74004409369588a656c-erdos-579",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:39+00:00",
    "updated_at": "2026-08-17T19:40:39+00:00"
  },
  "P10060": {
    "problem_number": 10060,
    "slug": "open-fc-eb1cc69dde6ef384d9be-green-15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:01+00:00",
    "updated_at": "2026-08-17T20:06:02+00:00"
  },
  "P3280": {
    "problem_number": 3280,
    "slug": "erdos-problem-236",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:40+00:00",
    "updated_at": "2026-08-12T06:02:42+00:00"
  },
  "P8314": {
    "problem_number": 8314,
    "slug": "open-fc-1f02e576fcb71972bbf8-erdos-236",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:34+00:00",
    "updated_at": "2026-08-17T18:39:34+00:00"
  },
  "P8484": {
    "problem_number": 8484,
    "slug": "open-fc-4c27fcd14e490d102ffd-erdos-409-variants-sigma-islittleo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:23+00:00",
    "updated_at": "2026-08-17T18:52:24+00:00"
  },
  "P11": {
    "problem_number": 11,
    "slug": "littlewood-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:17:21+00:00"
  },
  "P9268": {
    "problem_number": 9268,
    "slug": "open-fc-a1eeafd2e68c8a7003ec-mlc-general-exponent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:30+00:00",
    "updated_at": "2026-08-17T19:50:31+00:00"
  },
  "P9102": {
    "problem_number": 9102,
    "slug": "open-fc-c659e7c29b098a2f10a7-mlc",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:35+00:00",
    "updated_at": "2026-08-17T19:47:36+00:00"
  },
  "P11562": {
    "problem_number": 11562,
    "slug": "local-prime-exchange-balancing-mobius-cancellation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T17:03:54+00:00",
    "updated_at": "2026-09-05T18:00:00.226341+00:00"
  },
  "P3526": {
    "problem_number": 3526,
    "slug": "kourovka-21-133-local-subnormal-abelian-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:06+00:00",
    "updated_at": "2026-08-12T08:12:09+00:00"
  },
  "P3370": {
    "problem_number": 3370,
    "slug": "kourovka-21-7-local-to-global-iyb-structure-in-finite-soluble-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:44:30+00:00",
    "updated_at": "2026-08-12T07:45:11+00:00"
  },
  "P3418": {
    "problem_number": 3418,
    "slug": "kourovka-21-39-locally-finite-groups-with-few-characteristic-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:58:38+00:00",
    "updated_at": "2026-08-12T07:58:41+00:00"
  },
  "P9272": {
    "problem_number": 9272,
    "slug": "open-fc-a4ded4acb41e3235b27c-erdos-486",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:31+00:00",
    "updated_at": "2026-08-17T19:50:32+00:00"
  },
  "P2834": {
    "problem_number": 2834,
    "slug": "binary-word-logarithmic-dfa-separation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:05+00:00",
    "updated_at": "2026-08-01T11:32:50+00:00"
  },
  "P2896": {
    "problem_number": 2896,
    "slug": "almost-equilateral-banach-logarithmic-dimension",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:44:56+00:00",
    "updated_at": "2026-08-01T23:20:12+00:00"
  },
  "P33": {
    "problem_number": 33,
    "slug": "lonely-runner-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:17:47+00:00"
  },
  "P8570": {
    "problem_number": 8570,
    "slug": "open-fc-7b0e6751bc36eb1453aa-erdos-238",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:55:22+00:00",
    "updated_at": "2026-08-17T18:55:30+00:00"
  },
  "P12137": {
    "problem_number": 12137,
    "slug": "longest-consecutive-run-with-distinct-prime-factor-exponents",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:16:00+00:00",
    "updated_at": "2026-09-01T19:16:06+00:00"
  },
  "P3734": {
    "problem_number": 3734,
    "slug": "monotone-network-twelve-max-period",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:48:14+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3638": {
    "problem_number": 3638,
    "slug": "quintic-translation-cycle-f65537",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:49+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3612": {
    "problem_number": 3612,
    "slug": "mobius-no-positive-run-trillion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:59+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3616": {
    "problem_number": 3616,
    "slug": "irredundant-three-cycle-generators-a12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:04+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3606": {
    "problem_number": 3606,
    "slug": "affine-unitriangular-z4-five-period",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:53+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3694": {
    "problem_number": 3694,
    "slug": "promotion-staircase-six-max-orbit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:39+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2658": {
    "problem_number": 2658,
    "slug": "rainbow-divisor-count-run-1e12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:02+00:00",
    "updated_at": "2026-08-01T23:43:06+00:00"
  },
  "P3662": {
    "problem_number": 3662,
    "slug": "rowmotion-five-cube-max-orbit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:13+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3660": {
    "problem_number": 3660,
    "slug": "rule-110-ring-thirty-max-cycle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:09+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3730": {
    "problem_number": 3730,
    "slug": "binary-nfa-eight-longest-counterexample",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:47:30+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12009": {
    "problem_number": 12009,
    "slug": "longest-side-of-an-integer-triangle-with-fixed-inradius",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:39:56+00:00",
    "updated_at": "2026-09-01T18:40:29+00:00"
  },
  "P10074": {
    "problem_number": 10074,
    "slug": "open-fc-f44361dd9a8ef75142d0-snake-dim-nine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:14+00:00",
    "updated_at": "2026-08-17T20:06:15+00:00"
  },
  "P11700": {
    "problem_number": 11700,
    "slug": "look-and-say-partitions-and-distinct-run-lengths",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:53+00:00",
    "updated_at": "2026-08-30T11:16:00+00:00"
  },
  "P3238": {
    "problem_number": 3238,
    "slug": "erdos-problem-323",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:56:34+00:00",
    "updated_at": "2026-08-12T05:56:50+00:00"
  },
  "P8318": {
    "problem_number": 8318,
    "slug": "open-fc-1f3a340f1ed1e4b98268-erdos-323-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:35+00:00",
    "updated_at": "2026-08-17T18:39:37+00:00"
  },
  "P8998": {
    "problem_number": 8998,
    "slug": "open-fc-7a6be506310ec154dedd-green-16-lower-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:39+00:00",
    "updated_at": "2026-08-17T19:44:40+00:00"
  },
  "P9076": {
    "problem_number": 9076,
    "slug": "open-fc-b34c1cc8c3c9bb8d4623-green-60",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:59+00:00",
    "updated_at": "2026-08-17T19:47:01+00:00"
  },
  "P9266": {
    "problem_number": 9266,
    "slug": "open-fc-a081dad3e0a06374a428-w-3-21-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:30+00:00",
    "updated_at": "2026-08-17T19:50:30+00:00"
  },
  "P3184": {
    "problem_number": 3184,
    "slug": "erdos-problem-564",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:50:01+00:00",
    "updated_at": "2026-08-12T05:50:02+00:00"
  },
  "P8312": {
    "problem_number": 8312,
    "slug": "open-fc-1ee92131ef03045100e0-erdos-564",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:33+00:00",
    "updated_at": "2026-08-17T18:39:34+00:00"
  },
  "P9912": {
    "problem_number": 9912,
    "slug": "open-fc-7aeaad1b4e06e56be368-conjecture-4-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:30+00:00",
    "updated_at": "2026-08-17T20:04:30+00:00"
  },
  "P8546": {
    "problem_number": 8546,
    "slug": "open-fc-6df610a519b25b7f7bf2-conjecture-4-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:31+00:00",
    "updated_at": "2026-08-17T18:54:32+00:00"
  },
  "P9828": {
    "problem_number": 9828,
    "slug": "open-fc-f3e898ea731ec71d88b8-green-19-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:01+00:00",
    "updated_at": "2026-08-17T20:03:01+00:00"
  },
  "P8642": {
    "problem_number": 8642,
    "slug": "open-fc-492c873dcad7b88e6808-erdos-830-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:00+00:00",
    "updated_at": "2026-08-17T18:59:03+00:00"
  },
  "P10030": {
    "problem_number": 10030,
    "slug": "open-fc-d1b1902a9df880fd0dca-green-35-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:33+00:00",
    "updated_at": "2026-08-17T20:05:33+00:00"
  },
  "P9466": {
    "problem_number": 9466,
    "slug": "open-fc-818453fc6b941a8b13de-conjecture40",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:59+00:00",
    "updated_at": "2026-08-17T19:53:59+00:00"
  },
  "P9098": {
    "problem_number": 9098,
    "slug": "open-fc-c42086d9dd04ae5a7351-w-3-24-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:32+00:00",
    "updated_at": "2026-08-17T19:47:33+00:00"
  },
  "P9564": {
    "problem_number": 9564,
    "slug": "open-fc-c8a64770e97342a11d2d-w-3-38-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:26+00:00",
    "updated_at": "2026-08-17T19:55:28+00:00"
  },
  "P10052": {
    "problem_number": 10052,
    "slug": "open-fc-e5c01c03bea2267d01a1-w-3-39-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:52+00:00",
    "updated_at": "2026-08-17T20:05:54+00:00"
  },
  "P9548": {
    "problem_number": 9548,
    "slug": "open-fc-be6a057f9635aad78061-w-3-31-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:02+00:00",
    "updated_at": "2026-08-17T19:55:04+00:00"
  },
  "P9742": {
    "problem_number": 9742,
    "slug": "open-fc-b257db907b6e06daf756-w-3-37-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:14+00:00",
    "updated_at": "2026-08-17T20:02:14+00:00"
  },
  "P8584": {
    "problem_number": 8584,
    "slug": "open-fc-306acd054e6c518f10b1-green-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:19+00:00",
    "updated_at": "2026-08-17T19:04:28+00:00"
  },
  "P9446": {
    "problem_number": 9446,
    "slug": "open-fc-71cf49928fe638070f13-erdos-817",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:34+00:00",
    "updated_at": "2026-08-17T19:53:37+00:00"
  },
  "P3350": {
    "problem_number": 3350,
    "slug": "erdos-problem-817",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:08:19+00:00",
    "updated_at": "2026-08-12T06:08:23+00:00"
  },
  "P8218": {
    "problem_number": 8218,
    "slug": "open-fc-10f7db800ce1f9dfc2d6-erdos-789-variants-sq-isbigo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:15+00:00",
    "updated_at": "2026-08-17T18:37:16+00:00"
  },
  "P9284": {
    "problem_number": 9284,
    "slug": "open-fc-ad2826cb0a12fc14386b-w-3-27-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:37+00:00",
    "updated_at": "2026-08-17T19:50:37+00:00"
  },
  "P9040": {
    "problem_number": 9040,
    "slug": "open-fc-98dda7bfb9f35c1f6b0b-w-3-28-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:55+00:00",
    "updated_at": "2026-08-17T19:45:57+00:00"
  },
  "P9768": {
    "problem_number": 9768,
    "slug": "open-fc-c5a01348e2060341289b-w-3-29-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:28+00:00",
    "updated_at": "2026-08-17T20:02:28+00:00"
  },
  "P10026": {
    "problem_number": 10026,
    "slug": "open-fc-cef68f6229bc2f7353d2-w-3-35-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:32+00:00",
    "updated_at": "2026-08-17T20:05:32+00:00"
  },
  "P8606": {
    "problem_number": 8606,
    "slug": "open-fc-396a5e6d4926ffb4c762-w-3-23-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:57:26+00:00",
    "updated_at": "2026-08-17T18:57:36+00:00"
  },
  "P9604": {
    "problem_number": 9604,
    "slug": "open-fc-eafe22710af7265b932b-w-3-20-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:49+00:00",
    "updated_at": "2026-08-17T19:56:51+00:00"
  },
  "P9236": {
    "problem_number": 9236,
    "slug": "open-fc-858cc4bb7c7964c8aef9-w-3-26-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:15+00:00",
    "updated_at": "2026-08-17T19:50:15+00:00"
  },
  "P9132": {
    "problem_number": 9132,
    "slug": "open-fc-e15b11a6ba47e0b8841f-w-3-30-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:44+00:00",
    "updated_at": "2026-08-17T19:47:44+00:00"
  },
  "P8812": {
    "problem_number": 8812,
    "slug": "open-fc-94a9edba38e9faea6779-zhao-question",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:23:29+00:00",
    "updated_at": "2026-08-17T19:24:11+00:00"
  },
  "P8574": {
    "problem_number": 8574,
    "slug": "open-fc-7de1d13a7b43755c8469-conjecture141",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:55:50+00:00",
    "updated_at": "2026-08-17T18:55:58+00:00"
  },
  "P9428": {
    "problem_number": 9428,
    "slug": "open-fc-647c24e2ec010ce6b82e-erdos-340",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:49+00:00",
    "updated_at": "2026-08-17T19:52:52+00:00"
  },
  "P3270": {
    "problem_number": 3270,
    "slug": "erdos-problem-340",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:59:55+00:00",
    "updated_at": "2026-08-12T05:59:57+00:00"
  },
  "P9000": {
    "problem_number": 9000,
    "slug": "open-fc-7b10320b799538f99780-conjecture19",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:41+00:00",
    "updated_at": "2026-08-17T19:44:42+00:00"
  },
  "P8696": {
    "problem_number": 8696,
    "slug": "open-fc-2d2235915369520fc7ae-conjecture61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:12+00:00",
    "updated_at": "2026-08-17T19:10:29+00:00"
  },
  "P3564": {
    "problem_number": 3564,
    "slug": "permanent-formula-lower-bounds",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:51:41+00:00",
    "updated_at": "2026-08-18T06:09:35+00:00"
  },
  "P9690": {
    "problem_number": 9690,
    "slug": "open-fc-84909c0b3dfb36fcd9d1-erdos-821",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:48+00:00",
    "updated_at": "2026-08-17T20:01:49+00:00"
  },
  "P11564": {
    "problem_number": 11564,
    "slug": "lowest-energy-isobars-at-mass-numbers-261-and-265",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:33:07+00:00",
    "updated_at": "2026-08-30T04:33:14+00:00"
  },
  "P8086": {
    "problem_number": 8086,
    "slug": "open-fc-00d3fbed1b7942366f0c-exists-magic-square-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:36+00:00",
    "updated_at": "2026-08-17T18:34:37+00:00"
  },
  "P9378": {
    "problem_number": 9378,
    "slug": "open-fc-f5d0287eed6964f71e17-mahler-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:16+00:00",
    "updated_at": "2026-08-17T19:51:17+00:00"
  },
  "P8388": {
    "problem_number": 8388,
    "slug": "open-fc-27706ba2121dbb7a3f16-problem-10-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:03+00:00",
    "updated_at": "2026-08-17T18:49:05+00:00"
  },
  "P8394": {
    "problem_number": 8394,
    "slug": "open-fc-28848ed509ca5b3eeda3-complexity-two-pow",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:14+00:00",
    "updated_at": "2026-08-17T18:49:16+00:00"
  },
  "P3510": {
    "problem_number": 3510,
    "slug": "kourovka-21-125-mapping-tori-of-free-group-automorphisms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:12+00:00",
    "updated_at": "2026-08-12T08:10:18+00:00"
  },
  "P9142": {
    "problem_number": 9142,
    "slug": "open-fc-e7433df1b0145a6a2768-conjecture-1-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:48+00:00",
    "updated_at": "2026-08-17T19:47:48+00:00"
  },
  "P9554": {
    "problem_number": 9554,
    "slug": "open-fc-c384acc3a5e8ccb67140-conjclasssizes-iff-sym-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:12+00:00",
    "updated_at": "2026-08-17T19:55:12+00:00"
  },
  "P3120": {
    "problem_number": 3120,
    "slug": "matrix-spencer-discrepancy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:05+00:00",
    "updated_at": "2026-08-02T12:53:04+00:00"
  },
  "P12541": {
    "problem_number": 12541,
    "slug": "maximal-determinants-of-persymmetric-matrices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:46:09+00:00",
    "updated_at": "2026-09-02T21:46:21+00:00"
  },
  "P12207": {
    "problem_number": 12207,
    "slug": "maximal-nonrepunit-circular-primes-by-base",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:24:35+00:00",
    "updated_at": "2026-09-01T19:24:40+00:00"
  },
  "P3040": {
    "problem_number": 3040,
    "slug": "erdos-problem-126",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:12+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9432": {
    "problem_number": 9432,
    "slug": "open-fc-670671de474644ee71a1-erdos-126",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:01+00:00",
    "updated_at": "2026-08-17T19:53:03+00:00"
  },
  "P8364": {
    "problem_number": 8364,
    "slug": "open-fc-249b257772a5f9af0542-mutuallyunbiasedbases-dim10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:24+00:00",
    "updated_at": "2026-08-17T18:40:27+00:00"
  },
  "P8592": {
    "problem_number": 8592,
    "slug": "open-fc-33ce9547e4919fb91c28-mutuallyunbiasedbases-dim14",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:36+00:00",
    "updated_at": "2026-08-17T18:56:37+00:00"
  },
  "P8672": {
    "problem_number": 8672,
    "slug": "open-fc-3074ecc7008ee70a73b9-erdos-373-variants-maximal-solution",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:29+00:00",
    "updated_at": "2026-08-17T19:04:30+00:00"
  },
  "P9920": {
    "problem_number": 9920,
    "slug": "open-fc-80c60bd532f29d30df7b-exists-maximal-star",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:33+00:00",
    "updated_at": "2026-08-17T20:04:33+00:00"
  },
  "P9212": {
    "problem_number": 9212,
    "slug": "open-fc-6611726f51f125aa247d-erdos-757",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:32+00:00",
    "updated_at": "2026-08-17T19:49:34+00:00"
  },
  "P9224": {
    "problem_number": 9224,
    "slug": "open-fc-779bb8262e21dd11870b-erdos-503",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:46+00:00",
    "updated_at": "2026-08-17T19:49:49+00:00"
  },
  "P3718": {
    "problem_number": 3718,
    "slug": "odd-graph-five-maxcut",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:38+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P4218": {
    "problem_number": 4218,
    "slug": "maximal-determinant-sign-matrix-order-101",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:14+00:00",
    "updated_at": "2026-08-16T02:03:03+00:00"
  },
  "P4220": {
    "problem_number": 4220,
    "slug": "maximal-determinant-sign-matrix-order-105",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:16+00:00",
    "updated_at": "2026-08-16T02:03:03+00:00"
  },
  "P4222": {
    "problem_number": 4222,
    "slug": "maximal-determinant-sign-matrix-order-109",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:17+00:00",
    "updated_at": "2026-08-16T02:03:05+00:00"
  },
  "P4224": {
    "problem_number": 4224,
    "slug": "maximal-determinant-sign-matrix-order-113",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:19+00:00",
    "updated_at": "2026-08-16T02:03:05+00:00"
  },
  "P4226": {
    "problem_number": 4226,
    "slug": "maximal-determinant-sign-matrix-order-117",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:21+00:00",
    "updated_at": "2026-08-16T02:03:06+00:00"
  },
  "P4188": {
    "problem_number": 4188,
    "slug": "maximal-determinant-sign-matrix-order-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:12+00:00",
    "updated_at": "2026-08-16T02:03:07+00:00"
  },
  "P4190": {
    "problem_number": 4190,
    "slug": "maximal-determinant-sign-matrix-order-45",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:16+00:00",
    "updated_at": "2026-08-16T02:03:11+00:00"
  },
  "P4192": {
    "problem_number": 4192,
    "slug": "maximal-determinant-sign-matrix-order-49",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:24+00:00",
    "updated_at": "2026-08-16T02:03:11+00:00"
  },
  "P4194": {
    "problem_number": 4194,
    "slug": "maximal-determinant-sign-matrix-order-53",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:31+00:00",
    "updated_at": "2026-08-16T02:03:11+00:00"
  },
  "P4196": {
    "problem_number": 4196,
    "slug": "maximal-determinant-sign-matrix-order-57",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:36+00:00",
    "updated_at": "2026-08-16T02:03:11+00:00"
  },
  "P4198": {
    "problem_number": 4198,
    "slug": "maximal-determinant-sign-matrix-order-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:42+00:00",
    "updated_at": "2026-08-16T02:03:11+00:00"
  },
  "P4200": {
    "problem_number": 4200,
    "slug": "maximal-determinant-sign-matrix-order-65",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:48+00:00",
    "updated_at": "2026-08-16T02:03:12+00:00"
  },
  "P4202": {
    "problem_number": 4202,
    "slug": "maximal-determinant-sign-matrix-order-69",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:52+00:00",
    "updated_at": "2026-08-16T02:03:12+00:00"
  },
  "P4204": {
    "problem_number": 4204,
    "slug": "maximal-determinant-sign-matrix-order-73",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:55+00:00",
    "updated_at": "2026-08-16T02:03:12+00:00"
  },
  "P4206": {
    "problem_number": 4206,
    "slug": "maximal-determinant-sign-matrix-order-77",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:57+00:00",
    "updated_at": "2026-08-16T02:03:12+00:00"
  },
  "P4208": {
    "problem_number": 4208,
    "slug": "maximal-determinant-sign-matrix-order-81",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:28:59+00:00",
    "updated_at": "2026-08-16T02:03:15+00:00"
  },
  "P4210": {
    "problem_number": 4210,
    "slug": "maximal-determinant-sign-matrix-order-85",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:03+00:00",
    "updated_at": "2026-08-16T02:03:17+00:00"
  },
  "P4212": {
    "problem_number": 4212,
    "slug": "maximal-determinant-sign-matrix-order-89",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:06+00:00",
    "updated_at": "2026-08-16T02:03:19+00:00"
  },
  "P4214": {
    "problem_number": 4214,
    "slug": "maximal-determinant-sign-matrix-order-93",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:10+00:00",
    "updated_at": "2026-08-16T02:03:25+00:00"
  },
  "P4216": {
    "problem_number": 4216,
    "slug": "maximal-determinant-sign-matrix-order-97",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:29:12+00:00",
    "updated_at": "2026-08-16T02:03:31+00:00"
  },
  "P2640": {
    "problem_number": 2640,
    "slug": "skew-seidel-maxdet-34",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:55+00:00",
    "updated_at": "2026-07-29T20:56:38+00:00"
  },
  "P2440": {
    "problem_number": 2440,
    "slug": "binary-symmetric-toeplitz-maxdet-20",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:56:45+00:00",
    "updated_at": "2026-08-01T23:21:11+00:00"
  },
  "P12215": {
    "problem_number": 12215,
    "slug": "maximum-determinants-of-permutation-circulants",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:25:33+00:00",
    "updated_at": "2026-09-01T19:25:39+00:00"
  },
  "P3582": {
    "problem_number": 3582,
    "slug": "ternary-lrc-12-distance-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:18:31+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P3584": {
    "problem_number": 3584,
    "slug": "ternary-self-orthogonal-14-distance-nine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T15:19:29+00:00",
    "updated_at": "2026-08-22T16:00:02.772653+00:00"
  },
  "P9616": {
    "problem_number": 9616,
    "slug": "open-fc-f272624619031e68d203-green-51",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:11+00:00",
    "updated_at": "2026-08-17T19:57:13+00:00"
  },
  "P2722": {
    "problem_number": 2722,
    "slug": "q12-noise-stability-794",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:30+00:00",
    "updated_at": "2026-08-01T02:26:34+00:00"
  },
  "P3710": {
    "problem_number": 3710,
    "slug": "knight-eight-induced-matching",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:29+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8510": {
    "problem_number": 8510,
    "slug": "open-fc-5c3c13c310fb58b4fb5e-green-24",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:36+00:00",
    "updated_at": "2026-08-17T18:53:41+00:00"
  },
  "P3602": {
    "problem_number": 3602,
    "slug": "disjoint-kirkman-systems-fifteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:51+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9436": {
    "problem_number": 9436,
    "slug": "open-fc-696a553c46622ea4e472-mutuallyunbiasedbases-dim12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:12+00:00",
    "updated_at": "2026-08-17T19:53:14+00:00"
  },
  "P9454": {
    "problem_number": 9454,
    "slug": "open-fc-794fc12954c50160dd8e-mutuallyunbiasedbases-dim15",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:50+00:00",
    "updated_at": "2026-08-17T19:53:52+00:00"
  },
  "P9622": {
    "problem_number": 9622,
    "slug": "open-fc-f5fdb82a97cf4a6f9906-mutuallyunbiasedbases-dim6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:22+00:00",
    "updated_at": "2026-08-17T19:57:24+00:00"
  },
  "P3732": {
    "problem_number": 3732,
    "slug": "stable-marriage-ten-maximum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:47:52+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3554": {
    "problem_number": 3554,
    "slug": "maximum-3ap-count-8-subset-z19",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T01:31:08+00:00",
    "updated_at": "2026-08-13T01:35:25+00:00"
  },
  "P12747": {
    "problem_number": 12747,
    "slug": "maximum-queens-with-exactly-three-visible-attacks-each",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:40:36+00:00",
    "updated_at": "2026-09-02T22:41:05+00:00"
  },
  "P9168": {
    "problem_number": 9168,
    "slug": "open-fc-f8b2dc94aad503d5aac5-green-16",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:55+00:00",
    "updated_at": "2026-08-17T19:47:55+00:00"
  },
  "P9722": {
    "problem_number": 9722,
    "slug": "open-fc-a215fd1451e4a1a653f4-erdos-319",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:04+00:00",
    "updated_at": "2026-08-17T20:02:05+00:00"
  },
  "P3698": {
    "problem_number": 3698,
    "slug": "six-grid-max-total-one-persistence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8634": {
    "problem_number": 8634,
    "slug": "open-fc-8a871894f7aa2a2c1923-erdos-329",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:52+00:00",
    "updated_at": "2026-08-17T18:59:01+00:00"
  },
  "P11971": {
    "problem_number": 11971,
    "slug": "mean-curvatures-and-symmetry-of-convex-hypersurfaces",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T14:04:49+00:00",
    "updated_at": "2026-09-07T15:00:01.815969+00:00"
  },
  "P12393": {
    "problem_number": 12393,
    "slug": "median-euler-residues",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:31:19+00:00",
    "updated_at": "2026-09-02T21:31:32+00:00"
  },
  "P2588": {
    "problem_number": 2588,
    "slug": "random-two-sat-six-median",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:37+00:00",
    "updated_at": "2026-08-01T02:26:39+00:00"
  },
  "P9848": {
    "problem_number": 9848,
    "slug": "open-fc-41f2b204feed13edb3a1-erdos-340-variants-33-mem-sub",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:55+00:00",
    "updated_at": "2026-08-17T20:03:55+00:00"
  },
  "P2430": {
    "problem_number": 2430,
    "slug": "digit-product-iteration-trajectories",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-24T21:54:43+00:00",
    "updated_at": "2026-07-30T02:25:28+00:00"
  },
  "P8114": {
    "problem_number": 8114,
    "slug": "open-fc-03b0de8933195e65148e-erdos-881",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:44+00:00",
    "updated_at": "2026-08-17T18:34:45+00:00"
  },
  "P11152": {
    "problem_number": 11152,
    "slug": "minimal-normal-mode-couplings-recovering-band-limited-earth-structure",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-21T00:06:20+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P10044": {
    "problem_number": 10044,
    "slug": "open-fc-e0d7950735d65f78475e-erdos-872-variants-prime-question",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:42+00:00",
    "updated_at": "2026-08-17T20:05:44+00:00"
  },
  "P3480": {
    "problem_number": 3480,
    "slug": "kourovka-21-103-minimal-topological-groups-and-semidirect-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:40+00:00",
    "updated_at": "2026-08-12T08:06:47+00:00"
  },
  "P2744": {
    "problem_number": 2744,
    "slug": "minimal-vanishing-105th-root-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:00:41+00:00",
    "updated_at": "2026-08-01T02:26:04+00:00"
  },
  "P3068": {
    "problem_number": 3068,
    "slug": "avoidable-word-minimum-alphabet",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:53+00:00",
    "updated_at": "2026-08-02T12:47:19+00:00"
  },
  "P12585": {
    "problem_number": 12585,
    "slug": "minimum-diameter-under-bounded-difference-multiplicities",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:52:28+00:00",
    "updated_at": "2026-09-02T21:52:59+00:00"
  },
  "P2882": {
    "problem_number": 2882,
    "slug": "convex-polygon-diagonal-intersection-asymptotic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:43:03+00:00",
    "updated_at": "2026-08-01T23:23:14+00:00"
  },
  "P3708": {
    "problem_number": 3708,
    "slug": "paley-tournament-43-feedback-arcs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:29+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3864": {
    "problem_number": 3864,
    "slug": "toroidal-king-12-13-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:17+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3866": {
    "problem_number": 3866,
    "slug": "toroidal-king-12-14-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:20+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3868": {
    "problem_number": 3868,
    "slug": "toroidal-king-12-15-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:22+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3870": {
    "problem_number": 3870,
    "slug": "toroidal-king-12-17-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:22+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3872": {
    "problem_number": 3872,
    "slug": "toroidal-king-13-14-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:24+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3874": {
    "problem_number": 3874,
    "slug": "toroidal-king-13-15-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:25+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3876": {
    "problem_number": 3876,
    "slug": "toroidal-king-13-16-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:26+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3878": {
    "problem_number": 3878,
    "slug": "toroidal-king-13-17-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:28+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3880": {
    "problem_number": 3880,
    "slug": "toroidal-king-14-15-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:30+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3882": {
    "problem_number": 3882,
    "slug": "toroidal-king-14-16-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:34+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3884": {
    "problem_number": 3884,
    "slug": "toroidal-king-14-17-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:38+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3886": {
    "problem_number": 3886,
    "slug": "toroidal-king-14-18-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:42+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3888": {
    "problem_number": 3888,
    "slug": "toroidal-king-15-16-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:44+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3890": {
    "problem_number": 3890,
    "slug": "toroidal-king-15-17-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:48+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3892": {
    "problem_number": 3892,
    "slug": "toroidal-king-15-18-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:49+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3894": {
    "problem_number": 3894,
    "slug": "toroidal-king-16-17-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:52+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3896": {
    "problem_number": 3896,
    "slug": "toroidal-king-16-18-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:54+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3898": {
    "problem_number": 3898,
    "slug": "toroidal-king-16-19-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:33:59+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3900": {
    "problem_number": 3900,
    "slug": "toroidal-king-17-18-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:03+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3902": {
    "problem_number": 3902,
    "slug": "toroidal-king-17-19-identifying-code",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T18:34:05+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9006": {
    "problem_number": 9006,
    "slug": "open-fc-7fed0f9769ec7a48e645-erdos-409-variants-sigma",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:48+00:00",
    "updated_at": "2026-08-17T19:44:50+00:00"
  },
  "P2802": {
    "problem_number": 2802,
    "slug": "minimum-convex-pentagons-seventeen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:08+00:00",
    "updated_at": "2026-08-01T12:18:40+00:00"
  },
  "P12379": {
    "problem_number": 12379,
    "slug": "minimum-pieces-for-regular-polygon-to-square-dissections",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:45:37+00:00",
    "updated_at": "2026-09-01T19:45:42+00:00"
  },
  "P2576": {
    "problem_number": 2576,
    "slug": "propagation-complete-five-bit-parity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:34+00:00",
    "updated_at": "2026-08-01T02:26:29+00:00"
  },
  "P9242": {
    "problem_number": 9242,
    "slug": "open-fc-8fa5763c0822b32c0e02-green-37",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:17+00:00",
    "updated_at": "2026-08-17T19:50:18+00:00"
  },
  "P2502": {
    "problem_number": 2502,
    "slug": "regular-nonagon-tree-dilation",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:08+00:00",
    "updated_at": "2026-08-01T23:45:28+00:00"
  },
  "P3750": {
    "problem_number": 3750,
    "slug": "torus-five-gossip-rounds",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:09+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9124": {
    "problem_number": 9124,
    "slug": "open-fc-d8fde6d2376d1ac2e2c0-green-77",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:42+00:00",
    "updated_at": "2026-08-17T19:47:42+00:00"
  },
  "P3720": {
    "problem_number": 3720,
    "slug": "circulant-sixteen-xor-circuit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:38+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12549": {
    "problem_number": 12549,
    "slug": "missing-zero-counts-in-ternary-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:47:06+00:00",
    "updated_at": "2026-09-02T21:47:43+00:00"
  },
  "P12061": {
    "problem_number": 12061,
    "slug": "modular-periods-of-an-implicit-hyperbolic-cosine-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:59:34+00:00",
    "updated_at": "2026-09-01T18:59:43+00:00"
  },
  "P9468": {
    "problem_number": 9468,
    "slug": "open-fc-82b03fae9252c6eb3b39-erdos-172",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:00+00:00",
    "updated_at": "2026-08-17T19:54:00+00:00"
  },
  "P3194": {
    "problem_number": 3194,
    "slug": "erdos-problem-172",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:51:05+00:00",
    "updated_at": "2026-08-12T05:51:10+00:00"
  },
  "P3318": {
    "problem_number": 3318,
    "slug": "erdos-problem-1199",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:51+00:00",
    "updated_at": "2026-08-12T06:04:56+00:00"
  },
  "P8856": {
    "problem_number": 8856,
    "slug": "open-fc-b44ff0bb93ec7c8e36d8-erdos-196",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:55+00:00",
    "updated_at": "2026-08-17T19:27:02+00:00"
  },
  "P12707": {
    "problem_number": 12707,
    "slug": "monotonic-prime-densities-at-integer-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:23:17+00:00",
    "updated_at": "2026-09-02T22:23:41+00:00"
  },
  "P12167": {
    "problem_number": 12167,
    "slug": "monotonicity-of-above-average-gaps-in-farey-sequences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:19:44+00:00",
    "updated_at": "2026-09-01T19:19:49+00:00"
  },
  "P2536": {
    "problem_number": 2536,
    "slug": "permutation-no-consecutive-adjacency-monotone",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:19+00:00",
    "updated_at": "2026-08-01T23:38:57+00:00"
  },
  "P12573": {
    "problem_number": 12573,
    "slug": "monotonicity-of-partition-divisor-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:50:43+00:00",
    "updated_at": "2026-09-02T21:50:50+00:00"
  },
  "P9020": {
    "problem_number": 9020,
    "slug": "open-fc-88a0c1772be8d92c5df2-erdos-85",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:16+00:00",
    "updated_at": "2026-08-17T19:45:18+00:00"
  },
  "P3018": {
    "problem_number": 3018,
    "slug": "erdos-problem-85",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:44+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8970": {
    "problem_number": 8970,
    "slug": "open-fc-6272af39beb7a44613ca-mosers-worm-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:00+00:00",
    "updated_at": "2026-08-17T19:44:01+00:00"
  },
  "P2702": {
    "problem_number": 2702,
    "slug": "cubic-graph-twenty-ising-degeneracy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:21+00:00",
    "updated_at": "2026-08-01T02:04:56+00:00"
  },
  "P3636": {
    "problem_number": 3636,
    "slug": "disjoint-conics-pg2-13",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:44+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2666": {
    "problem_number": 2666,
    "slug": "binomial-divisor-record-1e6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:06+00:00",
    "updated_at": "2026-08-01T02:03:11+00:00"
  },
  "P2662": {
    "problem_number": 2662,
    "slug": "irreducible-quintic-f101-slices",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:04+00:00",
    "updated_at": "2026-08-01T23:30:49+00:00"
  },
  "P2682": {
    "problem_number": 2682,
    "slug": "distinct-slopes-ten-grid",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:12+00:00",
    "updated_at": "2026-08-01T23:24:23+00:00"
  },
  "P3748": {
    "problem_number": 3748,
    "slug": "three-uniform-twelve-minimal-transversals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3762": {
    "problem_number": 3762,
    "slug": "two-cnf-ten-max-muses",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:38+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2676": {
    "problem_number": 2676,
    "slug": "circulant-spanning-trees-101-degree10",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:09+00:00",
    "updated_at": "2026-08-01T23:22:21+00:00"
  },
  "P2716": {
    "problem_number": 2716,
    "slug": "twenty-points-ten-grid-max-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:27+00:00",
    "updated_at": "2026-07-29T20:56:59+00:00"
  },
  "P3640": {
    "problem_number": 3640,
    "slug": "unit-area-triangles-twenty-eight-grid",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:53+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3476": {
    "problem_number": 3476,
    "slug": "kourovka-21-98-multilinear-commutator-values-covered-by-cyclic-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:20+00:00",
    "updated_at": "2026-08-12T08:06:25+00:00"
  },
  "P2602": {
    "problem_number": 2602,
    "slug": "threshold-at-least-three-six-multiplicative-complexity",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:42+00:00",
    "updated_at": "2026-08-01T23:51:06+00:00"
  },
  "P8768": {
    "problem_number": 8768,
    "slug": "open-fc-7a48bdfda19df380c2ca-green-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:15:01+00:00",
    "updated_at": "2026-08-17T19:15:12+00:00"
  },
  "P12591": {
    "problem_number": 12591,
    "slug": "must-every-e-perfect-number-be-divisible-by-36",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:53:28+00:00",
    "updated_at": "2026-09-02T21:54:02+00:00"
  },
  "P11286": {
    "problem_number": 11286,
    "slug": "fibonacci-divisibility-squarefree-condition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:19:12+00:00",
    "updated_at": "2026-08-29T18:50:32+00:00"
  },
  "P11514": {
    "problem_number": 11514,
    "slug": "primitive-prime-powers-are-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:40:09+00:00",
    "updated_at": "2026-08-29T18:54:07+00:00"
  },
  "P9138": {
    "problem_number": 9138,
    "slug": "open-fc-e38182563d8f846bd141-erdos-218-variants-ge",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:46+00:00",
    "updated_at": "2026-08-17T19:47:46+00:00"
  },
  "P8566": {
    "problem_number": 8566,
    "slug": "open-fc-79b74a3532a97ec12735-erdos-218-variants-le",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:55:05+00:00",
    "updated_at": "2026-08-17T18:55:06+00:00"
  },
  "P3316": {
    "problem_number": 3316,
    "slug": "erdos-problem-218",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:04:41+00:00",
    "updated_at": "2026-08-12T06:04:50+00:00"
  },
  "P17": {
    "problem_number": 17,
    "slug": "navier-stokes-existence-and-smoothness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:19:05+00:00"
  },
  "P12087": {
    "problem_number": 12087,
    "slug": "near-minimal-composite-products-one-below-a-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:09:33+00:00",
    "updated_at": "2026-09-01T19:09:39+00:00"
  },
  "P8368": {
    "problem_number": 8368,
    "slug": "open-fc-25637c0cf1d6994ce266-latinsquareneartransversal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:44+00:00",
    "updated_at": "2026-08-17T18:48:37+00:00"
  },
  "P2718": {
    "problem_number": 2718,
    "slug": "hard-square-sixteen-zero-radius",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:28+00:00",
    "updated_at": "2026-08-01T02:09:54+00:00"
  },
  "P12213": {
    "problem_number": 12213,
    "slug": "negative-simple-roots-in-an-orthogonal-polynomial-family",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:25:19+00:00",
    "updated_at": "2026-09-01T19:25:25+00:00"
  },
  "P12475": {
    "problem_number": 12475,
    "slug": "next-prime-gaps-and-sierpinski-witnesses",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:39:40+00:00",
    "updated_at": "2026-09-02T21:39:48+00:00"
  },
  "P10064": {
    "problem_number": 10064,
    "slug": "open-fc-ee59915aee76368066c1-kotherconjecture-variants-two-by-two-matrix",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:04+00:00",
    "updated_at": "2026-08-17T20:06:06+00:00"
  },
  "P9214": {
    "problem_number": 9214,
    "slug": "open-fc-689148c79f0de0ff2295-kotherconjecture-variants-general-matrix",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:36+00:00",
    "updated_at": "2026-08-17T19:49:36+00:00"
  },
  "P3744": {
    "problem_number": 3744,
    "slug": "c4-saturation-game-k8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:50:59+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3652": {
    "problem_number": 3652,
    "slug": "lee-code-seventeen-square-nineteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:04+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11847": {
    "problem_number": 11847,
    "slug": "no-consecutive-factorial-prime-indices",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:14:45+00:00",
    "updated_at": "2026-08-30T16:14:49+00:00"
  },
  "P10764": {
    "problem_number": 10764,
    "slug": "unsolvedmath-0133-no-three-in-line-in-n-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:07+00:00",
    "updated_at": "2026-08-18T02:55:08+00:00"
  },
  "P3642": {
    "problem_number": 3642,
    "slug": "triangular-grid-side-eleven-no-three-collinear",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:56+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9680": {
    "problem_number": 9680,
    "slug": "open-fc-7abad9970b9741e9e157-eqsystem6-no-solution-d5-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:17+00:00",
    "updated_at": "2026-08-17T20:01:19+00:00"
  },
  "P8096": {
    "problem_number": 8096,
    "slug": "open-fc-02248f7b6878183c5212-eqsystem6-no-solution-d3-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:40+00:00",
    "updated_at": "2026-08-17T18:34:40+00:00"
  },
  "P9220": {
    "problem_number": 9220,
    "slug": "open-fc-71cf0b8f8d3e20ba67d1-eqsystem10-no-solution-d3-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:41+00:00",
    "updated_at": "2026-08-17T19:49:43+00:00"
  },
  "P8648": {
    "problem_number": 8648,
    "slug": "open-fc-4aafbff34b4abc3008ad-eqsystem6-no-solution-d3-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:12+00:00",
    "updated_at": "2026-08-17T18:59:28+00:00"
  },
  "P8730": {
    "problem_number": 8730,
    "slug": "open-fc-4c06252a0ccd69d745a7-eqsystem10-no-solution-d3-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:33+00:00",
    "updated_at": "2026-08-17T19:11:45+00:00"
  },
  "P9998": {
    "problem_number": 9998,
    "slug": "open-fc-baea5828de829b469542-eqsystem-no-solution-ge6-ge3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:18+00:00",
    "updated_at": "2026-08-17T20:05:18+00:00"
  },
  "P8734": {
    "problem_number": 8734,
    "slug": "open-fc-4e07ea87fea254e28b98-eqsystem10-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:11:48+00:00",
    "updated_at": "2026-08-17T19:11:59+00:00"
  },
  "P9552": {
    "problem_number": 9552,
    "slug": "open-fc-c28a323c929d83a14ee1-eqsystem16-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:11+00:00",
    "updated_at": "2026-08-17T19:55:12+00:00"
  },
  "P8974": {
    "problem_number": 8974,
    "slug": "open-fc-66f9f02950b056615269-eqsystem8-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:06+00:00",
    "updated_at": "2026-08-17T19:44:07+00:00"
  },
  "P9774": {
    "problem_number": 9774,
    "slug": "open-fc-c903e1972a78c5e05fb1-eqsystem8-no-solution-d3-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:32+00:00",
    "updated_at": "2026-08-17T20:02:33+00:00"
  },
  "P9586": {
    "problem_number": 9586,
    "slug": "open-fc-de2f3449cd5e65ff6f7a-eqsystem14-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:09+00:00",
    "updated_at": "2026-08-17T19:56:11+00:00"
  },
  "P8404": {
    "problem_number": 8404,
    "slug": "open-fc-2a9aac12024221450f56-eqsystem-no-solution-ge6-ge3-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:33+00:00",
    "updated_at": "2026-08-17T18:49:39+00:00"
  },
  "P8638": {
    "problem_number": 8638,
    "slug": "open-fc-476b800fceffc204a578-eqsystem6-no-solution-ge3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:58+00:00",
    "updated_at": "2026-08-17T18:58:59+00:00"
  },
  "P8716": {
    "problem_number": 8716,
    "slug": "open-fc-35f28eaae701216e2d5d-eqsystem6-no-solution-d5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:10:37+00:00",
    "updated_at": "2026-08-17T19:10:51+00:00"
  },
  "P9706": {
    "problem_number": 9706,
    "slug": "open-fc-987bd5826ac578233e4a-eqsystem6-no-solution-d4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:58+00:00",
    "updated_at": "2026-08-17T20:01:59+00:00"
  },
  "P9818": {
    "problem_number": 9818,
    "slug": "open-fc-ee188244adf14c6f0211-eqsystem6-no-solution-ge3-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:56+00:00",
    "updated_at": "2026-08-17T20:02:56+00:00"
  },
  "P8398": {
    "problem_number": 8398,
    "slug": "open-fc-28e840e23c56233e44b6-eqsystem6-no-solution-d3-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:21+00:00",
    "updated_at": "2026-08-17T18:49:23+00:00"
  },
  "P9934": {
    "problem_number": 9934,
    "slug": "open-fc-89703ca44b8a8517e5b9-eqsystem6-no-solution-ge3-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:40+00:00",
    "updated_at": "2026-08-17T20:04:41+00:00"
  },
  "P8432": {
    "problem_number": 8432,
    "slug": "open-fc-323d82c6fc6df177b023-eqsystem6-no-solution-d5-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:04+00:00",
    "updated_at": "2026-08-17T18:52:05+00:00"
  },
  "P9672": {
    "problem_number": 9672,
    "slug": "open-fc-6d19314a7e6ae42d689d-eqsystem10-no-solution-d8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:03+00:00",
    "updated_at": "2026-08-17T20:01:04+00:00"
  },
  "P9654": {
    "problem_number": 9654,
    "slug": "open-fc-50b67111a02058dd58c9-eqsystem10-no-solution-d5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:35+00:00",
    "updated_at": "2026-08-17T20:00:36+00:00"
  },
  "P9900": {
    "problem_number": 9900,
    "slug": "open-fc-7039b374c57e5ff928f2-eqsystem10-no-solution-d4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:22+00:00",
    "updated_at": "2026-08-17T20:04:23+00:00"
  },
  "P9160": {
    "problem_number": 9160,
    "slug": "open-fc-f2b9b79aedf9b8fe62fa-eqsystem10-no-solution-d9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:53+00:00",
    "updated_at": "2026-08-17T19:47:53+00:00"
  },
  "P10080": {
    "problem_number": 10080,
    "slug": "open-fc-f7cced06934857e06eb0-eqsystem10-no-solution-d7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:17+00:00",
    "updated_at": "2026-08-17T20:06:18+00:00"
  },
  "P9804": {
    "problem_number": 9804,
    "slug": "open-fc-e2d0b0614cf317b672f8-eqsystem10-no-solution-d6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:47+00:00",
    "updated_at": "2026-08-17T20:02:48+00:00"
  },
  "P9134": {
    "problem_number": 9134,
    "slug": "open-fc-e1c9eff0755ccf979604-eqsystem-no-solution-ge6-ge3-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:45+00:00",
    "updated_at": "2026-08-17T19:47:45+00:00"
  },
  "P8118": {
    "problem_number": 8118,
    "slug": "open-fc-03fc76ff3f512837bc31-eqsystem12-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:46+00:00",
    "updated_at": "2026-08-17T18:34:48+00:00"
  },
  "P2998": {
    "problem_number": 2998,
    "slug": "erdos-problem-50",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:13+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8756": {
    "problem_number": 8756,
    "slug": "open-fc-63da559efa5fde6bbfac-erdos-50",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:13:42+00:00",
    "updated_at": "2026-08-17T19:13:55+00:00"
  },
  "P8684": {
    "problem_number": 8684,
    "slug": "open-fc-35b6b4cf93d9ee57227b-eqsystem-no-solution-ge6-ge3-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:46+00:00",
    "updated_at": "2026-08-17T19:04:47+00:00"
  },
  "P8296": {
    "problem_number": 8296,
    "slug": "open-fc-1d4772706f8dc1659a8c-eqsystem8-no-solution-d3-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:42+00:00",
    "updated_at": "2026-08-17T18:38:48+00:00"
  },
  "P9764": {
    "problem_number": 9764,
    "slug": "open-fc-c3bc28d12e0f059aaf7f-eqsystem6-no-solution-d5-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:27+00:00",
    "updated_at": "2026-08-17T20:02:27+00:00"
  },
  "P8252": {
    "problem_number": 8252,
    "slug": "open-fc-1650e3fcee69061ba11b-eqsystem10-no-solution-d3-real",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:45+00:00",
    "updated_at": "2026-08-17T18:37:47+00:00"
  },
  "P9838": {
    "problem_number": 9838,
    "slug": "open-fc-fb43dd014012f05f1e67-eqsystem6-no-solution-ge3-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:05+00:00",
    "updated_at": "2026-08-17T20:03:06+00:00"
  },
  "P9406": {
    "problem_number": 9406,
    "slug": "open-fc-5134ff89f0f43f1e9785-eqsystem8-no-solution-d3-trinary-int",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:25+00:00",
    "updated_at": "2026-08-17T19:52:26+00:00"
  },
  "P9624": {
    "problem_number": 9624,
    "slug": "open-fc-f6d592a5852f5efbc107-beaver-math-olympiad-problem-2-antihydra",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:26+00:00",
    "updated_at": "2026-08-17T19:57:27+00:00"
  },
  "P3424": {
    "problem_number": 3424,
    "slug": "kourovka-21-42-non-self-similar-three-generator-nilpotent-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:59:24+00:00",
    "updated_at": "2026-08-12T07:59:28+00:00"
  },
  "P9904": {
    "problem_number": 9904,
    "slug": "open-fc-7371e51e9d4cf40b9af5-erdos-91",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:25+00:00",
    "updated_at": "2026-08-17T20:04:25+00:00"
  },
  "P3022": {
    "problem_number": 3022,
    "slug": "erdos-problem-91",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:50+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8130": {
    "problem_number": 8130,
    "slug": "open-fc-04e17693b1d02326d7e9-problem-10-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:57+00:00",
    "updated_at": "2026-08-17T18:34:57+00:00"
  },
  "P9404": {
    "problem_number": 9404,
    "slug": "open-fc-50a1553c877b37c6241f-twofiveperfect",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:23+00:00",
    "updated_at": "2026-08-17T19:52:24+00:00"
  },
  "P9328": {
    "problem_number": 9328,
    "slug": "open-fc-cf9fabb2b30121acaa87-eqsystem6-no-solution-d3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:55+00:00",
    "updated_at": "2026-08-17T19:50:55+00:00"
  },
  "P8904": {
    "problem_number": 8904,
    "slug": "open-fc-d69ee9e75fa0b20e6c41-lander-parkin-selfridge-variants-five-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:10+00:00",
    "updated_at": "2026-08-17T19:40:10+00:00"
  },
  "P38": {
    "problem_number": 38,
    "slug": "nonexistence-of-odd-perfect-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:20:28+00:00"
  },
  "P11917": {
    "problem_number": 11917,
    "slug": "nonexistence-of-odd-superperfect-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:22:54+00:00",
    "updated_at": "2026-08-30T16:23:02+00:00"
  },
  "P11818": {
    "problem_number": 11818,
    "slug": "noninitial-fixed-points-in-a-two-predecessor-prime-factor-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:57:27+00:00",
    "updated_at": "2026-08-30T12:59:12+00:00"
  },
  "P12037": {
    "problem_number": 12037,
    "slug": "nonmerging-gcd-growth-sequences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:54:47+00:00",
    "updated_at": "2026-09-01T18:54:58+00:00"
  },
  "P12101": {
    "problem_number": 12101,
    "slug": "nonnegative-liouville-sums-along-the-yellowstone-permutation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:11:13+00:00",
    "updated_at": "2026-09-01T19:11:18+00:00"
  },
  "P11991": {
    "problem_number": 11991,
    "slug": "nontrivial-cycles-of-the-5x-plus-1-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:30:05+00:00",
    "updated_at": "2026-09-01T18:30:35+00:00"
  },
  "P2422": {
    "problem_number": 2422,
    "slug": "baum-sweet-hankel-nonvanishing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-24T21:54:03+00:00",
    "updated_at": "2026-07-30T02:23:55+00:00"
  },
  "P2420": {
    "problem_number": 2420,
    "slug": "rudin-shapiro-hankel-nonvanishing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-24T21:53:53+00:00",
    "updated_at": "2026-07-30T02:27:44+00:00"
  },
  "P12117": {
    "problem_number": 12117,
    "slug": "nonvanishing-prime-sum-hankel-determinants-after-size-fifteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:13:34+00:00",
    "updated_at": "2026-09-01T19:13:40+00:00"
  },
  "P1": {
    "problem_number": 1,
    "slug": "fib-problem-nonzero-support",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T00:55:55+00:00",
    "updated_at": "2026-07-22T00:55:55+00:00"
  },
  "P3446": {
    "problem_number": 3446,
    "slug": "kourovka-21-64-normal-subgroups-of-sylow-subgroups-in-p-soluble-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:04:10+00:00",
    "updated_at": "2026-08-12T08:04:12+00:00"
  },
  "P12575": {
    "problem_number": 12575,
    "slug": "normality-of-concatenated-prime-repetends",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:50:57+00:00",
    "updated_at": "2026-09-02T21:51:05+00:00"
  },
  "P12185": {
    "problem_number": 12185,
    "slug": "normality-of-the-decimal-prime-gap-constant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:21:56+00:00",
    "updated_at": "2026-09-01T19:22:01+00:00"
  },
  "P8424": {
    "problem_number": 8424,
    "slug": "open-fc-2d86105e808a3b9d0cf7-pi-normal-base-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:02+00:00",
    "updated_at": "2026-08-17T18:52:02+00:00"
  },
  "P51": {
    "problem_number": 51,
    "slug": "novikov-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:21:05+00:00"
  },
  "P2660": {
    "problem_number": 2660,
    "slug": "reduced-latin-squares-order-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:03+00:00",
    "updated_at": "2026-07-29T20:56:27+00:00"
  },
  "P2728": {
    "problem_number": 2728,
    "slug": "real-singular-binary-matrices-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:33+00:00",
    "updated_at": "2026-07-29T20:56:21+00:00"
  },
  "P10222": {
    "problem_number": 10222,
    "slug": "open-fc-cd64c8760c7392c647e7-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:51+00:00",
    "updated_at": "2026-08-18T02:51:52+00:00"
  },
  "P10098": {
    "problem_number": 10098,
    "slug": "open-fc-0fac83b214e18c2058e1-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:09+00:00",
    "updated_at": "2026-08-18T02:51:09+00:00"
  },
  "P10198": {
    "problem_number": 10198,
    "slug": "open-fc-9a41d0ec72a9d6ee2ffb-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:43+00:00",
    "updated_at": "2026-08-18T02:51:43+00:00"
  },
  "P10120": {
    "problem_number": 10120,
    "slug": "open-fc-1d7a93be57678321acb2-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:16+00:00",
    "updated_at": "2026-08-18T02:51:16+00:00"
  },
  "P10168": {
    "problem_number": 10168,
    "slug": "open-fc-4d9a348f49a5f7ddc974-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:32+00:00",
    "updated_at": "2026-08-18T02:51:33+00:00"
  },
  "P10176": {
    "problem_number": 10176,
    "slug": "open-fc-6686542cdec5ba5d35b9-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:35+00:00",
    "updated_at": "2026-08-18T02:51:35+00:00"
  },
  "P10226": {
    "problem_number": 10226,
    "slug": "open-fc-cedb9f3e928437599556-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:53+00:00",
    "updated_at": "2026-08-18T02:51:54+00:00"
  },
  "P10224": {
    "problem_number": 10224,
    "slug": "open-fc-cdbdcc34d1b9513ac931-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:52+00:00",
    "updated_at": "2026-08-18T02:51:53+00:00"
  },
  "P10188": {
    "problem_number": 10188,
    "slug": "open-fc-85e97fdb17c1e84152ac-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:39+00:00",
    "updated_at": "2026-08-18T02:51:40+00:00"
  },
  "P10212": {
    "problem_number": 10212,
    "slug": "open-fc-bd58a5e0b4e4bd5c28ce-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:48+00:00",
    "updated_at": "2026-08-18T02:51:48+00:00"
  },
  "P10156": {
    "problem_number": 10156,
    "slug": "open-fc-40fec66fb04d2b6d7dc9-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:28+00:00",
    "updated_at": "2026-08-18T02:51:28+00:00"
  },
  "P12523": {
    "problem_number": 12523,
    "slug": "numbers-sharing-their-cube-s-digit-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:44:23+00:00",
    "updated_at": "2026-09-02T21:44:35+00:00"
  },
  "P8954": {
    "problem_number": 8954,
    "slug": "open-fc-fb51ff49d43d188e3fe7-erdos-593-variants-obligatory-implies-two-colorable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:17+00:00",
    "updated_at": "2026-08-17T19:41:17+00:00"
  },
  "P12711": {
    "problem_number": 12711,
    "slug": "odd-and-even-fundamental-discriminants-of-fixed-class-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:26:02+00:00",
    "updated_at": "2026-09-02T22:26:28+00:00"
  },
  "P9286": {
    "problem_number": 9286,
    "slug": "open-fc-af809432e52e43486c9e-odd-perfect-number-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:38+00:00",
    "updated_at": "2026-08-17T19:50:38+00:00"
  },
  "P12635": {
    "problem_number": 12635,
    "slug": "odd-squarefree-kernels-of-binomial-row-lcms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:06:08+00:00",
    "updated_at": "2026-09-02T22:06:41+00:00"
  },
  "P12175": {
    "problem_number": 12175,
    "slug": "odd-values-missing-from-the-aliquot-difference-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:20:42+00:00",
    "updated_at": "2026-09-01T19:20:48+00:00"
  },
  "P12513": {
    "problem_number": 12513,
    "slug": "odious-and-evil-prime-inequalities",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:43:18+00:00",
    "updated_at": "2026-09-02T21:43:30+00:00"
  },
  "P11812": {
    "problem_number": 11812,
    "slug": "off-edge-traps-for-the-diagonally-numbered-greedy-knight",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:48:59+00:00",
    "updated_at": "2026-08-30T16:36:12+00:00"
  },
  "P11833": {
    "problem_number": 11833,
    "slug": "on-eigenvalue-bounds-for-bounded-genus-graphs-and-minor-free-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T15:59:24+00:00",
    "updated_at": "2026-09-06T16:00:00.337587+00:00"
  },
  "P11831": {
    "problem_number": 11831,
    "slug": "on-some-aspects-of-discrete-groups-acting-ergodically-on-the-boundary",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T15:57:19+00:00",
    "updated_at": "2026-09-06T16:00:00.337587+00:00"
  },
  "P12469": {
    "problem_number": 12469,
    "slug": "one-bits-in-powers-of-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:39:04+00:00",
    "updated_at": "2026-09-02T21:39:15+00:00"
  },
  "P2924": {
    "problem_number": 2924,
    "slug": "l1z-convolution-open-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:48:38+00:00",
    "updated_at": "2026-08-01T23:33:05+00:00"
  },
  "P9656": {
    "problem_number": 9656,
    "slug": "open-fc-54f0fcabc7431b6c97c5-oppermann-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:39+00:00",
    "updated_at": "2026-08-17T20:00:41+00:00"
  },
  "P9682": {
    "problem_number": 9682,
    "slug": "open-fc-7e1a2b04e0fd3b350e5f-oppermann-conjecture-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:21+00:00",
    "updated_at": "2026-08-17T20:01:24+00:00"
  },
  "P8436": {
    "problem_number": 8436,
    "slug": "open-fc-34b1e7271007acfea42d-opposite-parity-amicable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:05+00:00",
    "updated_at": "2026-08-17T18:52:05+00:00"
  },
  "P2590": {
    "problem_number": 2590,
    "slug": "balanced-subset-mastermind-twelve",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:38+00:00",
    "updated_at": "2026-08-01T02:02:47+00:00"
  },
  "P9538": {
    "problem_number": 9538,
    "slug": "open-fc-b67493b4e8dc5b94208b-erdos-887-variants-rosenfeld-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:49+00:00",
    "updated_at": "2026-08-17T19:54:51+00:00"
  },
  "P3728": {
    "problem_number": 3728,
    "slug": "avoider-triangle-k8-survival",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:47:08+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2518": {
    "problem_number": 2518,
    "slug": "optimal-three-point-c2-quadrature",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:13+00:00",
    "updated_at": "2026-08-01T23:37:41+00:00"
  },
  "P8452": {
    "problem_number": 8452,
    "slug": "open-fc-3dffe2ddd7168197aa5c-green-42",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:09+00:00",
    "updated_at": "2026-08-17T18:52:10+00:00"
  },
  "P3288": {
    "problem_number": 3288,
    "slug": "erdos-problem-1084",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:57+00:00",
    "updated_at": "2026-08-12T06:03:04+00:00"
  },
  "P12441": {
    "problem_number": 12441,
    "slug": "order-consecutive-set-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:36:06+00:00",
    "updated_at": "2026-09-02T21:36:17+00:00"
  },
  "P3360": {
    "problem_number": 3360,
    "slug": "kourovka-21-2-order-divisibility-bijections-with-finite-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:40:35+00:00",
    "updated_at": "2026-08-12T07:40:56+00:00"
  },
  "P2878": {
    "problem_number": 2878,
    "slug": "ternary-orthogonal-full-row-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:42:30+00:00",
    "updated_at": "2026-08-01T12:32:33+00:00"
  },
  "P11104": {
    "problem_number": 11104,
    "slug": "ordinary-partition-reciprocal-coprimality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T07:32:59+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P3552": {
    "problem_number": 3552,
    "slug": "kourovka-21-149-outer-order-automorphisms-of-dlab-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:15:03+00:00",
    "updated_at": "2026-08-12T08:15:10+00:00"
  },
  "P39": {
    "problem_number": 39,
    "slug": "p-versus-np",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:22:49+00:00"
  },
  "P12485": {
    "problem_number": 12485,
    "slug": "p-adic-growth-in-a-sqrt-2-factorial-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:39+00:00",
    "updated_at": "2026-09-02T21:40:46+00:00"
  },
  "P3656": {
    "problem_number": 3656,
    "slug": "cross-pentomino-pack-thirty-grid-158",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8102": {
    "problem_number": 8102,
    "slug": "open-fc-02b5b2c97d5251d9d909-rectangles-pack-unit-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:41+00:00",
    "updated_at": "2026-08-17T18:34:42+00:00"
  },
  "P12463": {
    "problem_number": 12463,
    "slug": "palindromic-primes-with-digit-sum-eleven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:38:22+00:00",
    "updated_at": "2026-09-02T21:38:34+00:00"
  },
  "P12767": {
    "problem_number": 12767,
    "slug": "palindromic-difference-subsequences-and-constrained-subsets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:49:46+00:00",
    "updated_at": "2026-09-02T22:50:22+00:00"
  },
  "P12397": {
    "problem_number": 12397,
    "slug": "parity-of-the-least-preimage-under-euler-s-totient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:31:46+00:00",
    "updated_at": "2026-09-02T21:31:54+00:00"
  },
  "P11826": {
    "problem_number": 11826,
    "slug": "parity-pairing-when-euler-s-totient-has-exactly-two-preimages",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T13:06:02+00:00",
    "updated_at": "2026-08-30T13:08:00+00:00"
  },
  "P12187": {
    "problem_number": 12187,
    "slug": "parity-controlled-growth-of-strict-knapsack-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:22:11+00:00",
    "updated_at": "2026-09-01T19:22:16+00:00"
  },
  "P3356": {
    "problem_number": 3356,
    "slug": "kourovka-21-89-partition-divisibility",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:53:58+00:00",
    "updated_at": "2026-08-12T06:55:09+00:00"
  },
  "P9892": {
    "problem_number": 9892,
    "slug": "open-fc-69f54bcb62ae4d049b1f-erdos-197",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:18+00:00",
    "updated_at": "2026-08-17T20:04:20+00:00"
  },
  "P14": {
    "problem_number": 14,
    "slug": "perfect-cuboid-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:23:17+00:00"
  },
  "P11180": {
    "problem_number": 11180,
    "slug": "perfect-mondrian-partition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T07:40:49+00:00",
    "updated_at": "2026-09-02T08:00:00.749162+00:00"
  },
  "P9562": {
    "problem_number": 9562,
    "slug": "open-fc-c7f13af870397c31a05c-nopowerpartitionnumber",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:22+00:00",
    "updated_at": "2026-08-17T19:55:24+00:00"
  },
  "P11953": {
    "problem_number": 11953,
    "slug": "perfect-powers-among-the-values-pi-2-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:35:07+00:00",
    "updated_at": "2026-08-30T16:35:21+00:00"
  },
  "P3178": {
    "problem_number": 3178,
    "slug": "erdos-problem-672",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:49:28+00:00",
    "updated_at": "2026-08-12T05:49:30+00:00"
  },
  "P8162": {
    "problem_number": 8162,
    "slug": "open-fc-093c7a4e9886719e6e75-erdos-672",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:36+00:00",
    "updated_at": "2026-08-17T18:35:46+00:00"
  },
  "P8094": {
    "problem_number": 8094,
    "slug": "open-fc-01f3a77237b3f3f6320c-erdos-930",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:39+00:00",
    "updated_at": "2026-08-17T18:34:40+00:00"
  },
  "P12221": {
    "problem_number": 12221,
    "slug": "period-k-congruences-for-a-factorial-binomial-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:26:17+00:00",
    "updated_at": "2026-09-01T19:26:22+00:00"
  },
  "P3474": {
    "problem_number": 3474,
    "slug": "kourovka-21-96-periodic-groups-with-locally-finite-even-centralizers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:06:16+00:00",
    "updated_at": "2026-08-12T08:06:18+00:00"
  },
  "P12253": {
    "problem_number": 12253,
    "slug": "periodic-second-differences-in-the-tetrastix-graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:30:14+00:00",
    "updated_at": "2026-09-01T19:30:21+00:00"
  },
  "P12489": {
    "problem_number": 12489,
    "slug": "periods-of-langton-ant-block-colonies",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:58+00:00",
    "updated_at": "2026-09-02T21:41:11+00:00"
  },
  "P11804": {
    "problem_number": 11804,
    "slug": "permutation-behavior-of-the-proper-divisor-count-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:45:43+00:00",
    "updated_at": "2026-08-30T12:45:53+00:00"
  },
  "P11642": {
    "problem_number": 11642,
    "slug": "permutation-status-of-the-distinct-sum-product-omega-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:42:33+00:00",
    "updated_at": "2026-08-30T04:42:40+00:00"
  },
  "P3096": {
    "problem_number": 3096,
    "slug": "euler-material-line-exponential-growth",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:59+00:00",
    "updated_at": "2026-08-02T12:49:15+00:00"
  },
  "P11925": {
    "problem_number": 11925,
    "slug": "persistent-leading-divisor-count-classes-in-a-feedback-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:23:48+00:00",
    "updated_at": "2026-08-30T16:23:56+00:00"
  },
  "P9140": {
    "problem_number": 9140,
    "slug": "open-fc-e68cd5c0b145f7d6ba4b-pillais-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:47+00:00",
    "updated_at": "2026-08-17T19:47:47+00:00"
  },
  "P12363": {
    "problem_number": 12363,
    "slug": "pillai-s-fixed-gap-conjecture-for-consecutive-perfect-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:43:38+00:00",
    "updated_at": "2026-09-01T19:43:43+00:00"
  },
  "P2922": {
    "problem_number": 2922,
    "slug": "planar-drums-finitely-different-spectra",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:48:22+00:00",
    "updated_at": "2026-08-01T23:40:36+00:00"
  },
  "P24": {
    "problem_number": 24,
    "slug": "plane-jacobian-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:24:12+00:00"
  },
  "P2892": {
    "problem_number": 2892,
    "slug": "five-cell-lattice-animal-plane-tiling",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:44:24+00:00",
    "updated_at": "2026-08-01T23:27:21+00:00"
  },
  "P9720": {
    "problem_number": 9720,
    "slug": "open-fc-a0eb6233550486abeb29-polignac-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:04+00:00",
    "updated_at": "2026-08-17T20:02:04+00:00"
  },
  "P9484": {
    "problem_number": 9484,
    "slug": "open-fc-8df8f0e6349fea119823-pollock-tetrahedral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:15+00:00",
    "updated_at": "2026-08-17T19:54:17+00:00"
  },
  "P9196": {
    "problem_number": 9196,
    "slug": "open-fc-4afc280dab268af04f40-babai-seress-conjecture-alternating",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:10+00:00",
    "updated_at": "2026-08-17T19:49:11+00:00"
  },
  "P2832": {
    "problem_number": 2832,
    "slug": "two-way-nfa-polynomial-determinization",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:04+00:00",
    "updated_at": "2026-07-30T00:55:16+00:00"
  },
  "P12547": {
    "problem_number": 12547,
    "slug": "polynomial-factors-in-fibonacci-bit-columns",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:46:53+00:00",
    "updated_at": "2026-09-02T21:47:02+00:00"
  },
  "P9390": {
    "problem_number": 9390,
    "slug": "open-fc-ffb55ef696835e572191-green-14-polynomial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:21+00:00",
    "updated_at": "2026-08-17T19:51:21+00:00"
  },
  "P9826": {
    "problem_number": 9826,
    "slug": "open-fc-f277f8591e1429ac96ac-erdos-18c",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:01+00:00",
    "updated_at": "2026-08-17T20:03:01+00:00"
  },
  "P9136": {
    "problem_number": 9136,
    "slug": "open-fc-e27029f97db61b9ece29-erdos-961",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:46+00:00",
    "updated_at": "2026-08-17T19:47:46+00:00"
  },
  "P8992": {
    "problem_number": 8992,
    "slug": "open-fc-73d4bf9c98aa07cf12f8-green-29",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:30+00:00",
    "updated_at": "2026-08-17T19:44:31+00:00"
  },
  "P12113": {
    "problem_number": 12113,
    "slug": "polynomial-recurrences-for-coefficient-subsequences-of-a103885",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:13:05+00:00",
    "updated_at": "2026-09-01T19:13:11+00:00"
  },
  "P10774": {
    "problem_number": 10774,
    "slug": "unsolvedmath-1099-polynomial-solutions-in-dense-sets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:10+00:00",
    "updated_at": "2026-08-18T02:55:11+00:00"
  },
  "P9662": {
    "problem_number": 9662,
    "slug": "open-fc-5e11e711e8f082f6e3a9-green-41-variants-polynomial-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:49+00:00",
    "updated_at": "2026-08-17T20:00:51+00:00"
  },
  "P3568": {
    "problem_number": 3568,
    "slug": "cvp-polynomial-hardness",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:52:43+00:00",
    "updated_at": "2026-08-18T06:09:33+00:00"
  },
  "P11961": {
    "problem_number": 11961,
    "slug": "polynomial-time-recognition-of-squarefree-and-triangular-divisor-free-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:53:34+00:00",
    "updated_at": "2026-08-31T03:53:37+00:00"
  },
  "P3130": {
    "problem_number": 3130,
    "slug": "planted-clique-below-square-root",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:07+00:00",
    "updated_at": "2026-08-02T12:54:28+00:00"
  },
  "P8480": {
    "problem_number": 8480,
    "slug": "open-fc-4aa7b12bf923b16737cc-agrawal-conjecture-variants-popovych",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:20+00:00",
    "updated_at": "2026-08-17T18:52:21+00:00"
  },
  "P9262": {
    "problem_number": 9262,
    "slug": "open-fc-9ce93c6c33490ca56b83-erdos-340-variants-sub-hasposdensity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:29+00:00",
    "updated_at": "2026-08-17T19:50:29+00:00"
  },
  "P8428": {
    "problem_number": 8428,
    "slug": "open-fc-2f9077233b9d5e1920ca-erdos-968",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:03+00:00",
    "updated_at": "2026-08-17T18:52:03+00:00"
  },
  "P9478": {
    "problem_number": 9478,
    "slug": "open-fc-8925e1028056b93bec90-erdos-424",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:05+00:00",
    "updated_at": "2026-08-17T19:54:07+00:00"
  },
  "P8894": {
    "problem_number": 8894,
    "slug": "open-fc-ce28288cdff3b671719d-erdos-244",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:39:55+00:00",
    "updated_at": "2026-08-17T19:40:07+00:00"
  },
  "P3138": {
    "problem_number": 3138,
    "slug": "standard-map-positive-metric-entropy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:09+00:00",
    "updated_at": "2026-08-02T12:55:46+00:00"
  },
  "P4026": {
    "problem_number": 4026,
    "slug": "positive-toeplitz-operators-on-pluriharmonic-fock-space-schatten-class-criteria-and-sharp-norm-comparisons",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T19:52:36+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P2960": {
    "problem_number": 2960,
    "slug": "erdos-problem-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:27+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8198": {
    "problem_number": 8198,
    "slug": "open-fc-0d105d551d4a410a4abc-erdos-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:55+00:00",
    "updated_at": "2026-08-17T18:36:57+00:00"
  },
  "P9460": {
    "problem_number": 9460,
    "slug": "open-fc-7dfa7669466b99ba93b6-green-7-variants-positive-density",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:57+00:00",
    "updated_at": "2026-08-17T19:53:57+00:00"
  },
  "P8332": {
    "problem_number": 8332,
    "slug": "open-fc-2156ad68dd2df0aee835-conjecture-1-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:58+00:00",
    "updated_at": "2026-08-17T18:40:02+00:00"
  },
  "P2902": {
    "problem_number": 2902,
    "slug": "p-element-centralizer-generalized-character",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:45:43+00:00",
    "updated_at": "2026-08-01T12:22:25+00:00"
  },
  "P3532": {
    "problem_number": 3532,
    "slug": "kourovka-21-137-power-subgroups-in-finite-p-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:26+00:00",
    "updated_at": "2026-08-12T08:12:31+00:00"
  },
  "P9238": {
    "problem_number": 9238,
    "slug": "open-fc-88a7402bba0e6fe91791-erdos-978-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:16+00:00",
    "updated_at": "2026-08-17T19:50:16+00:00"
  },
  "P12071": {
    "problem_number": 12071,
    "slug": "power-sum-bases-counted-by-divisors-of-consecutive-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:08:00+00:00",
    "updated_at": "2026-09-01T19:08:06+00:00"
  },
  "P3042": {
    "problem_number": 3042,
    "slug": "erdos-problem-137",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:29:14+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8122": {
    "problem_number": 8122,
    "slug": "open-fc-048dfadf9b1116e7bc5c-erdos-137",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:50+00:00",
    "updated_at": "2026-08-17T18:34:52+00:00"
  },
  "P8150": {
    "problem_number": 8150,
    "slug": "open-fc-07a1fd8f126901835b02-erdos-936-variants-two-pow-add-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:20+00:00",
    "updated_at": "2026-08-17T18:35:21+00:00"
  },
  "P3286": {
    "problem_number": 3286,
    "slug": "erdos-problem-936",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:54+00:00",
    "updated_at": "2026-08-12T06:02:56+00:00"
  },
  "P9994": {
    "problem_number": 9994,
    "slug": "open-fc-b6fccb1d77e67ee6d34f-erdos-936-variants-factorial-add-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:16+00:00",
    "updated_at": "2026-08-17T20:05:17+00:00"
  },
  "P9896": {
    "problem_number": 9896,
    "slug": "open-fc-6d730fcd1af380df6f52-erdos-936-variants-two-pow-sub-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:22+00:00",
    "updated_at": "2026-08-17T20:04:22+00:00"
  },
  "P9928": {
    "problem_number": 9928,
    "slug": "open-fc-84bedebd72b6d33aa974-erdos-936-variants-factorial-sub-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:37+00:00",
    "updated_at": "2026-08-17T20:04:38+00:00"
  },
  "P3442": {
    "problem_number": 3442,
    "slug": "kourovka-21-61-presentations-of-finitely-generated-free-by-cyclic-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:03:25+00:00",
    "updated_at": "2026-08-12T08:03:43+00:00"
  },
  "P8654": {
    "problem_number": 8654,
    "slug": "open-fc-8dc544c725c3d668828e-mathoverflow-31809",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:38+00:00",
    "updated_at": "2026-08-17T18:59:50+00:00"
  },
  "P12621": {
    "problem_number": 12621,
    "slug": "primality-and-displacement-in-the-block-rotation-limit",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:58:33+00:00",
    "updated_at": "2026-09-02T22:29:37+00:00"
  },
  "P11706": {
    "problem_number": 11706,
    "slug": "primality-of-every-lesser-fortunate-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:16:20+00:00",
    "updated_at": "2026-08-30T11:16:27+00:00"
  },
  "P8682": {
    "problem_number": 8682,
    "slug": "open-fc-351944707595e5a15741-prime-add-one-of-a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:43+00:00",
    "updated_at": "2026-08-17T19:04:45+00:00"
  },
  "P12749": {
    "problem_number": 12749,
    "slug": "primality-or-weak-fermat-pseudoprimality-of-a-quotient",
    "resolution_state": "proved_formally",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": true,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "verified",
        "verified": true,
        "kernelAccepted": true,
        "label": "Lean-verified",
        "reason": "A current formalization has a pinned Lean world, a signed accepted verifier result, and an exact binding to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A signed Lean verification is attached.",
      "summary": "Resolved. Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:40:55+00:00",
    "updated_at": "2026-09-02T23:04:39+00:00"
  },
  "P9060": {
    "problem_number": 9060,
    "slug": "open-fc-a62298341ef69dbb0e3e-oppermann-conjecture-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:31+00:00",
    "updated_at": "2026-08-17T19:46:33+00:00"
  },
  "P8688": {
    "problem_number": 8688,
    "slug": "open-fc-3710028d9385d32a49c2-kurepa-conjecture-variants-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:54+00:00",
    "updated_at": "2026-08-17T19:04:57+00:00"
  },
  "P12097": {
    "problem_number": 12097,
    "slug": "prime-centers-minimizing-paired-totient-divisor-identities",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:10:43+00:00",
    "updated_at": "2026-09-01T19:10:49+00:00"
  },
  "P12351": {
    "problem_number": 12351,
    "slug": "prime-concatenations-of-three-consecutive-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:42:07+00:00",
    "updated_at": "2026-09-01T19:42:12+00:00"
  },
  "P12451": {
    "problem_number": 12451,
    "slug": "prime-coverage-by-odd-digit-sums-of-powers-of-seven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:37:13+00:00",
    "updated_at": "2026-09-02T21:37:25+00:00"
  },
  "P12715": {
    "problem_number": 12715,
    "slug": "prime-digit-permutations-with-optional-zeros",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:27:13+00:00",
    "updated_at": "2026-09-02T22:27:48+00:00"
  },
  "P11666": {
    "problem_number": 11666,
    "slug": "prime-digit-sums-using-only-3-and-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:04+00:00",
    "updated_at": "2026-08-30T16:33:45+00:00"
  },
  "P12275": {
    "problem_number": 12275,
    "slug": "prime-divisors-in-odd-digit-sums-of-powers-of-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:32:58+00:00",
    "updated_at": "2026-09-01T19:33:04+00:00"
  },
  "P12265": {
    "problem_number": 12265,
    "slug": "prime-divisors-of-a-quadratic-product-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:31:45+00:00",
    "updated_at": "2026-09-01T19:31:50+00:00"
  },
  "P2738": {
    "problem_number": 2738,
    "slug": "markoff-graph-prime-connectivity-exceptions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:00:38+00:00",
    "updated_at": "2026-08-16T22:56:14+00:00"
  },
  "P9172": {
    "problem_number": 9172,
    "slug": "open-fc-fb920e2dd304bcaf0a75-erdos-931-variants-exists-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:56+00:00",
    "updated_at": "2026-08-17T19:47:56+00:00"
  },
  "P12059": {
    "problem_number": 12059,
    "slug": "prime-indices-of-zeros-in-a-gcd-descent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:59:11+00:00",
    "updated_at": "2026-09-01T18:59:21+00:00"
  },
  "P12051": {
    "problem_number": 12051,
    "slug": "prime-occupancy-of-twin-prime-square-root-intervals",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:57:33+00:00",
    "updated_at": "2026-09-01T18:57:43+00:00"
  },
  "P12537": {
    "problem_number": 12537,
    "slug": "prime-offsets-after-factorials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:45:44+00:00",
    "updated_at": "2026-09-02T21:45:57+00:00"
  },
  "P8534": {
    "problem_number": 8534,
    "slug": "open-fc-684f87f3fbaa51fec507-erdos-287-variants-prime-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:20+00:00",
    "updated_at": "2026-08-17T18:54:21+00:00"
  },
  "P11983": {
    "problem_number": 11983,
    "slug": "prime-pairs-p-and-2p-minus-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:27:51+00:00",
    "updated_at": "2026-09-01T18:28:01+00:00"
  },
  "P12567": {
    "problem_number": 12567,
    "slug": "prime-pairs-symmetric-about-p-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:49:43+00:00",
    "updated_at": "2026-09-02T21:49:50+00:00"
  },
  "P12007": {
    "problem_number": 12007,
    "slug": "prime-plus-a-pronic-number-for-every-odd-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:39:00+00:00",
    "updated_at": "2026-09-01T18:39:25+00:00"
  },
  "P12017": {
    "problem_number": 12017,
    "slug": "prime-plus-lucas-plus-catalan-representation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:50:53+00:00",
    "updated_at": "2026-09-01T18:51:04+00:00"
  },
  "P12115": {
    "problem_number": 12115,
    "slug": "prime-plus-one-fibonacci-number-plus-twice-another",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:13:19+00:00",
    "updated_at": "2026-09-01T19:13:25+00:00"
  },
  "P12367": {
    "problem_number": 12367,
    "slug": "prime-plus-one-power-of-two-and-three-times-another",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:44:07+00:00",
    "updated_at": "2026-09-01T19:44:13+00:00"
  },
  "P12157": {
    "problem_number": 12157,
    "slug": "prime-resets-in-a-gcd-subtraction-recurrence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:18:30+00:00",
    "updated_at": "2026-09-01T19:18:36+00:00"
  },
  "P12709": {
    "problem_number": 12709,
    "slug": "prime-resets-in-a-linear-gcd-descent",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:25:11+00:00",
    "updated_at": "2026-09-02T22:25:44+00:00"
  },
  "P12483": {
    "problem_number": 12483,
    "slug": "prime-sums-and-differences-modulo-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:28+00:00",
    "updated_at": "2026-09-02T21:40:36+00:00"
  },
  "P9486": {
    "problem_number": 9486,
    "slug": "open-fc-907d0c5aa4c55b2de510-prime-triplets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:19+00:00",
    "updated_at": "2026-08-17T19:54:22+00:00"
  },
  "P12271": {
    "problem_number": 12271,
    "slug": "prime-values-of-2-k-minus-a-fixed-odd-integer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:32:29+00:00",
    "updated_at": "2026-09-01T19:32:34+00:00"
  },
  "P11929": {
    "problem_number": 11929,
    "slug": "prime-values-of-sophie-germain-coefficient-polynomials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:27:32+00:00",
    "updated_at": "2026-08-30T16:28:37+00:00"
  },
  "P11610": {
    "problem_number": 11610,
    "slug": "prime-values-of-the-diagonal-divisor-power-sum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:38:25+00:00",
    "updated_at": "2026-08-30T04:38:32+00:00"
  },
  "P12173": {
    "problem_number": 12173,
    "slug": "prime-adic-types-in-imaginary-factorial-products",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:20:28+00:00",
    "updated_at": "2026-09-01T19:20:33+00:00"
  },
  "P12349": {
    "problem_number": 12349,
    "slug": "prime-cube-residues-in-a-plane-partition-product-diagonal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:41:52+00:00",
    "updated_at": "2026-09-01T19:41:57+00:00"
  },
  "P12555": {
    "problem_number": 12555,
    "slug": "prime-free-concatenations-of-integer-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:48:22+00:00",
    "updated_at": "2026-09-02T21:48:29+00:00"
  },
  "P10238": {
    "problem_number": 10238,
    "slug": "open-fc-e1f4a8690cba83139b9d-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:58+00:00",
    "updated_at": "2026-08-18T02:51:59+00:00"
  },
  "P10150": {
    "problem_number": 10150,
    "slug": "open-fc-3aba6d4aaa59ab5d419c-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:25+00:00",
    "updated_at": "2026-08-18T02:51:26+00:00"
  },
  "P10116": {
    "problem_number": 10116,
    "slug": "open-fc-1a5871d90b817ac95764-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:14+00:00",
    "updated_at": "2026-08-18T02:51:15+00:00"
  },
  "P10164": {
    "problem_number": 10164,
    "slug": "open-fc-47c6a96211f6440ff479-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:30+00:00",
    "updated_at": "2026-08-18T02:51:31+00:00"
  },
  "P10244": {
    "problem_number": 10244,
    "slug": "open-fc-ecf703a5370c0a76300e-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:01+00:00",
    "updated_at": "2026-08-18T02:52:01+00:00"
  },
  "P10112": {
    "problem_number": 10112,
    "slug": "open-fc-1577ec3742d10a8cb5b7-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:13+00:00",
    "updated_at": "2026-08-18T02:51:14+00:00"
  },
  "P10124": {
    "problem_number": 10124,
    "slug": "open-fc-226a7c2bd6ed4b1c174a-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:17+00:00",
    "updated_at": "2026-08-18T02:51:18+00:00"
  },
  "P10158": {
    "problem_number": 10158,
    "slug": "open-fc-4161d35a293105c3b8c3-conjecture1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:28+00:00",
    "updated_at": "2026-08-18T02:51:29+00:00"
  },
  "P10234": {
    "problem_number": 10234,
    "slug": "open-fc-db2e8fab1fbe2c1626cf-conjecture1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:56+00:00",
    "updated_at": "2026-08-18T02:51:57+00:00"
  },
  "P10134": {
    "problem_number": 10134,
    "slug": "open-fc-2785a3c5e0cd7e4f4e60-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:20+00:00",
    "updated_at": "2026-08-18T02:51:21+00:00"
  },
  "P10180": {
    "problem_number": 10180,
    "slug": "open-fc-6e868a56d784af2ec7fc-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:36+00:00",
    "updated_at": "2026-08-18T02:51:37+00:00"
  },
  "P12293": {
    "problem_number": 12293,
    "slug": "prime-power-congruences-for-a-cyclotomic-quotient-diagonal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:35:12+00:00",
    "updated_at": "2026-09-01T19:35:17+00:00"
  },
  "P12417": {
    "problem_number": 12417,
    "slug": "primes-after-euclid-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:33:39+00:00",
    "updated_at": "2026-09-02T21:33:52+00:00"
  },
  "P12391": {
    "problem_number": 12391,
    "slug": "primitive-necklaces-and-zagier-cycles",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:30:51+00:00",
    "updated_at": "2026-09-02T21:31:06+00:00"
  },
  "P8406": {
    "problem_number": 8406,
    "slug": "open-fc-2ab92a2c9f915ca7519b-erdos-985",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:49:40+00:00",
    "updated_at": "2026-08-17T18:49:45+00:00"
  },
  "P3322": {
    "problem_number": 3322,
    "slug": "erdos-problem-985",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:05:40+00:00",
    "updated_at": "2026-08-12T06:05:53+00:00"
  },
  "P8762": {
    "problem_number": 8762,
    "slug": "open-fc-5d91c95e59daa75f5394-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:14:25+00:00",
    "updated_at": "2026-08-17T19:14:45+00:00"
  },
  "P12285": {
    "problem_number": 12285,
    "slug": "primorial-gaps-in-the-first-shared-divisor-prime-pairs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:34:12+00:00",
    "updated_at": "2026-09-01T19:34:18+00:00"
  },
  "P12143": {
    "problem_number": 12143,
    "slug": "primorial-jumping-champions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:16:44+00:00",
    "updated_at": "2026-09-01T19:16:50+00:00"
  },
  "P10248": {
    "problem_number": 10248,
    "slug": "open-fc-f83ecde6d28d0fbc6319-problem-10-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:02+00:00",
    "updated_at": "2026-08-18T02:52:03+00:00"
  },
  "P10220": {
    "problem_number": 10220,
    "slug": "open-fc-c5db4e638d342c90377a-problem-10-6-variant-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:51+00:00",
    "updated_at": "2026-08-18T02:51:51+00:00"
  },
  "P10250": {
    "problem_number": 10250,
    "slug": "open-fc-fe5385e12af7246a02e3-problem-10-8",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:52:03+00:00",
    "updated_at": "2026-08-18T02:52:03+00:00"
  },
  "P10228": {
    "problem_number": 10228,
    "slug": "open-fc-d0d3bed20ec0de84bb39-problem-10-9",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:54+00:00",
    "updated_at": "2026-08-18T02:51:55+00:00"
  },
  "P3396": {
    "problem_number": 3396,
    "slug": "kourovka-21-27-products-of-two-derangements-in-finite-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:56:30+00:00",
    "updated_at": "2026-08-12T07:56:42+00:00"
  },
  "P9252": {
    "problem_number": 9252,
    "slug": "open-fc-97b46e6553f8ce1b0201-green-62",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:24+00:00",
    "updated_at": "2026-08-17T19:50:25+00:00"
  },
  "P10800": {
    "problem_number": 10800,
    "slug": "unsolvedmath-0106-progressions-in-f-3-n-with-boolean-common-differences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:18+00:00",
    "updated_at": "2026-08-18T02:55:19+00:00"
  },
  "P10066": {
    "problem_number": 10066,
    "slug": "open-fc-efa5975a5b43329a9845-problem-4-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:06+00:00",
    "updated_at": "2026-08-17T20:06:07+00:00"
  },
  "P8328": {
    "problem_number": 8328,
    "slug": "open-fc-20a6a78163b7f70a4710-erdos-602",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:46+00:00",
    "updated_at": "2026-08-17T18:39:55+00:00"
  },
  "P11672": {
    "problem_number": 11672,
    "slug": "pure-periodicity-of-euler-secant-numbers-modulo-every-modulus",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:24+00:00",
    "updated_at": "2026-08-30T11:05:28+00:00"
  },
  "P3132": {
    "problem_number": 3132,
    "slug": "purely-cosmetic-surgery-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:07+00:00",
    "updated_at": "2026-08-02T12:54:43+00:00"
  },
  "P9772": {
    "problem_number": 9772,
    "slug": "open-fc-c7f2383981c681082252-kourovka-20-76",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:31+00:00",
    "updated_at": "2026-08-17T20:02:31+00:00"
  },
  "P12085": {
    "problem_number": 12085,
    "slug": "quadratic-growth-of-primitive-antiharmonic-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:09:22+00:00",
    "updated_at": "2026-09-01T19:09:27+00:00"
  },
  "P8624": {
    "problem_number": 8624,
    "slug": "open-fc-407e6ac19f31b8a4b2ea-green-41",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:24+00:00",
    "updated_at": "2026-08-17T18:58:39+00:00"
  },
  "P11141": {
    "problem_number": 11141,
    "slug": "quantitative-stability-coordinate-pythagorean-near-isotropy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-20T01:41:42+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P42": {
    "problem_number": 42,
    "slug": "quantum-pcp-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:26:02+00:00"
  },
  "P3518": {
    "problem_number": 3518,
    "slug": "kourovka-21-129-quasi-isometry-of-spherical-type-artin-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:57+00:00",
    "updated_at": "2026-08-12T08:11:19+00:00"
  },
  "P3546": {
    "problem_number": 3546,
    "slug": "kourovka-21-145-quasi-isometry-types-involving-thompson-s-group-f",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:13:55+00:00",
    "updated_at": "2026-08-12T08:14:15+00:00"
  },
  "P3500": {
    "problem_number": 3500,
    "slug": "kourovka-21-118-quotients-of-residually-finite-groups-by-amenable-kernels",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:08:41+00:00",
    "updated_at": "2026-08-12T08:08:56+00:00"
  },
  "P2894": {
    "problem_number": 2894,
    "slug": "rainbow-perfect-matching-ten-vertices-eight-colors",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:44:40+00:00",
    "updated_at": "2026-08-01T12:26:28+00:00"
  },
  "P9176": {
    "problem_number": 9176,
    "slug": "open-fc-feeea7d299e074f69394-green-25-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:57+00:00",
    "updated_at": "2026-08-17T19:47:57+00:00"
  },
  "P8982": {
    "problem_number": 8982,
    "slug": "open-fc-6b95a92d53d616a60f0f-erdos-566",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:18+00:00",
    "updated_at": "2026-08-17T19:44:19+00:00"
  },
  "P3196": {
    "problem_number": 3196,
    "slug": "erdos-problem-566",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:51:13+00:00",
    "updated_at": "2026-08-12T05:51:23+00:00"
  },
  "P3330": {
    "problem_number": 3330,
    "slug": "erdos-problem-567",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:23+00:00",
    "updated_at": "2026-08-12T06:06:25+00:00"
  },
  "P8544": {
    "problem_number": 8544,
    "slug": "open-fc-6bcf22509651e5019987-erdos-567-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:29+00:00",
    "updated_at": "2026-08-17T18:54:31+00:00"
  },
  "P9502": {
    "problem_number": 9502,
    "slug": "open-fc-9ac665b69cd7a0d2ea39-erdos-567-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:29+00:00",
    "updated_at": "2026-08-17T19:54:30+00:00"
  },
  "P8494": {
    "problem_number": 8494,
    "slug": "open-fc-5186e545a988dc8d6d79-erdos-567-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:32+00:00",
    "updated_at": "2026-08-17T18:52:35+00:00"
  },
  "P10780": {
    "problem_number": 10780,
    "slug": "unsolvedmath-0141-random-permutations-fixing-k-sets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:12+00:00",
    "updated_at": "2026-08-18T02:55:12+00:00"
  },
  "P10760": {
    "problem_number": 10760,
    "slug": "unsolvedmath-0177-random-walk-mixing-on-alternating-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:06+00:00",
    "updated_at": "2026-08-18T02:55:06+00:00"
  },
  "P2598": {
    "problem_number": 2598,
    "slug": "symmetric-binary-matrix-rank-log-concavity",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:41+00:00",
    "updated_at": "2026-08-01T23:49:05+00:00"
  },
  "P12545": {
    "problem_number": 12545,
    "slug": "ratio-limit-for-the-zorach-diagonal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:46:36+00:00",
    "updated_at": "2026-09-02T21:46:43+00:00"
  },
  "P2762": {
    "problem_number": 2762,
    "slug": "rational-points-y2-x6-minus-x2-plus1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:02:54+00:00",
    "updated_at": "2026-08-01T23:45:13+00:00"
  },
  "P8594": {
    "problem_number": 8594,
    "slug": "open-fc-80e93ca20e7ddb682e44-erdos-269-variants-rational",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:39+00:00",
    "updated_at": "2026-08-17T19:21:34+00:00"
  },
  "P12011": {
    "problem_number": 12011,
    "slug": "reachability-in-a-choice-version-of-the-3x-1-graph",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:41:09+00:00",
    "updated_at": "2026-09-01T18:45:14+00:00"
  },
  "P12557": {
    "problem_number": 12557,
    "slug": "real-roots-of-lambert-w-derivative-polynomials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:48:35+00:00",
    "updated_at": "2026-09-02T21:48:42+00:00"
  },
  "P3404": {
    "problem_number": 3404,
    "slug": "kourovka-21-32-realizing-finite-groups-as-derived-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:57:38+00:00",
    "updated_at": "2026-08-12T07:57:42+00:00"
  },
  "P3450": {
    "problem_number": 3450,
    "slug": "kourovka-21-68-recognition-of-finite-semi-abelian-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:14+00:00",
    "updated_at": "2026-08-12T08:05:18+00:00"
  },
  "P11108": {
    "problem_number": 11108,
    "slug": "record-composition-enumeration-alternating-permutations",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T08:25:54+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P12491": {
    "problem_number": 12491,
    "slug": "record-gaps-between-squarefree-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:41:16+00:00",
    "updated_at": "2026-09-02T21:41:23+00:00"
  },
  "P12421": {
    "problem_number": 12421,
    "slug": "record-prime-gaps-below-n-squared",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:34:08+00:00",
    "updated_at": "2026-09-02T21:34:16+00:00"
  },
  "P2800": {
    "problem_number": 2800,
    "slug": "rectilinear-crossing-k28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:07+00:00",
    "updated_at": "2026-08-01T12:27:27+00:00"
  },
  "P4428": {
    "problem_number": 4428,
    "slug": "rectilinear-crossing-number-k-29-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:45+00:00",
    "updated_at": "2026-08-16T02:05:34+00:00"
  },
  "P4430": {
    "problem_number": 4430,
    "slug": "rectilinear-crossing-number-k-30-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:49+00:00",
    "updated_at": "2026-08-16T02:05:39+00:00"
  },
  "P4432": {
    "problem_number": 4432,
    "slug": "rectilinear-crossing-number-k-31-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:52+00:00",
    "updated_at": "2026-08-16T02:05:43+00:00"
  },
  "P4434": {
    "problem_number": 4434,
    "slug": "rectilinear-crossing-number-k-32-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:57+00:00",
    "updated_at": "2026-08-16T02:05:44+00:00"
  },
  "P4436": {
    "problem_number": 4436,
    "slug": "rectilinear-crossing-number-k-33-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:38:58+00:00",
    "updated_at": "2026-08-16T02:05:45+00:00"
  },
  "P4438": {
    "problem_number": 4438,
    "slug": "rectilinear-crossing-number-k-34-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:05+00:00",
    "updated_at": "2026-08-16T02:05:46+00:00"
  },
  "P4440": {
    "problem_number": 4440,
    "slug": "rectilinear-crossing-number-k-35-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:08+00:00",
    "updated_at": "2026-08-16T02:05:46+00:00"
  },
  "P4442": {
    "problem_number": 4442,
    "slug": "rectilinear-crossing-number-k-36-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:10+00:00",
    "updated_at": "2026-08-16T02:05:47+00:00"
  },
  "P4444": {
    "problem_number": 4444,
    "slug": "rectilinear-crossing-number-k-37-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:15+00:00",
    "updated_at": "2026-08-16T02:05:47+00:00"
  },
  "P4446": {
    "problem_number": 4446,
    "slug": "rectilinear-crossing-number-k-38-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:18+00:00",
    "updated_at": "2026-08-16T02:05:48+00:00"
  },
  "P4448": {
    "problem_number": 4448,
    "slug": "rectilinear-crossing-number-k-39-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:21+00:00",
    "updated_at": "2026-08-16T02:05:48+00:00"
  },
  "P4450": {
    "problem_number": 4450,
    "slug": "rectilinear-crossing-number-k-40-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:26+00:00",
    "updated_at": "2026-08-16T02:05:48+00:00"
  },
  "P4452": {
    "problem_number": 4452,
    "slug": "rectilinear-crossing-number-k-41-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:27+00:00",
    "updated_at": "2026-08-16T02:05:51+00:00"
  },
  "P4454": {
    "problem_number": 4454,
    "slug": "rectilinear-crossing-number-k-42-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:32+00:00",
    "updated_at": "2026-08-16T02:05:53+00:00"
  },
  "P4456": {
    "problem_number": 4456,
    "slug": "rectilinear-crossing-number-k-43-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:35+00:00",
    "updated_at": "2026-08-16T02:05:55+00:00"
  },
  "P4458": {
    "problem_number": 4458,
    "slug": "rectilinear-crossing-number-k-44-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:37+00:00",
    "updated_at": "2026-08-16T02:05:55+00:00"
  },
  "P4460": {
    "problem_number": 4460,
    "slug": "rectilinear-crossing-number-k-45-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:38+00:00",
    "updated_at": "2026-08-16T02:05:57+00:00"
  },
  "P4462": {
    "problem_number": 4462,
    "slug": "rectilinear-crossing-number-k-46-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:41+00:00",
    "updated_at": "2026-08-16T02:06:02+00:00"
  },
  "P4464": {
    "problem_number": 4464,
    "slug": "rectilinear-crossing-number-k-47-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:39:48+00:00",
    "updated_at": "2026-08-16T02:06:04+00:00"
  },
  "P4466": {
    "problem_number": 4466,
    "slug": "rectilinear-crossing-number-k-48-exact",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T20:40:00+00:00",
    "updated_at": "2026-08-16T02:06:08+00:00"
  },
  "P11586": {
    "problem_number": 11586,
    "slug": "recurrence-for-the-ratio-determined-insertion-sequence-i-0-0833344",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:02+00:00",
    "updated_at": "2026-08-30T04:36:09+00:00"
  },
  "P12503": {
    "problem_number": 12503,
    "slug": "recurring-descents-in-four-square-minima",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:23+00:00",
    "updated_at": "2026-09-02T21:42:35+00:00"
  },
  "P11935": {
    "problem_number": 11935,
    "slug": "recursive-generation-of-the-partition-code-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:30:14+00:00",
    "updated_at": "2026-08-30T16:30:31+00:00"
  },
  "P9388": {
    "problem_number": 9388,
    "slug": "open-fc-fddb50b2396387c343a3-reed-conjecture-6-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:21+00:00",
    "updated_at": "2026-08-17T19:51:21+00:00"
  },
  "P9346": {
    "problem_number": 9346,
    "slug": "open-fc-e15b928bd2f510096a01-reed-omega-delta-chi-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:03+00:00",
    "updated_at": "2026-08-17T19:51:03+00:00"
  },
  "P9852": {
    "problem_number": 9852,
    "slug": "open-fc-47cf06ea360dba7c8a8e-reed-omega-delta-chi-conjecture-for-finite-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:57+00:00",
    "updated_at": "2026-08-17T20:03:58+00:00"
  },
  "P11913": {
    "problem_number": 11913,
    "slug": "regular-hadamard-matrices-of-every-even-square-order",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:22:28+00:00",
    "updated_at": "2026-08-30T16:22:36+00:00"
  },
  "P3402": {
    "problem_number": 3402,
    "slug": "kourovka-21-31-regular-subgroups-in-holomorphs-of-soluble-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:57:28+00:00",
    "updated_at": "2026-08-12T07:57:32+00:00"
  },
  "P8478": {
    "problem_number": 8478,
    "slug": "open-fc-4a0de05646114ee6ac20-erdos-686-variants-twenty-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:19+00:00",
    "updated_at": "2026-08-17T18:52:20+00:00"
  },
  "P8476": {
    "problem_number": 8476,
    "slug": "open-fc-491ec2d3af61b9bd3413-erdos-686-variants-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:18+00:00",
    "updated_at": "2026-08-17T18:52:19+00:00"
  },
  "P9702": {
    "problem_number": 9702,
    "slug": "open-fc-9535012d1aabf3b3982a-erdos-940-variants-large-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:57+00:00",
    "updated_at": "2026-08-17T20:01:57+00:00"
  },
  "P3278": {
    "problem_number": 3278,
    "slug": "erdos-problem-849",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:02:30+00:00",
    "updated_at": "2026-08-12T06:02:38+00:00"
  },
  "P8112": {
    "problem_number": 8112,
    "slug": "open-fc-038871f1727308973705-erdos-849",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:44+00:00",
    "updated_at": "2026-08-17T18:34:44+00:00"
  },
  "P8078": {
    "problem_number": 8078,
    "slug": "open-fc-003186a9587e583f17ca-erdos-686-variants-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:33+00:00",
    "updated_at": "2026-08-17T18:34:34+00:00"
  },
  "P11664": {
    "problem_number": 11664,
    "slug": "representing-every-integer-from-5340-by-three-prime-partial-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:03+00:00",
    "updated_at": "2026-08-30T11:04:10+00:00"
  },
  "P2560": {
    "problem_number": 2560,
    "slug": "cyclic-pair-compression-reset-threshold",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:28+00:00",
    "updated_at": "2026-08-01T02:05:50+00:00"
  },
  "P3524": {
    "problem_number": 3524,
    "slug": "kourovka-21-132-residually-finite-p-groups-with-finite-centre",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:02+00:00",
    "updated_at": "2026-08-12T08:12:04+00:00"
  },
  "P12473": {
    "problem_number": 12473,
    "slug": "residues-of-arcsin-tan-x-coefficients",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:39:29+00:00",
    "updated_at": "2026-09-02T21:39:37+00:00"
  },
  "P10144": {
    "problem_number": 10144,
    "slug": "open-fc-30150edba06158a13bd1-restricted-prime-number-theorem-variants-even-subsequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:23+00:00",
    "updated_at": "2026-08-18T02:51:24+00:00"
  },
  "P31": {
    "problem_number": 31,
    "slug": "riemann-hypothesis",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:27:49+00:00"
  },
  "P11150": {
    "problem_number": 11150,
    "slug": "riemann-zeta-limit-zero-motion-morse-molecular-bond",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-20T22:21:01+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P12099": {
    "problem_number": 12099,
    "slug": "rigidity-at-drops-of-the-largest-quadratic-residue",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:10:58+00:00",
    "updated_at": "2026-09-01T19:11:04+00:00"
  },
  "P10240": {
    "problem_number": 10240,
    "slug": "open-fc-e3b46d7a08e30e8acb7f-ringel-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:59+00:00",
    "updated_at": "2026-08-18T02:52:00+00:00"
  },
  "P12395": {
    "problem_number": 12395,
    "slug": "rook-tours-on-a-2-by-3-board",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:31:23+00:00",
    "updated_at": "2026-09-02T21:31:37+00:00"
  },
  "P45": {
    "problem_number": 45,
    "slug": "rotas-basis-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:28:23+00:00"
  },
  "P9582": {
    "problem_number": 9582,
    "slug": "open-fc-d9c35b54aa9f17596fa9-rudins-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:56:02+00:00",
    "updated_at": "2026-08-17T19:56:03+00:00"
  },
  "P12069": {
    "problem_number": 12069,
    "slug": "run-lengths-in-the-second-binary-digit-of-fibonacci-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:07:49+00:00",
    "updated_at": "2026-09-01T19:07:54+00:00"
  },
  "P3136": {
    "problem_number": 3136,
    "slug": "ryser-hypergraph-cover-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:08+00:00",
    "updated_at": "2026-08-02T12:55:29+00:00"
  },
  "P3150": {
    "problem_number": 3150,
    "slug": "ryser-odd-order-latin-square-transversal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-03T00:00:39+00:00",
    "updated_at": "2026-08-10T01:00:00.431219+00:00"
  },
  "P3064": {
    "problem_number": 3064,
    "slug": "sabidussi-compatibility-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:46:41+00:00",
    "updated_at": "2026-08-02T12:55:30+00:00"
  },
  "P12249": {
    "problem_number": 12249,
    "slug": "safe-primes-and-a-modular-perfect-power-threshold",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:29:44+00:00",
    "updated_at": "2026-09-01T19:29:50+00:00"
  },
  "P9948": {
    "problem_number": 9948,
    "slug": "open-fc-960087bb547c1d0b1844-same-parity-betrothed",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:51+00:00",
    "updated_at": "2026-08-17T20:04:52+00:00"
  },
  "P15": {
    "problem_number": 15,
    "slug": "schanuel-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:29:36+00:00"
  },
  "P8800": {
    "problem_number": 8800,
    "slug": "open-fc-86fe3f433654c82e0157-schanuel-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:22:05+00:00",
    "updated_at": "2026-08-17T19:22:15+00:00"
  },
  "P9746": {
    "problem_number": 9746,
    "slug": "open-fc-b5b6ed6498e1abe1f264-erdos-242-variants-schinzel-generalization",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:15+00:00",
    "updated_at": "2026-08-17T20:02:15+00:00"
  },
  "P8488": {
    "problem_number": 8488,
    "slug": "open-fc-4f25c968d462b7c11f7a-schinzel-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:26+00:00",
    "updated_at": "2026-08-17T18:52:26+00:00"
  },
  "P8444": {
    "problem_number": 8444,
    "slug": "open-fc-3716548b1d89099e8f3b-scholz-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:08+00:00",
    "updated_at": "2026-08-17T18:52:08+00:00"
  },
  "P12021": {
    "problem_number": 12021,
    "slug": "second-hardy-littlewood-prime-counting-inequality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:51:38+00:00",
    "updated_at": "2026-09-01T18:51:47+00:00"
  },
  "P3242": {
    "problem_number": 3242,
    "slug": "erdos-problem-855",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:57:08+00:00",
    "updated_at": "2026-08-12T05:57:12+00:00"
  },
  "P8308": {
    "problem_number": 8308,
    "slug": "open-fc-1ece003c3b6acbb98665-erdos-855",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:39:17+00:00",
    "updated_at": "2026-08-17T18:39:33+00:00"
  },
  "P3422": {
    "problem_number": 3422,
    "slug": "kourovka-21-41-self-similar-metabelian-groups-containing-a-wreath-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:59:13+00:00",
    "updated_at": "2026-08-12T07:59:20+00:00"
  },
  "P9676": {
    "problem_number": 9676,
    "slug": "open-fc-730462e7c5b810492b8d-selfridge-seq-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:10+00:00",
    "updated_at": "2026-08-17T20:01:11+00:00"
  },
  "P9066": {
    "problem_number": 9066,
    "slug": "open-fc-ab5eccaf883712f28882-selfridge-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:41+00:00",
    "updated_at": "2026-08-17T19:46:43+00:00"
  },
  "P9248": {
    "problem_number": 9248,
    "slug": "open-fc-94ef103528c6ca17dd18-selfridge-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:23+00:00",
    "updated_at": "2026-08-17T19:50:23+00:00"
  },
  "P8082": {
    "problem_number": 8082,
    "slug": "open-fc-0091ec2a7278a56a2190-exists-semi-magic-square-cubes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:35+00:00",
    "updated_at": "2026-08-17T18:34:35+00:00"
  },
  "P9434": {
    "problem_number": 9434,
    "slug": "open-fc-68ab1ec067859250752f-sendov-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:07+00:00",
    "updated_at": "2026-08-17T19:53:09+00:00"
  },
  "P2866": {
    "problem_number": 2866,
    "slug": "space-curves-set-theoretic-complete-intersection",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:40:53+00:00",
    "updated_at": "2026-08-01T12:30:28+00:00"
  },
  "P3670": {
    "problem_number": 3670,
    "slug": "discrete-markov-129-grid-degree-twelve",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:19+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P9524": {
    "problem_number": 9524,
    "slug": "open-fc-ab7359a40de0cc0570c8-green-5",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:37+00:00",
    "updated_at": "2026-08-17T19:54:37+00:00"
  },
  "P2730": {
    "problem_number": 2730,
    "slug": "cyclic-hilbert-l4-norm-31",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:33+00:00",
    "updated_at": "2026-08-01T23:23:44+00:00"
  },
  "P3676": {
    "problem_number": 3676,
    "slug": "c7-square-sharp-l4-sobolev",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:27+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2692": {
    "problem_number": 2692,
    "slug": "c31-centered-maximal-l2-norm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:16+00:00",
    "updated_at": "2026-08-01T02:03:55+00:00"
  },
  "P2456": {
    "problem_number": 2456,
    "slug": "balanced-binary-multiplier-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:56:51+00:00",
    "updated_at": "2026-08-01T02:02:25+00:00"
  },
  "P11154": {
    "problem_number": 11154,
    "slug": "sharp-summability-of-nevanlinna-defects-for-finite-lower-order-holomorphic-curves",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-21T03:06:24+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9510": {
    "problem_number": 9510,
    "slug": "open-fc-a0d5fde822de54aca02c-erdos-357-variants-hegyvari",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:32+00:00",
    "updated_at": "2026-08-17T19:54:32+00:00"
  },
  "P3098": {
    "problem_number": 3098,
    "slug": "eventual-categoricity-aecs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:00+00:00",
    "updated_at": "2026-08-02T12:49:31+00:00"
  },
  "P2608": {
    "problem_number": 2608,
    "slug": "mersenne-127-addition-chain",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:44+00:00",
    "updated_at": "2026-07-30T02:26:36+00:00"
  },
  "P2600": {
    "problem_number": 2600,
    "slug": "length-eight-lyndon-superstring",
    "resolution_state": "proved_formally",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": true,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "verified",
        "verified": true,
        "kernelAccepted": true,
        "label": "Lean-verified",
        "reason": "A current formalization has a pinned Lean world, a signed accepted verifier result, and an exact binding to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A signed Lean verification is attached.",
      "summary": "Resolved. Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:42+00:00",
    "updated_at": "2026-08-01T02:11:00+00:00"
  },
  "P9842": {
    "problem_number": 9842,
    "slug": "open-fc-fe3c6623c606f8f7aa33-sidorenko-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:08+00:00",
    "updated_at": "2026-08-17T20:03:09+00:00"
  },
  "P3462": {
    "problem_number": 3462,
    "slug": "kourovka-21-82-simple-characteristic-quotients-of-free-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:51+00:00",
    "updated_at": "2026-08-12T08:05:53+00:00"
  },
  "P2920": {
    "problem_number": 2920,
    "slug": "generic-kahler-laplacian-simple-spectrum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:48:06+00:00",
    "updated_at": "2026-08-01T12:09:54+00:00"
  },
  "P9522": {
    "problem_number": 9522,
    "slug": "open-fc-aac852fa374bb545eeab-kourovka-19-25",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:37+00:00",
    "updated_at": "2026-08-17T19:54:37+00:00"
  },
  "P8814": {
    "problem_number": 8814,
    "slug": "open-fc-9a627366de708a64d3fb-singmaster",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:24:04+00:00",
    "updated_at": "2026-08-17T19:24:17+00:00"
  },
  "P3644": {
    "problem_number": 3644,
    "slug": "acute-six-set-eight-cubical-lattice",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:57+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11162": {
    "problem_number": 11162,
    "slug": "six-palindrome-geometric-progression",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:03:48+00:00",
    "updated_at": "2026-08-29T18:48:29+00:00"
  },
  "P12641": {
    "problem_number": 12641,
    "slug": "six-formulas-for-first-positions-in-a050128",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:07:12+00:00",
    "updated_at": "2026-09-02T22:07:18+00:00"
  },
  "P12753": {
    "problem_number": 12753,
    "slug": "six-step-growth-cycles-under-base-11-inverse-digit-addition",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:42:06+00:00",
    "updated_at": "2026-09-02T22:42:49+00:00"
  },
  "P8632": {
    "problem_number": 8632,
    "slug": "open-fc-44ae588c81fe7e8d987b-mean-value-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:51+00:00",
    "updated_at": "2026-08-17T18:58:52+00:00"
  },
  "P11668": {
    "problem_number": 11668,
    "slug": "small-prime-irreducibility-witnesses-for-reversed-schroeder-polynomials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:04:12+00:00",
    "updated_at": "2026-08-30T11:04:22+00:00"
  },
  "P9708": {
    "problem_number": 9708,
    "slug": "open-fc-995b68ce13cefba4a465-least-fifteen-circle-packing-in-circle",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:59+00:00",
    "updated_at": "2026-08-17T20:02:00+00:00"
  },
  "P3598": {
    "problem_number": 3598,
    "slug": "cyclic-latin-eleven-defining-set",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:47+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3712": {
    "problem_number": 3712,
    "slug": "directed-cayley-257-four-generator-diameter",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:31+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P8460": {
    "problem_number": 8460,
    "slug": "open-fc-414606c1250e2c78c6ae-erdos-188",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:11+00:00",
    "updated_at": "2026-08-17T18:52:12+00:00"
  },
  "P3206": {
    "problem_number": 3206,
    "slug": "erdos-problem-188",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:52:32+00:00",
    "updated_at": "2026-08-12T05:52:37+00:00"
  },
  "P3716": {
    "problem_number": 3716,
    "slug": "ltl-period-sixteen-exact-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:37+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3726": {
    "problem_number": 3726,
    "slug": "grid-three-four-reachability-obdd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:57+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3770": {
    "problem_number": 3770,
    "slug": "perfect-hash-twelve-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:52:34+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3608": {
    "problem_number": 3608,
    "slug": "line-separating-set-pg2-11",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:56+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3600": {
    "problem_number": 3600,
    "slug": "balanced-covering-17-6-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:49+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3604": {
    "problem_number": 3604,
    "slug": "rotation-saturating-set-ag3-7",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:53+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3630": {
    "problem_number": 3630,
    "slug": "circle-separating-set-f13-plane",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:20+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2572": {
    "problem_number": 2572,
    "slug": "middle-product-bit-obdd-six",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "An informal proof is recorded. No Lean formalization is attached.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:32+00:00",
    "updated_at": "2026-08-01T23:37:08+00:00"
  },
  "P3764": {
    "problem_number": 3764,
    "slug": "k6-spanning-tree-zdd",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:46+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P26": {
    "problem_number": 26,
    "slug": "smooth-four-dimensional-poincare-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:30:02+00:00"
  },
  "P9566": {
    "problem_number": 9566,
    "slug": "open-fc-caf6a0cf1ea266536f1d-poincare-conjecture-variants-smooth-dimension-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:29+00:00",
    "updated_at": "2026-08-17T19:55:32+00:00"
  },
  "P8346": {
    "problem_number": 8346,
    "slug": "open-fc-226881cd8947dcff1ce6-poincare-conjecture-variants-smooth-other-cases",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:09+00:00",
    "updated_at": "2026-08-17T18:40:11+00:00"
  },
  "P8170": {
    "problem_number": 8170,
    "slug": "open-fc-09786a28425d85eeed4d-is-ten-solitary",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:10+00:00",
    "updated_at": "2026-08-17T18:36:11+00:00"
  },
  "P12433": {
    "problem_number": 12433,
    "slug": "solutions-of-2-m-congruent-to-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:35:17+00:00",
    "updated_at": "2026-09-02T21:35:29+00:00"
  },
  "P10782": {
    "problem_number": 10782,
    "slug": "unsolvedmath-0151-solutions-to-polynomial-equations-in-dense-sets",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:13+00:00",
    "updated_at": "2026-08-18T02:55:13+00:00"
  },
  "P2638": {
    "problem_number": 2638,
    "slug": "prime-indicator-recurrence-weight-600",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:55+00:00",
    "updated_at": "2026-08-01T23:41:29+00:00"
  },
  "P3622": {
    "problem_number": 3622,
    "slug": "sparse-multilinear-identity-m2-f3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:12+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3620": {
    "problem_number": 3620,
    "slug": "primitive-idempotent-c31-square",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:43:07+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P10128": {
    "problem_number": 10128,
    "slug": "open-fc-24638e8d14bcb9c2563b-spectrum-xi-alpha-pow-countable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:51:18+00:00",
    "updated_at": "2026-08-18T02:51:19+00:00"
  },
  "P3722": {
    "problem_number": 3722,
    "slug": "arc-kayles-six-seven-grid-grundy",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:42+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P12449": {
    "problem_number": 12449,
    "slug": "square-divisibility-of-stirling-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:36:57+00:00",
    "updated_at": "2026-09-02T21:37:09+00:00"
  },
  "P13": {
    "problem_number": 13,
    "slug": "square-peg-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:30:55+00:00"
  },
  "P2742": {
    "problem_number": 2742,
    "slug": "pell-lucas-squareclass-collisions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:00:40+00:00",
    "updated_at": "2026-08-01T23:38:40+00:00"
  },
  "P8174": {
    "problem_number": 8174,
    "slug": "open-fc-0a39412e7fd98c0da70f-all-fermat-squarefree",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:14+00:00",
    "updated_at": "2026-08-17T18:36:16+00:00"
  },
  "P11885": {
    "problem_number": 11885,
    "slug": "square-jump-inverse-positions-at-the-square-root-scale",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:19:55+00:00",
    "updated_at": "2026-08-30T16:20:02+00:00"
  },
  "P12027": {
    "problem_number": 12027,
    "slug": "square-root-scale-error-for-a-swinging-factorial-quotient",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:52:40+00:00",
    "updated_at": "2026-09-01T18:52:49+00:00"
  },
  "P11750": {
    "problem_number": 11750,
    "slug": "squarefree-multiples-of-the-primorial-base-logarithm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:22:34+00:00",
    "updated_at": "2026-08-30T12:22:42+00:00"
  },
  "P12497": {
    "problem_number": 12497,
    "slug": "squarefree-numerators-of-prime-reciprocal-sums",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:41:45+00:00",
    "updated_at": "2026-09-02T21:41:55+00:00"
  },
  "P12487": {
    "problem_number": 12487,
    "slug": "squarefree-quotients-of-4-k-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:51+00:00",
    "updated_at": "2026-09-02T21:41:02+00:00"
  },
  "P9628": {
    "problem_number": 9628,
    "slug": "open-fc-faf4378c9edda1b1ce87-euclid-numbers-are-square-free",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:35+00:00",
    "updated_at": "2026-08-17T19:57:37+00:00"
  },
  "P11614": {
    "problem_number": 11614,
    "slug": "stability-of-the-known-kimberling-shuffle-valleys",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:38:51+00:00",
    "updated_at": "2026-08-30T04:38:58+00:00"
  },
  "P3514": {
    "problem_number": 3514,
    "slug": "kourovka-21-127-stable-commutator-length-in-right-angled-artin-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:25+00:00",
    "updated_at": "2026-08-12T08:10:29+00:00"
  },
  "P10812": {
    "problem_number": 10812,
    "slug": "unsolvedmath-0143-stable-density-on-subspaces",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:28+00:00",
    "updated_at": "2026-08-18T02:55:33+00:00"
  },
  "P11576": {
    "problem_number": 11576,
    "slug": "stamp-folding-factorization-into-meander-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:34:53+00:00",
    "updated_at": "2026-08-30T04:35:01+00:00"
  },
  "P3682": {
    "problem_number": 3682,
    "slug": "straight-tromino-four-five-six-box-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:54+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11806": {
    "problem_number": 11806,
    "slug": "strict-decrease-of-roots-of-prime-indexed-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:45:56+00:00",
    "updated_at": "2026-08-30T12:46:05+00:00"
  },
  "P3558": {
    "problem_number": 3558,
    "slug": "binary-code-upper-bounds",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": true,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "verified",
        "verified": true,
        "kernelAccepted": true,
        "label": "Lean-verified",
        "reason": "A current formalization has a pinned Lean world, a signed accepted verifier result, and an exact binding to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A signed Lean verification is attached.",
      "summary": "Claimed checked, not independently verified. Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:50:44+00:00",
    "updated_at": "2026-08-18T06:09:33+00:00"
  },
  "P8914": {
    "problem_number": 8914,
    "slug": "open-fc-e147fd36b387b6432f8d-erdos-317-variants-claim2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:23+00:00",
    "updated_at": "2026-08-17T19:40:25+00:00"
  },
  "P8862": {
    "problem_number": 8862,
    "slug": "open-fc-b71796d8aced7b07a17d-w-3-32-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:23+00:00",
    "updated_at": "2026-08-17T19:35:28+00:00"
  },
  "P9858": {
    "problem_number": 9858,
    "slug": "open-fc-4d11e2af6f909414dac8-w-3-33-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:02+00:00",
    "updated_at": "2026-08-17T20:04:02+00:00"
  },
  "P9114": {
    "problem_number": 9114,
    "slug": "open-fc-cf8bdc60ce392f21b53e-w-3-36-lower",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:40+00:00",
    "updated_at": "2026-08-17T19:47:40+00:00"
  },
  "P2830": {
    "problem_number": 2830,
    "slug": "life-strong-block-universality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:05:03+00:00",
    "updated_at": "2026-07-30T00:55:05+00:00"
  },
  "P12153": {
    "problem_number": 12153,
    "slug": "strong-coprimality-and-working-cardboard-braids",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:18:01+00:00",
    "updated_at": "2026-09-01T19:18:06+00:00"
  },
  "P3140": {
    "problem_number": 3140,
    "slug": "strong-exponential-time-hypothesis",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:09+00:00",
    "updated_at": "2026-08-02T12:56:07+00:00"
  },
  "P9470": {
    "problem_number": 9470,
    "slug": "open-fc-835a45d4af08c4dd7d27-rudins-conjecture-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:01+00:00",
    "updated_at": "2026-08-17T19:54:01+00:00"
  },
  "P9884": {
    "problem_number": 9884,
    "slug": "open-fc-654c379ec025b0d52e66-erdos-535-variants-sunflower-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:15+00:00",
    "updated_at": "2026-08-17T20:04:15+00:00"
  },
  "P9108": {
    "problem_number": 9108,
    "slug": "open-fc-ca05b26f580f42a96b3d-erdos-100-variants-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:38+00:00",
    "updated_at": "2026-08-17T19:47:38+00:00"
  },
  "P9174": {
    "problem_number": 9174,
    "slug": "open-fc-fd690a16768fc83ae66d-exists-k-stronger",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:56+00:00",
    "updated_at": "2026-08-17T19:47:57+00:00"
  },
  "P3534": {
    "problem_number": 3534,
    "slug": "kourovka-21-138-subgroup-structure-of-finitely-presented-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:33+00:00",
    "updated_at": "2026-08-12T08:12:38+00:00"
  },
  "P3522": {
    "problem_number": 3522,
    "slug": "kourovka-21-131-subgroups-of-golod-groups-mapping-onto-infinite-at-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:11:44+00:00",
    "updated_at": "2026-08-12T08:11:56+00:00"
  },
  "P3544": {
    "problem_number": 3544,
    "slug": "kourovka-21-144-subgroups-of-thompson-s-group-f",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:13:26+00:00",
    "updated_at": "2026-08-12T08:13:41+00:00"
  },
  "P11901": {
    "problem_number": 11901,
    "slug": "submultiplicativity-of-maximal-permanents-in-the-indecomposable-3-regular-class",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:21:19+00:00",
    "updated_at": "2026-08-30T16:21:25+00:00"
  },
  "P9824": {
    "problem_number": 9824,
    "slug": "open-fc-f1df484692b05648870c-green-9-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:59+00:00",
    "updated_at": "2026-08-17T20:03:00+00:00"
  },
  "P8246": {
    "problem_number": 8246,
    "slug": "open-fc-1539b3a5ce3fa15b6658-erdos-593-variants-two-colorable-implies-obligatory",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:40+00:00",
    "updated_at": "2026-08-17T18:37:42+00:00"
  },
  "P8508": {
    "problem_number": 8508,
    "slug": "open-fc-5b38e72d6445dd03e285-erdos-332",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:29+00:00",
    "updated_at": "2026-08-17T18:53:34+00:00"
  },
  "P10": {
    "problem_number": 10,
    "slug": "sum-of-three-cubes-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:31:40+00:00"
  },
  "P3328": {
    "problem_number": 3328,
    "slug": "erdos-problem-1107",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:06:17+00:00",
    "updated_at": "2026-08-12T06:06:20+00:00"
  },
  "P8430": {
    "problem_number": 8430,
    "slug": "open-fc-307f13e10c51b8ad0d8f-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:03+00:00",
    "updated_at": "2026-08-17T18:52:04+00:00"
  },
  "P8182": {
    "problem_number": 8182,
    "slug": "open-fc-0b607831fb1aaad1c534-general-supercongruence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:32+00:00",
    "updated_at": "2026-08-17T18:36:35+00:00"
  },
  "P11774": {
    "problem_number": 11774,
    "slug": "supercongruences-for-a-height-2-factorial-ratio-family",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:26:51+00:00",
    "updated_at": "2026-08-30T12:28:50+00:00"
  },
  "P12341": {
    "problem_number": 12341,
    "slug": "supercongruences-for-a-rational-function-diagonal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:40:53+00:00",
    "updated_at": "2026-09-01T19:40:58+00:00"
  },
  "P12291": {
    "problem_number": 12291,
    "slug": "supercongruences-for-bounded-adjacency-multiset-words",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:34:56+00:00",
    "updated_at": "2026-09-01T19:35:03+00:00"
  },
  "P12147": {
    "problem_number": 12147,
    "slug": "supercongruences-for-coefficient-families-from-a-reverted-series",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:17:13+00:00",
    "updated_at": "2026-09-01T19:17:19+00:00"
  },
  "P12149": {
    "problem_number": 12149,
    "slug": "supercongruences-from-a-weighted-overpartition-product",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:17:32+00:00",
    "updated_at": "2026-09-01T19:17:38+00:00"
  },
  "P12339": {
    "problem_number": 12339,
    "slug": "supercongruences-from-truncated-schr-der-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:40:38+00:00",
    "updated_at": "2026-09-01T19:40:44+00:00"
  },
  "P12125": {
    "problem_number": 12125,
    "slug": "supercongruences-inherited-by-exponential-coefficient-lifts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:14:31+00:00",
    "updated_at": "2026-09-01T19:14:37+00:00"
  },
  "P12297": {
    "problem_number": 12297,
    "slug": "superdiagonal-series-for-zeta-2",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:35:41+00:00",
    "updated_at": "2026-09-01T19:35:46+00:00"
  },
  "P9410": {
    "problem_number": 9410,
    "slug": "open-fc-55a2bdb3108412f59a03-lam-litt-variants-omega-integrality-implies-algebraicity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:28+00:00",
    "updated_at": "2026-08-17T19:52:29+00:00"
  },
  "P11965": {
    "problem_number": 11965,
    "slug": "surjectivity-of-a-capped-step-recaman-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:58:20+00:00",
    "updated_at": "2026-08-31T03:58:34+00:00"
  },
  "P12145": {
    "problem_number": 12145,
    "slug": "surjectivity-of-the-greedy-coprime-neighbor-spiral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:16:58+00:00",
    "updated_at": "2026-09-01T19:17:04+00:00"
  },
  "P9640": {
    "problem_number": 9640,
    "slug": "open-fc-3ab41145f778b4ce3a8d-erdos-422-variants-surjective",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:17+00:00",
    "updated_at": "2026-08-17T20:00:18+00:00"
  },
  "P9802": {
    "problem_number": 9802,
    "slug": "open-fc-e220a6e0d33ad6d15c72-erdos-373-variants-suranyi",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:47+00:00",
    "updated_at": "2026-08-17T20:02:47+00:00"
  },
  "P3596": {
    "problem_number": 3596,
    "slug": "k12-factorization-switch-diameter",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:45+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3590": {
    "problem_number": 3590,
    "slug": "symmetric-anticommuting-four-f3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:42:42+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11895": {
    "problem_number": 11895,
    "slug": "symmetric-three-term-recurrences-for-sampled-partial-map-counts",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:49+00:00",
    "updated_at": "2026-08-30T16:20:55+00:00"
  },
  "P9728": {
    "problem_number": 9728,
    "slug": "open-fc-a76c90bcf51e6088190d-erdos-272-variants-szabo-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:07+00:00",
    "updated_at": "2026-08-17T20:02:08+00:00"
  },
  "P2714": {
    "problem_number": 2714,
    "slug": "tammes-fifteen-separation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:26+00:00",
    "updated_at": "2026-07-29T20:56:44+00:00"
  },
  "P9668": {
    "problem_number": 9668,
    "slug": "open-fc-6837f765b8e214aa6cd5-mem-ioc-c1a",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:58+00:00",
    "updated_at": "2026-08-17T20:00:59+00:00"
  },
  "P8244": {
    "problem_number": 8244,
    "slug": "open-fc-15093fbdc3ce0e1a47ff-c1a-eq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:39+00:00",
    "updated_at": "2026-08-17T18:37:41+00:00"
  },
  "P3492": {
    "problem_number": 3492,
    "slug": "kourovka-21-111-tau-automorphisms-of-finite-simple-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:07:23+00:00",
    "updated_at": "2026-08-12T08:07:31+00:00"
  },
  "P3686": {
    "problem_number": 3686,
    "slug": "ten-points-regular-pentagon-packing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:45:00+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P11596": {
    "problem_number": 11596,
    "slug": "termination-of-gf-2-factor-encoding-product-orbits",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:59+00:00",
    "updated_at": "2026-08-30T04:37:06+00:00"
  },
  "P8708": {
    "problem_number": 8708,
    "slug": "open-fc-3166381dd5c752a266f3-erdos-282-variants-sq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:06:25+00:00",
    "updated_at": "2026-08-17T20:00:02+00:00"
  },
  "P9744": {
    "problem_number": 9744,
    "slug": "open-fc-b3ac28d26bc33eda5882-erdos-409-variants-sigma-prime-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:15+00:00",
    "updated_at": "2026-08-17T20:02:15+00:00"
  },
  "P9308": {
    "problem_number": 9308,
    "slug": "open-fc-c2822e8894c0efd10c21-erdos-282",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:48+00:00",
    "updated_at": "2026-08-17T19:50:48+00:00"
  },
  "P8670": {
    "problem_number": 8670,
    "slug": "open-fc-2ee180e8471918de817f-erdos-409-variants-sigma-termination",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:21+00:00",
    "updated_at": "2026-08-17T19:04:25+00:00"
  },
  "P11100": {
    "problem_number": 11100,
    "slug": "ternary-partition-polynomial-minus-one-evaluation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T07:23:58+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P11102": {
    "problem_number": 11102,
    "slug": "ternary-partition-polynomial-at-one-recurrence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T07:31:19+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P2858": {
    "problem_number": 2858,
    "slug": "finite-order-integer-matrix-ternary-conjugate",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:39:47+00:00",
    "updated_at": "2026-08-01T23:26:19+00:00"
  },
  "P11110": {
    "problem_number": 11110,
    "slug": "thakur-h1-unique-carry-free-maximizer",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T08:28:06+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P9394": {
    "problem_number": 9394,
    "slug": "open-fc-42d2053c27e5b7993189-padic-littlewood-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:12+00:00",
    "updated_at": "2026-08-17T19:52:13+00:00"
  },
  "P10006": {
    "problem_number": 10006,
    "slug": "open-fc-c12483fed5aa14a0d7fe-conjecture-1-3-to-2-3",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:21+00:00",
    "updated_at": "2026-08-17T20:05:21+00:00"
  },
  "P9992": {
    "problem_number": 9992,
    "slug": "open-fc-b5fa57bf173e95b979b2-omega-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:16+00:00",
    "updated_at": "2026-08-17T20:05:16+00:00"
  },
  "P3010": {
    "problem_number": 3010,
    "slug": "erdos-problem-70",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:33+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8358": {
    "problem_number": 8358,
    "slug": "open-fc-239acd0c41bfe77d671f-erdos-70",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:18+00:00",
    "updated_at": "2026-08-17T18:40:20+00:00"
  },
  "P3354": {
    "problem_number": 3354,
    "slug": "kourovka-21-28-simple-derangement-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:52:52+00:00",
    "updated_at": "2026-08-12T06:53:06+00:00"
  },
  "P9082": {
    "problem_number": 9082,
    "slug": "open-fc-b74af0d622d427c859df-agoh-giuga",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:09+00:00",
    "updated_at": "2026-08-17T19:47:10+00:00"
  },
  "P12333": {
    "problem_number": 12333,
    "slug": "the-average-digit-sum-of-powers-of-thirteen",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:39:54+00:00",
    "updated_at": "2026-09-01T19:39:59+00:00"
  },
  "P9246": {
    "problem_number": 9246,
    "slug": "open-fc-92a9915c85d5cfaacc58-banach-mazur-rotation-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:21+00:00",
    "updated_at": "2026-08-17T19:50:22+00:00"
  },
  "P8098": {
    "problem_number": 8098,
    "slug": "open-fc-02a24419e32c2beb5081-no-lychrel-numbers-base10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:40+00:00",
    "updated_at": "2026-08-17T18:34:41+00:00"
  },
  "P8718": {
    "problem_number": 8718,
    "slug": "open-fc-4249eeb6811f6795f2a1-bateman-horn-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:10:41+00:00",
    "updated_at": "2026-08-17T19:10:57+00:00"
  },
  "P10042": {
    "problem_number": 10042,
    "slug": "open-fc-de9530da9e4bf5a6e5c6-beal-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:39+00:00",
    "updated_at": "2026-08-17T20:05:41+00:00"
  },
  "P8140": {
    "problem_number": 8140,
    "slug": "open-fc-05c1e65a0dc3396f4682-beck-fiala-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:05+00:00",
    "updated_at": "2026-08-17T18:35:06+00:00"
  },
  "P8288": {
    "problem_number": 8288,
    "slug": "open-fc-1c4e8e3a8d06a4645e8b-bing-borsuk-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:38:18+00:00",
    "updated_at": "2026-08-17T18:38:27+00:00"
  },
  "P9396": {
    "problem_number": 9396,
    "slug": "open-fc-4673a58bda6cc2d63da2-bounded-burnside-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:13+00:00",
    "updated_at": "2026-08-17T19:52:14+00:00"
  },
  "P9128": {
    "problem_number": 9128,
    "slug": "open-fc-dca19c8852a0f164141c-bunyakovsky-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:43+00:00",
    "updated_at": "2026-08-17T19:47:43+00:00"
  },
  "P9782": {
    "problem_number": 9782,
    "slug": "open-fc-cffcdf5b1d2dad5dddee-casas-alvero-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:36+00:00",
    "updated_at": "2026-08-17T20:02:36+00:00"
  },
  "P9792": {
    "problem_number": 9792,
    "slug": "open-fc-da5ebb4ec784012da8d2-collatz-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:41+00:00",
    "updated_at": "2026-08-17T20:02:42+00:00"
  },
  "P11612": {
    "problem_number": 11612,
    "slug": "the-conjecturally-unbounded-sigma-phi-orbit-from-270",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:38:37+00:00",
    "updated_at": "2026-08-30T04:38:45+00:00"
  },
  "P3458": {
    "problem_number": 3458,
    "slug": "kourovka-21-73-the-conjugacy-problem-in-the-class-transposition-group",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:40+00:00",
    "updated_at": "2026-08-12T08:05:44+00:00"
  },
  "P9372": {
    "problem_number": 9372,
    "slug": "open-fc-f26df143e50a52068086-curling-number-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:14+00:00",
    "updated_at": "2026-08-17T19:51:14+00:00"
  },
  "P12359": {
    "problem_number": 12359,
    "slug": "the-curling-number-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:43:07+00:00",
    "updated_at": "2026-09-01T19:43:13+00:00"
  },
  "P3368": {
    "problem_number": 3368,
    "slug": "kourovka-21-6-the-cyclic-block-property-for-transitive-sylow-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:43:50+00:00",
    "updated_at": "2026-08-12T07:44:29+00:00"
  },
  "P12325": {
    "problem_number": 12325,
    "slug": "the-density-of-partitions-into-two-nonzero-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:38:57+00:00",
    "updated_at": "2026-09-01T19:39:03+00:00"
  },
  "P8416": {
    "problem_number": 8416,
    "slug": "open-fc-2b990f427ade6e7df12d-determinantal-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:32+00:00",
    "updated_at": "2026-08-17T18:50:34+00:00"
  },
  "P11178": {
    "problem_number": 11178,
    "slug": "ehrenfeucht-mycielski-balance-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T03:33:36+00:00",
    "updated_at": "2026-08-29T18:48:44+00:00"
  },
  "P11662": {
    "problem_number": 11662,
    "slug": "the-eldar-ordowski-gcd-criterion-for-wolstenholme-numerators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:03:52+00:00",
    "updated_at": "2026-08-30T16:33:29+00:00"
  },
  "P9886": {
    "problem_number": 9886,
    "slug": "open-fc-66e4fe8a15b76db6eca6-elliott-halberstam",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:16+00:00",
    "updated_at": "2026-08-17T20:04:16+00:00"
  },
  "P9302": {
    "problem_number": 9302,
    "slug": "open-fc-bce9007f1b12a9980e95-erdos-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:44+00:00",
    "updated_at": "2026-08-17T19:50:44+00:00"
  },
  "P3004": {
    "problem_number": 3004,
    "slug": "erdos-problem-61",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:28:21+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P11969": {
    "problem_number": 11969,
    "slug": "the-exact-erdos-sarkozy-bound-for-property-p",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T03:59:38+00:00",
    "updated_at": "2026-08-31T03:59:53+00:00"
  },
  "P11728": {
    "problem_number": 11728,
    "slug": "the-exact-eventual-excess-in-a-monotone-totient-subsequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:20:52+00:00",
    "updated_at": "2026-08-30T11:22:08+00:00"
  },
  "P8854": {
    "problem_number": 8854,
    "slug": "open-fc-b32681fd169576da5def-extended-sierpinski-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:26:43+00:00",
    "updated_at": "2026-08-17T19:26:52+00:00"
  },
  "P9192": {
    "problem_number": 9192,
    "slug": "open-fc-45b4ae5b1ec0f5131d16-feit-thompson-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:09+00:00",
    "updated_at": "2026-08-17T19:49:10+00:00"
  },
  "P8840": {
    "problem_number": 8840,
    "slug": "open-fc-a82eb1d9216bbe0d3751-fermat-catalan",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:25:30+00:00",
    "updated_at": "2026-08-17T19:25:41+00:00"
  },
  "P12461": {
    "problem_number": 12461,
    "slug": "the-first-perimeter-8-polyiamond",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:38:13+00:00",
    "updated_at": "2026-09-02T21:38:23+00:00"
  },
  "P8890": {
    "problem_number": 8890,
    "slug": "open-fc-cb76296c7ede769e7b8a-four-exponentials-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:36+00:00",
    "updated_at": "2026-08-17T19:36:40+00:00"
  },
  "P8942": {
    "problem_number": 8942,
    "slug": "open-fc-f28009e2af544e415ac4-gap-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:41:04+00:00",
    "updated_at": "2026-08-17T19:41:06+00:00"
  },
  "P12151": {
    "problem_number": 12151,
    "slug": "the-growth-ratio-for-equal-collatz-stopping-times",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:17:46+00:00",
    "updated_at": "2026-09-01T19:17:52+00:00"
  },
  "P3400": {
    "problem_number": 3400,
    "slug": "kourovka-21-30-the-haagerup-property-for-one-relator-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:57:23+00:00",
    "updated_at": "2026-08-12T07:57:26+00:00"
  },
  "P3344": {
    "problem_number": 3344,
    "slug": "erdos-problem-508",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:07:40+00:00",
    "updated_at": "2026-08-12T06:07:48+00:00"
  },
  "P8700": {
    "problem_number": 8700,
    "slug": "open-fc-2df05e8feac1c6895933-hadwigernelsonproblem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:35+00:00",
    "updated_at": "2026-08-17T19:59:57+00:00"
  },
  "P9980": {
    "problem_number": 9980,
    "slug": "open-fc-ab9e3a0450a8f1a7b396-erdos-107",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:11+00:00",
    "updated_at": "2026-08-17T20:05:12+00:00"
  },
  "P3172": {
    "problem_number": 3172,
    "slug": "erdos-problem-107",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:48:10+00:00",
    "updated_at": "2026-08-12T05:48:15+00:00"
  },
  "P11652": {
    "problem_number": 11652,
    "slug": "the-hardy-littlewood-asymptotic-for-prime-five-tuples-of-diameter-12",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:52:41+00:00",
    "updated_at": "2026-08-30T04:53:38+00:00"
  },
  "P9918": {
    "problem_number": 9918,
    "slug": "open-fc-7f77d9fe3b2c543f6e12-herzog-schonheim",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:32+00:00",
    "updated_at": "2026-08-17T20:04:32+00:00"
  },
  "P9438": {
    "problem_number": 9438,
    "slug": "open-fc-6ab198b7a6dcacfba86d-erdos-274",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:17+00:00",
    "updated_at": "2026-08-17T19:53:19+00:00"
  },
  "P8360": {
    "problem_number": 8360,
    "slug": "open-fc-241879377578549156bd-hilbert-smith-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:21+00:00",
    "updated_at": "2026-08-17T18:40:23+00:00"
  },
  "P8380": {
    "problem_number": 8380,
    "slug": "open-fc-2652f0d66f4458af40d1-inscribed-square-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:48:49+00:00",
    "updated_at": "2026-08-17T18:48:50+00:00"
  },
  "P9012": {
    "problem_number": 9012,
    "slug": "open-fc-8324ac98ca8660417a0e-invariant-subspace-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:00+00:00",
    "updated_at": "2026-08-17T19:45:02+00:00"
  },
  "P10022": {
    "problem_number": 10022,
    "slug": "open-fc-cb3568595fa124539e55-inverse-galois-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:29+00:00",
    "updated_at": "2026-08-17T20:05:30+00:00"
  },
  "P8600": {
    "problem_number": 8600,
    "slug": "open-fc-827e4fb148b1eb4c61da-juggler-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:58+00:00",
    "updated_at": "2026-08-17T19:50:13+00:00"
  },
  "P9718": {
    "problem_number": 9718,
    "slug": "open-fc-9ed0110d7506ed1047f1-kakeya-set-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:03+00:00",
    "updated_at": "2026-08-17T20:02:04+00:00"
  },
  "P10088": {
    "problem_number": 10088,
    "slug": "open-fc-feb7d62593b1d45e9058-komlos-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:23+00:00",
    "updated_at": "2026-08-17T20:06:24+00:00"
  },
  "P8928": {
    "problem_number": 8928,
    "slug": "open-fc-e9aa04cb2ee8a223d37b-kummer-vandiver",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:44+00:00",
    "updated_at": "2026-08-17T19:40:45+00:00"
  },
  "P8454": {
    "problem_number": 8454,
    "slug": "open-fc-3eadb1105166838e6ddc-kotheconjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:10+00:00",
    "updated_at": "2026-08-17T18:52:10+00:00"
  },
  "P9960": {
    "problem_number": 9960,
    "slug": "open-fc-9ca8e54ffe55d37bfa81-lander-parkin-selfridge",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:55+00:00",
    "updated_at": "2026-08-17T20:04:56+00:00"
  },
  "P11762": {
    "problem_number": 11762,
    "slug": "the-last-non-repunit-two-step-revenant-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:23:36+00:00",
    "updated_at": "2026-08-30T12:23:47+00:00"
  },
  "P11768": {
    "problem_number": 11768,
    "slug": "the-last-unresolved-12-vertex-neighborly-4-polytope",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:24:24+00:00",
    "updated_at": "2026-08-30T12:24:33+00:00"
  },
  "P8550": {
    "problem_number": 8550,
    "slug": "open-fc-6f5f8cbfafac09dd290e-lebesgue-nagell",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:36+00:00",
    "updated_at": "2026-08-17T18:54:37+00:00"
  },
  "P8482": {
    "problem_number": 8482,
    "slug": "open-fc-4bbfa4d6fef6d3f39235-erdos-950-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:21+00:00",
    "updated_at": "2026-08-17T18:52:22+00:00"
  },
  "P8598": {
    "problem_number": 8598,
    "slug": "open-fc-35c0f03dcd79f4eb0378-erdos-36",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:53+00:00",
    "updated_at": "2026-08-17T18:57:05+00:00"
  },
  "P2988": {
    "problem_number": 2988,
    "slug": "erdos-problem-36",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:58+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P8134": {
    "problem_number": 8134,
    "slug": "open-fc-054176c415046edb1394-erdos-950-parts-ii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:59+00:00",
    "updated_at": "2026-08-17T18:35:01+00:00"
  },
  "P8238": {
    "problem_number": 8238,
    "slug": "open-fc-14485577e0215fe68496-erdos-495",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:34+00:00",
    "updated_at": "2026-08-17T18:37:35+00:00"
  },
  "P8516": {
    "problem_number": 8516,
    "slug": "open-fc-5e42e0dd88717281edeb-littlewood-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:53:59+00:00",
    "updated_at": "2026-08-17T18:54:05+00:00"
  },
  "P9304": {
    "problem_number": 9304,
    "slug": "open-fc-be683f922e9502245bce-lonely-runner-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:44+00:00",
    "updated_at": "2026-08-17T19:50:45+00:00"
  },
  "P9808": {
    "problem_number": 9808,
    "slug": "open-fc-e6de49d189f6ba8a3f2a-mutuallyunbiasedbases",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:51+00:00",
    "updated_at": "2026-08-17T20:02:52+00:00"
  },
  "P8370": {
    "problem_number": 8370,
    "slug": "open-fc-257742404c82ce5321de-erdos-33",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:40:50+00:00",
    "updated_at": "2026-08-17T18:40:58+00:00"
  },
  "P2986": {
    "problem_number": 2986,
    "slug": "erdos-problem-33",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:55+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P3154": {
    "problem_number": 3154,
    "slug": "erdos-problem-742",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:38:02+00:00",
    "updated_at": "2026-08-12T05:39:09+00:00"
  },
  "P8938": {
    "problem_number": 8938,
    "slug": "open-fc-f13b6201a4c0dfe38309-new-mersenne-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:58+00:00",
    "updated_at": "2026-08-17T19:41:00+00:00"
  },
  "P9542": {
    "problem_number": 9542,
    "slug": "open-fc-ba23231c05b8eb88d04b-new-mersenne-conjecture-variants-prime",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:54+00:00",
    "updated_at": "2026-08-17T19:54:55+00:00"
  },
  "P10086": {
    "problem_number": 10086,
    "slug": "open-fc-fcfaf72454a26dff29f6-nokinline",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:06:21+00:00",
    "updated_at": "2026-08-17T20:06:22+00:00"
  },
  "P10000": {
    "problem_number": 10000,
    "slug": "open-fc-bc3914e56c2be65265f8-np-ne-conp",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:18+00:00",
    "updated_at": "2026-08-17T20:05:18+00:00"
  },
  "P3104": {
    "problem_number": 3104,
    "slug": "gaussian-centered-ellipsoid-fitting-quarter-threshold",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:01+00:00",
    "updated_at": "2026-08-02T12:50:34+00:00"
  },
  "P9292": {
    "problem_number": 9292,
    "slug": "open-fc-b51160eaccf8338b5255-omega-times-two-four",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:40+00:00",
    "updated_at": "2026-08-17T19:50:40+00:00"
  },
  "P9964": {
    "problem_number": 9964,
    "slug": "open-fc-9fd35b973c621728d4d4-p-ne-np",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:58+00:00",
    "updated_at": "2026-08-17T20:04:58+00:00"
  },
  "P8128": {
    "problem_number": 8128,
    "slug": "open-fc-04da5f7fb18070582135-hilbert-smith-padic-formulation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:54+00:00",
    "updated_at": "2026-08-17T18:34:56+00:00"
  },
  "P8880": {
    "problem_number": 8880,
    "slug": "open-fc-c4aa47643b2d2365f5ed-pebbling-number-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:15+00:00",
    "updated_at": "2026-08-17T19:36:18+00:00"
  },
  "P9794": {
    "problem_number": 9794,
    "slug": "open-fc-dbe855d4044d939ee641-pierce-birkhoff-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:43+00:00",
    "updated_at": "2026-08-17T20:02:43+00:00"
  },
  "P12195": {
    "problem_number": 12195,
    "slug": "the-predicted-density-of-balanced-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:23:07+00:00",
    "updated_at": "2026-09-01T19:23:12+00:00"
  },
  "P9546": {
    "problem_number": 9546,
    "slug": "open-fc-bd353001e721a8c43474-erdos-723",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:59+00:00",
    "updated_at": "2026-08-17T19:55:00+00:00"
  },
  "P3176": {
    "problem_number": 3176,
    "slug": "erdos-problem-723",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:49:12+00:00",
    "updated_at": "2026-08-12T05:49:24+00:00"
  },
  "P9462": {
    "problem_number": 9462,
    "slug": "open-fc-7f528eda4264a8ff1f1b-prime-sierpinski-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:53:58+00:00",
    "updated_at": "2026-08-17T19:53:58+00:00"
  },
  "P9880": {
    "problem_number": 9880,
    "slug": "open-fc-611dcfa45585d811973c-ramsey-number-five-five",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:12+00:00",
    "updated_at": "2026-08-17T20:04:13+00:00"
  },
  "P8124": {
    "problem_number": 8124,
    "slug": "open-fc-049bcd9017c0cfed97cf-rational-distance-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:52+00:00",
    "updated_at": "2026-08-17T18:34:53+00:00"
  },
  "P12065": {
    "problem_number": 12065,
    "slug": "the-remaining-squared-factor-in-melham-s-fibonacci-sum-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:07:23+00:00",
    "updated_at": "2026-09-01T19:07:29+00:00"
  },
  "P9788": {
    "problem_number": 9788,
    "slug": "open-fc-d5828bf5ad06958fce1f-riemannhypothesis",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:40+00:00",
    "updated_at": "2026-08-17T20:02:40+00:00"
  },
  "P9036": {
    "problem_number": 9036,
    "slug": "open-fc-96135084ff8a01ffd930-pollock-tetrahedral-salzer-levine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:47+00:00",
    "updated_at": "2026-08-17T19:45:49+00:00"
  },
  "P8918": {
    "problem_number": 8918,
    "slug": "open-fc-e245b0739cae3afbf21e-second-hardy-littlewood-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:29+00:00",
    "updated_at": "2026-08-17T19:40:31+00:00"
  },
  "P2516": {
    "problem_number": 2516,
    "slug": "two-moment-poincare-constant",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:13+00:00",
    "updated_at": "2026-08-01T23:52:12+00:00"
  },
  "P11778": {
    "problem_number": 11778,
    "slug": "the-six-missing-2p-twin-peak-cases",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:32:23+00:00",
    "updated_at": "2026-08-30T12:34:22+00:00"
  },
  "P9418": {
    "problem_number": 9418,
    "slug": "open-fc-5cd299d473662992122e-bb-6",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:35+00:00",
    "updated_at": "2026-08-17T19:52:37+00:00"
  },
  "P12255": {
    "problem_number": 12255,
    "slug": "the-smallest-kempner-gap-for-consecutive-squarefree-integers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:30:30+00:00",
    "updated_at": "2026-09-01T19:30:35+00:00"
  },
  "P3466": {
    "problem_number": 3466,
    "slug": "kourovka-21-86-the-sofic-group-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:05:58+00:00",
    "updated_at": "2026-08-12T08:06:02+00:00"
  },
  "P12405": {
    "problem_number": 12405,
    "slug": "the-square-sieve-in-four-stages",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:32:28+00:00",
    "updated_at": "2026-09-02T21:32:40+00:00"
  },
  "P8658": {
    "problem_number": 8658,
    "slug": "open-fc-8ee6eaf0a8401bb6ff3d-strong-sensitivity-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:59:52+00:00",
    "updated_at": "2026-08-17T19:23:08+00:00"
  },
  "P12481": {
    "problem_number": 12481,
    "slug": "the-substring-333-in-3n-cubed",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:40:12+00:00",
    "updated_at": "2026-09-02T21:40:24+00:00"
  },
  "P12445": {
    "problem_number": 12445,
    "slug": "the-substring-666-in-powers-of-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:36:29+00:00",
    "updated_at": "2026-09-02T21:36:43+00:00"
  },
  "P11690": {
    "problem_number": 11690,
    "slug": "the-sum-of-two-squares-criterion-for-conference-matrix-orders",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:09+00:00",
    "updated_at": "2026-08-30T11:15:16+00:00"
  },
  "P9254": {
    "problem_number": 9254,
    "slug": "open-fc-98f733c37ef19ccfcbe5-dedekind-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:25+00:00",
    "updated_at": "2026-08-17T19:50:25+00:00"
  },
  "P9156": {
    "problem_number": 9156,
    "slug": "open-fc-f1860ca3c6e7616d5e6b-m-eq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:51+00:00",
    "updated_at": "2026-08-17T19:47:52+00:00"
  },
  "P2818": {
    "problem_number": 2818,
    "slug": "circular-distinct-squares-three-halves",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:14+00:00",
    "updated_at": "2026-07-30T02:24:45+00:00"
  },
  "P3142": {
    "problem_number": 3142,
    "slug": "total-coloring-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:10+00:00",
    "updated_at": "2026-08-02T12:56:29+00:00"
  },
  "P11760": {
    "problem_number": 11760,
    "slug": "the-triangular-factorial-equation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:23:25+00:00",
    "updated_at": "2026-08-30T12:23:34+00:00"
  },
  "P9282": {
    "problem_number": 9282,
    "slug": "open-fc-ac7d0e814b32d50c1060-twin-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:36+00:00",
    "updated_at": "2026-08-17T19:50:37+00:00"
  },
  "P11146": {
    "problem_number": 11146,
    "slug": "the-unfair-0-1-polynomial-problem-and-high-degree-trinomials",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-20T09:22:29+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P8706": {
    "problem_number": 8706,
    "slug": "open-fc-3d7e34870a7209b62f9f-union-closed",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:06:11+00:00",
    "updated_at": "2026-08-17T19:52:08+00:00"
  },
  "P11873": {
    "problem_number": 11873,
    "slug": "the-unresolved-49-and-77-home-prime-trajectory",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:32+00:00",
    "updated_at": "2026-08-30T16:16:37+00:00"
  },
  "P2912": {
    "problem_number": 2912,
    "slug": "levine-two-player-seven-twentieths",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:47:02+00:00",
    "updated_at": "2026-07-29T20:55:52+00:00"
  },
  "P9888": {
    "problem_number": 9888,
    "slug": "open-fc-68496513e13ba958fbd5-green-40-f-two-eq-one",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:17+00:00",
    "updated_at": "2026-08-17T20:04:17+00:00"
  },
  "P9540": {
    "problem_number": 9540,
    "slug": "open-fc-b7a5d1cd92003cd7c4b5-vaught-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:52+00:00",
    "updated_at": "2026-08-17T19:54:53+00:00"
  },
  "P11608": {
    "problem_number": 11608,
    "slug": "the-wieferich-prime-orbit-of-47",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:38:11+00:00",
    "updated_at": "2026-08-30T04:38:19+00:00"
  },
  "P8200": {
    "problem_number": 8200,
    "slug": "open-fc-0d9557db43a4770c3b27-zariski-cancellation-problem",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:58+00:00",
    "updated_at": "2026-08-17T18:37:00+00:00"
  },
  "P9580": {
    "problem_number": 9580,
    "slug": "open-fc-d81274b4af335c728acb-cerny-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:57+00:00",
    "updated_at": "2026-08-17T19:56:00+00:00"
  },
  "P11158": {
    "problem_number": 11158,
    "slug": "third-level-log-concavity-riemann-xi-kernel",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-24T18:57:50+00:00",
    "updated_at": "2026-08-31T19:00:29.907336+00:00"
  },
  "P11897": {
    "problem_number": 11897,
    "slug": "three-conjectural-zeros-in-a-totient-addition-equation",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:20:59+00:00",
    "updated_at": "2026-08-30T16:21:05+00:00"
  },
  "P11776": {
    "problem_number": 11776,
    "slug": "three-generalized-square-pyramidal-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:28:59+00:00",
    "updated_at": "2026-08-30T12:31:01+00:00"
  },
  "P2534": {
    "problem_number": 2534,
    "slug": "three-mols-order-10",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:19+00:00",
    "updated_at": "2026-07-29T20:56:54+00:00"
  },
  "P11927": {
    "problem_number": 11927,
    "slug": "three-primes-1-modulo-4-summing-to-every-later-prime-3-modulo-4",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:24:01+00:00",
    "updated_at": "2026-08-30T16:24:05+00:00"
  },
  "P12015": {
    "problem_number": 12015,
    "slug": "three-cycle-conjecture-for-the-3x-1-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:50:34+00:00",
    "updated_at": "2026-09-01T18:50:44+00:00"
  },
  "P29": {
    "problem_number": 29,
    "slug": "three-dimensional-euler-regularity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:32:57+00:00"
  },
  "P12411": {
    "problem_number": 12411,
    "slug": "three-square-exceptions-and-scaling",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:33:08+00:00",
    "updated_at": "2026-09-02T21:33:16+00:00"
  },
  "P12745": {
    "problem_number": 12745,
    "slug": "three-square-representations-of-powers-of-nine",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:39:39+00:00",
    "updated_at": "2026-09-02T22:40:13+00:00"
  },
  "P3756": {
    "problem_number": 3756,
    "slug": "grid-five-six-token-slide-diameter",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:24+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2814": {
    "problem_number": 2814,
    "slug": "king-grid-independence-homology-torsion-free",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:03:12+00:00",
    "updated_at": "2026-08-01T23:31:52+00:00"
  },
  "P11937": {
    "problem_number": 11937,
    "slug": "total-definition-of-the-six-seed-hofstadter-q-relative",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:30:40+00:00",
    "updated_at": "2026-08-30T16:30:57+00:00"
  },
  "P9806": {
    "problem_number": 9806,
    "slug": "open-fc-e47c87ed35d76b2c4c26-conjecture291",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:49+00:00",
    "updated_at": "2026-08-17T20:02:50+00:00"
  },
  "P12217": {
    "problem_number": 12217,
    "slug": "total-variation-of-consecutive-prime-gaps",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:25:48+00:00",
    "updated_at": "2026-09-01T19:25:54+00:00"
  },
  "P11588": {
    "problem_number": 11588,
    "slug": "totality-of-the-unused-prime-divisibility-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:36:15+00:00",
    "updated_at": "2026-08-30T04:36:20+00:00"
  },
  "P12721": {
    "problem_number": 12721,
    "slug": "totient-equation-solutions-and-pierpont-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:30:29+00:00",
    "updated_at": "2026-09-02T22:30:51+00:00"
  },
  "P10772": {
    "problem_number": 10772,
    "slug": "unsolvedmath-0145-trace-reconstruction",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-18T02:55:10+00:00",
    "updated_at": "2026-08-18T02:55:10+00:00"
  },
  "P2750": {
    "problem_number": 2750,
    "slug": "sl2-f5-triple-trace-fibers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T18:00:44+00:00",
    "updated_at": "2026-08-01T23:47:21+00:00"
  },
  "P8084": {
    "problem_number": 8084,
    "slug": "open-fc-00b31dfe44be81dab666-pi-pow-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:36+00:00",
    "updated_at": "2026-08-17T18:34:36+00:00"
  },
  "P9336": {
    "problem_number": 9336,
    "slug": "open-fc-d7a227d7cffd897884f8-pi-pow-exp-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:59+00:00",
    "updated_at": "2026-08-17T19:51:00+00:00"
  },
  "P8690": {
    "problem_number": 8690,
    "slug": "open-fc-377e668de86d233c482f-pi-pow-sqrt-two-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:58+00:00",
    "updated_at": "2026-08-17T19:05:01+00:00"
  },
  "P9062": {
    "problem_number": 9062,
    "slug": "open-fc-a8aed48a3088639579f6-exp-add-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:46:35+00:00",
    "updated_at": "2026-08-17T19:46:36+00:00"
  },
  "P9686": {
    "problem_number": 9686,
    "slug": "open-fc-81bf802bb79edd2ffc7b-exp-exp-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:01:33+00:00",
    "updated_at": "2026-08-17T20:01:36+00:00"
  },
  "P8666": {
    "problem_number": 8666,
    "slug": "open-fc-2d235d8c8110ba294b4a-exp-pow-pi-sq-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:11+00:00",
    "updated_at": "2026-08-17T19:04:16+00:00"
  },
  "P9814": {
    "problem_number": 9814,
    "slug": "open-fc-eb05f5f18693c9368b0c-two-pow-three-pow-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:53+00:00",
    "updated_at": "2026-08-17T20:02:54+00:00"
  },
  "P8586": {
    "problem_number": 8586,
    "slug": "open-fc-7f5c8f9d45b697e78d77-transcendental-gamma-one-div",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:19+00:00",
    "updated_at": "2026-08-17T18:56:32+00:00"
  },
  "P8680": {
    "problem_number": 8680,
    "slug": "open-fc-34d4396e5eb1b0629acb-erdos-247",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:41+00:00",
    "updated_at": "2026-08-17T19:04:42+00:00"
  },
  "P8542": {
    "problem_number": 8542,
    "slug": "open-fc-6ab5e69c35ce5d471132-transcendental-catalanconstant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:54:28+00:00",
    "updated_at": "2026-08-17T18:54:29+00:00"
  },
  "P9218": {
    "problem_number": 9218,
    "slug": "open-fc-6e37c7a4547772436df8-pi-pow-pi-pow-pi-pow-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:39+00:00",
    "updated_at": "2026-08-17T19:49:40+00:00"
  },
  "P9496": {
    "problem_number": 9496,
    "slug": "open-fc-97efa650ec0e2a37c65f-transcendental-gompertzconstant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:25+00:00",
    "updated_at": "2026-08-17T19:54:26+00:00"
  },
  "P9558": {
    "problem_number": 9558,
    "slug": "open-fc-c56806174082e0e6489f-rlog-rlog-two-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:55:16+00:00",
    "updated_at": "2026-08-17T19:55:16+00:00"
  },
  "P8492": {
    "problem_number": 8492,
    "slug": "open-fc-50da5062df679bba388c-rlog-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:28+00:00",
    "updated_at": "2026-08-17T18:52:29+00:00"
  },
  "P9274": {
    "problem_number": 9274,
    "slug": "open-fc-a70dc07c15c98fc4039b-exp-mul-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:33+00:00",
    "updated_at": "2026-08-17T19:50:33+00:00"
  },
  "P9296": {
    "problem_number": 9296,
    "slug": "open-fc-b78fa80e620fd26493d6-sin-exp-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:41+00:00",
    "updated_at": "2026-08-17T19:50:42+00:00"
  },
  "P8572": {
    "problem_number": 8572,
    "slug": "open-fc-7ce44470081a224ab433-pi-pow-pi-pow-pi-transcendental",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:55:36+00:00",
    "updated_at": "2026-08-17T18:55:45+00:00"
  },
  "P3366": {
    "problem_number": 3366,
    "slug": "kourovka-21-5-transitive-sylow-subgroups-of-finitary-permutation-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:42:56+00:00",
    "updated_at": "2026-08-12T07:43:44+00:00"
  },
  "P11682": {
    "problem_number": 11682,
    "slug": "trapping-the-origin-first-three-dimensional-knight-walk",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:09:17+00:00",
    "updated_at": "2026-08-30T16:35:39+00:00"
  },
  "P11949": {
    "problem_number": 11949,
    "slug": "triangular-numbers-with-every-even-divisor-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:34:06+00:00",
    "updated_at": "2026-08-30T16:34:18+00:00"
  },
  "P9154": {
    "problem_number": 9154,
    "slug": "open-fc-f062cc840475efd84524-tunnell-even-converse",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:50+00:00",
    "updated_at": "2026-08-17T19:47:51+00:00"
  },
  "P3654": {
    "problem_number": 3654,
    "slug": "lee-cover-seventeen-square-twenty-seven",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:44:06+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3704": {
    "problem_number": 3704,
    "slug": "z11-euclidean-torus-code-twenty-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:22+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P28": {
    "problem_number": 28,
    "slug": "twin-prime-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:33:40+00:00"
  },
  "P12031": {
    "problem_number": 12031,
    "slug": "twin-prime-free-intervals-between-consecutive-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:53:20+00:00",
    "updated_at": "2026-09-01T18:53:48+00:00"
  },
  "P11909": {
    "problem_number": 11909,
    "slug": "twin-prime-free-intervals-between-prime-indexed-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:22:00+00:00",
    "updated_at": "2026-08-30T16:22:05+00:00"
  },
  "P12563": {
    "problem_number": 12563,
    "slug": "two-definitions-of-good-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:49:09+00:00",
    "updated_at": "2026-09-02T21:49:34+00:00"
  },
  "P12493": {
    "problem_number": 12493,
    "slug": "two-equinumerous-pattern-avoidance-classes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:41:22+00:00",
    "updated_at": "2026-09-02T21:41:33+00:00"
  },
  "P11947": {
    "problem_number": 11947,
    "slug": "two-last-exception-descriptions-for-divisor-counts-of-p-n-minus-1",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:32:50+00:00",
    "updated_at": "2026-08-30T16:33:09+00:00"
  },
  "P12447": {
    "problem_number": 12447,
    "slug": "two-step-growth-in-a-bitwise-or-greedy-sequence",
    "resolution_state": "open",
    "solution_state": "submitted",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "candidate_resolution",
        "label": "Solution submitted",
        "tone": "candidate",
        "reason": "A complete answer is reported without an accepted resolution review.",
        "transitionRule": "A complete answer is reported without an accepted resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": {
          "id": null,
          "slug": "oeis-a057923-source-audit-batch-004-result-474ecbe1324bf0ba-claim",
          "title": "Claim from Submit the complete bit-clearing proof of two-step growth for independent mathematical review.",
          "url": "/research/changes/?proposal_id=tdbrpp1%3A66dc8bed7839819d3840cf0ed9bf8b53",
          "proposalId": "tdbrpp1:66dc8bed7839819d3840cf0ed9bf8b53"
        }
      },
      "proofMessage": "A solution has been submitted and awaits independent review. Lean source is attached; signed verification is pending.",
      "summary": "Solution submitted. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:36:49+00:00",
    "updated_at": "2026-09-02T21:37:00+00:00"
  },
  "P3538": {
    "problem_number": 3538,
    "slug": "kourovka-21-140-type-f-infinity-at-infinite-cohomological-dimension",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:43+00:00",
    "updated_at": "2026-08-12T08:12:47+00:00"
  },
  "P12521": {
    "problem_number": 12521,
    "slug": "unary-binary-trees-and-repeated-differences",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:44:06+00:00",
    "updated_at": "2026-09-02T21:44:18+00:00"
  },
  "P11644": {
    "problem_number": 11644,
    "slug": "unbounded-clockwise-winding-of-twin-prime-final-digits",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:44:46+00:00",
    "updated_at": "2026-08-30T04:45:48+00:00"
  },
  "P2848": {
    "problem_number": 2848,
    "slug": "pi-not-badly-approximable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:38:27+00:00",
    "updated_at": "2026-08-01T23:40:03+00:00"
  },
  "P8192": {
    "problem_number": 8192,
    "slug": "open-fc-0c8916e4de234fa9e31d-erdos-853-parts-i",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:36:47+00:00",
    "updated_at": "2026-08-17T18:36:48+00:00"
  },
  "P3232": {
    "problem_number": 3232,
    "slug": "erdos-problem-853",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:55:33+00:00",
    "updated_at": "2026-08-12T05:55:40+00:00"
  },
  "P11877": {
    "problem_number": 11877,
    "slug": "unbounded-joining-times-for-the-n-plus-divisor-count-map",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:16:46+00:00",
    "updated_at": "2026-08-30T16:16:51+00:00"
  },
  "P11624": {
    "problem_number": 11624,
    "slug": "unbounded-multiplicity-of-prime-sums-in-the-3-by-3-spiral",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:40:12+00:00",
    "updated_at": "2026-08-30T04:40:19+00:00"
  },
  "P2850": {
    "problem_number": 2850,
    "slug": "unbounded-integral-points-minimal-elliptic-curves",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:38:43+00:00",
    "updated_at": "2026-08-01T23:52:31+00:00"
  },
  "P12219": {
    "problem_number": 12219,
    "slug": "unbounded-orbits-in-post-s-tag-system",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:26:03+00:00",
    "updated_at": "2026-09-01T19:26:08+00:00"
  },
  "P3434": {
    "problem_number": 3434,
    "slug": "kourovka-21-48-unbounded-quasimorphisms-and-free-subgroups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:01:48+00:00",
    "updated_at": "2026-08-12T08:01:54+00:00"
  },
  "P8108": {
    "problem_number": 8108,
    "slug": "open-fc-02fcbd6130d956a7c27c-unbounded-rank-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:34:43+00:00",
    "updated_at": "2026-08-17T18:34:43+00:00"
  },
  "P12247": {
    "problem_number": 12247,
    "slug": "unbounded-record-ratios-in-a-cellular-automaton-limit-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:29:29+00:00",
    "updated_at": "2026-09-01T19:29:35+00:00"
  },
  "P2980": {
    "problem_number": 2980,
    "slug": "erdos-problem-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-01T11:27:46+00:00",
    "updated_at": "2026-08-14T06:46:15.163700+00:00"
  },
  "P9488": {
    "problem_number": 9488,
    "slug": "open-fc-9159d9c6a6a719a450de-erdos-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:23+00:00",
    "updated_at": "2026-08-17T19:54:24+00:00"
  },
  "P12029": {
    "problem_number": 12029,
    "slug": "unbounded-runs-of-odious-consecutive-primes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T18:52:59+00:00",
    "updated_at": "2026-09-01T18:53:10+00:00"
  },
  "P11740": {
    "problem_number": 11740,
    "slug": "unbounded-zero-runs-in-a-self-indexing-binary-substring-sequence",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:31:58+00:00",
    "updated_at": "2026-08-30T11:33:22+00:00"
  },
  "P3234": {
    "problem_number": 3234,
    "slug": "erdos-problem-454",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:55:49+00:00",
    "updated_at": "2026-08-12T05:55:55+00:00"
  },
  "P8500": {
    "problem_number": 8500,
    "slug": "open-fc-55e6e3d0dbda32091070-erdos-454",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:54+00:00",
    "updated_at": "2026-08-17T18:53:00+00:00"
  },
  "P3250": {
    "problem_number": 3250,
    "slug": "erdos-problem-979",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:01+00:00",
    "updated_at": "2026-08-12T05:58:04+00:00"
  },
  "P8866": {
    "problem_number": 8866,
    "slug": "open-fc-bb1d6ee10def950fce31-erdos-979",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:35:38+00:00",
    "updated_at": "2026-08-17T19:35:43+00:00"
  },
  "P8154": {
    "problem_number": 8154,
    "slug": "open-fc-085693f993180efb2556-a-unbounded",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:35:22+00:00",
    "updated_at": "2026-08-17T18:35:24+00:00"
  },
  "P3152": {
    "problem_number": 3152,
    "slug": "uncertainty-scaled-detection-floors-versus-length-gates-for-road-descents-from-noisy-elevation-profiles",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-09T12:02:07+00:00",
    "updated_at": "2026-08-16T13:00:02.445781+00:00"
  },
  "P12131": {
    "problem_number": 12131,
    "slug": "uniform-denominator-clearing-constants-for-a-factorial-ratio",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:15:14+00:00",
    "updated_at": "2026-09-01T19:15:19+00:00"
  },
  "P8490": {
    "problem_number": 8490,
    "slug": "open-fc-5042450829a86c2a1bea-green-28",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:52:26+00:00",
    "updated_at": "2026-08-17T18:52:28+00:00"
  },
  "P3566": {
    "problem_number": 3566,
    "slug": "quantum-parallel-repetition",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:52:25+00:00",
    "updated_at": "2026-08-18T06:09:35+00:00"
  },
  "P3444": {
    "problem_number": 3444,
    "slug": "kourovka-21-62-uniform-subgroup-membership-for-free-by-cyclic-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:03:55+00:00",
    "updated_at": "2026-08-12T08:04:06+00:00"
  },
  "P41": {
    "problem_number": 41,
    "slug": "union-closed-sets-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-16T22:56:40+00:00"
  },
  "P12577": {
    "problem_number": 12577,
    "slug": "unique-factorial-residues-modulo-composite-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:51:10+00:00",
    "updated_at": "2026-09-02T21:51:51+00:00"
  },
  "P44": {
    "problem_number": 44,
    "slug": "unique-games-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:34:34+00:00"
  },
  "P3408": {
    "problem_number": 3408,
    "slug": "kourovka-21-34-unique-product-groups-outside-the-diffuse-class",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T07:57:52+00:00",
    "updated_at": "2026-08-12T07:57:55+00:00"
  },
  "P9200": {
    "problem_number": 9200,
    "slug": "open-fc-512510c0e5a21cea9582-erdos-477-variants-x-pow-three",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:13+00:00",
    "updated_at": "2026-08-17T19:49:13+00:00"
  },
  "P9968": {
    "problem_number": 9968,
    "slug": "open-fc-a237e391a5b22dab849d-erdos-477-variants-monomial",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:00+00:00",
    "updated_at": "2026-08-17T20:05:01+00:00"
  },
  "P11692": {
    "problem_number": 11692,
    "slug": "uniqueness-of-consecutive-reciprocal-sums-with-shifted-prime-denominators",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:15:18+00:00",
    "updated_at": "2026-08-30T11:15:24+00:00"
  },
  "P8916": {
    "problem_number": 8916,
    "slug": "open-fc-e1b410d6fe889e84e744-crystals-components-unique",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:26+00:00",
    "updated_at": "2026-08-17T19:40:28+00:00"
  },
  "P12243": {
    "problem_number": 12243,
    "slug": "uniqueness-of-markoff-triples-with-a-fixed-maximum",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:29:00+00:00",
    "updated_at": "2026-09-01T19:29:05+00:00"
  },
  "P12287": {
    "problem_number": 12287,
    "slug": "uniqueness-of-markoff-triples-with-fixed-largest-entry",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:34:27+00:00",
    "updated_at": "2026-09-01T19:34:33+00:00"
  },
  "P8678": {
    "problem_number": 8678,
    "slug": "open-fc-34abbb904aac0314888f-rudins-conjecture-unique",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:04:38+00:00",
    "updated_at": "2026-08-17T19:04:40+00:00"
  },
  "P12105": {
    "problem_number": 12105,
    "slug": "uniqueness-of-the-infinite-divisor-subtraction-branch",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:11:41+00:00",
    "updated_at": "2026-09-01T19:11:47+00:00"
  },
  "P9630": {
    "problem_number": 9630,
    "slug": "open-fc-fc21e0048070c34dd370-unique-primitive-108",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:39+00:00",
    "updated_at": "2026-08-17T19:57:41+00:00"
  },
  "P11600": {
    "problem_number": 11600,
    "slug": "universal-divisibility-constraints-on-powers-that-are-twin-ranks",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:37:23+00:00",
    "updated_at": "2026-08-30T04:37:29+00:00"
  },
  "P11726": {
    "problem_number": 11726,
    "slug": "universal-nonnegative-representations-by-four-quadratic-forms",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:18:35+00:00",
    "updated_at": "2026-08-30T11:19:56+00:00"
  },
  "P12163": {
    "problem_number": 12163,
    "slug": "universal-primes-as-continued-fraction-fixed-points",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:19:15+00:00",
    "updated_at": "2026-09-01T19:19:20+00:00"
  },
  "P8902": {
    "problem_number": 8902,
    "slug": "open-fc-d3be1e57a45ce1f53b0b-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:09+00:00",
    "updated_at": "2026-08-17T19:40:09+00:00"
  },
  "P11931": {
    "problem_number": 11931,
    "slug": "universal-translated-containers-for-fixed-polyominoes",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:29:14+00:00",
    "updated_at": "2026-08-30T16:29:37+00:00"
  },
  "P11640": {
    "problem_number": 11640,
    "slug": "universal-value-coverage-in-the-repeated-sum-product-omega-recursion",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:42:21+00:00",
    "updated_at": "2026-08-30T04:42:27+00:00"
  },
  "P12501": {
    "problem_number": 12501,
    "slug": "universal-values-of-a-symmetric-bilinear-form",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:42:08+00:00",
    "updated_at": "2026-09-02T21:42:19+00:00"
  },
  "P11734": {
    "problem_number": 11734,
    "slug": "universal-weighted-sums-of-eight-fifth-powers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:24:59+00:00",
    "updated_at": "2026-08-30T16:35:53+00:00"
  },
  "P11973": {
    "problem_number": 11973,
    "slug": "hardy-z-cue-normalized-zero-jet-universality",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-31T20:55:23+00:00",
    "updated_at": "2026-09-07T21:00:00.506625+00:00"
  },
  "P12615": {
    "problem_number": 12615,
    "slug": "unused-primes-in-distinct-prime-partitions",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:58:07+00:00",
    "updated_at": "2026-09-02T21:58:15+00:00"
  },
  "P8872": {
    "problem_number": 8872,
    "slug": "open-fc-bf75e2ba7819468d8371-erdos-873",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:36:02+00:00",
    "updated_at": "2026-08-17T19:36:05+00:00"
  },
  "P9240": {
    "problem_number": 9240,
    "slug": "open-fc-8c6b08e1a882185f82e8-erdos-695-variants-upperbound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:16+00:00",
    "updated_at": "2026-08-17T19:50:16+00:00"
  },
  "P9756": {
    "problem_number": 9756,
    "slug": "open-fc-bd6ad95c566d6b20e818-erdos-539-variants-isbigo-sq",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:23+00:00",
    "updated_at": "2026-08-17T20:02:23+00:00"
  },
  "P8782": {
    "problem_number": 8782,
    "slug": "open-fc-56c0a6720bc649fdc765-green-19-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:19:59+00:00",
    "updated_at": "2026-08-17T19:20:09+00:00"
  },
  "P10032": {
    "problem_number": 10032,
    "slug": "open-fc-d37180d17d69e6c685eb-erdos-507-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:05:34+00:00",
    "updated_at": "2026-08-17T20:05:35+00:00"
  },
  "P9422": {
    "problem_number": 9422,
    "slug": "open-fc-5e839ef2605fbeefca67-erdos-688-parts-i-upper-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:52:40+00:00",
    "updated_at": "2026-08-17T19:52:41+00:00"
  },
  "P9386": {
    "problem_number": 9386,
    "slug": "open-fc-fbd8dfc892959a75fc51-green-16-upper-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:20+00:00",
    "updated_at": "2026-08-17T19:51:21+00:00"
  },
  "P8590": {
    "problem_number": 8590,
    "slug": "open-fc-32647d0aa6f238ca0939-erdos-700-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:56:29+00:00",
    "updated_at": "2026-08-17T18:56:35+00:00"
  },
  "P9626": {
    "problem_number": 9626,
    "slug": "open-fc-f920bf375516f7fa1724-erdos-357-variants-monotone-parts-ii-bigo-version-symm",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:57:29+00:00",
    "updated_at": "2026-08-17T19:57:32+00:00"
  },
  "P9924": {
    "problem_number": 9924,
    "slug": "open-fc-82bce63e761d0a50dfae-erdos-789-variants-isbigo-cube-root-linearithmic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:35+00:00",
    "updated_at": "2026-08-17T20:04:35+00:00"
  },
  "P3256": {
    "problem_number": 3256,
    "slug": "erdos-problem-1085",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T05:58:39+00:00",
    "updated_at": "2026-08-12T05:58:41+00:00"
  },
  "P9508": {
    "problem_number": 9508,
    "slug": "open-fc-9e8fe80def3a23dfdc00-erdos-142-variants-upper",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:31+00:00",
    "updated_at": "2026-08-17T19:54:32+00:00"
  },
  "P9344": {
    "problem_number": 9344,
    "slug": "open-fc-dfb326fd27d270697883-erdos-208-variants-log-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:03+00:00",
    "updated_at": "2026-08-17T19:51:03+00:00"
  },
  "P8248": {
    "problem_number": 8248,
    "slug": "open-fc-158a9e8147593ddbcaad-conjecture100",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:37:42+00:00",
    "updated_at": "2026-08-17T18:37:43+00:00"
  },
  "P9190": {
    "problem_number": 9190,
    "slug": "open-fc-428b4de5f07d0ee7b804-maximallength-le-strong",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:49:06+00:00",
    "updated_at": "2026-08-17T19:49:07+00:00"
  },
  "P3342": {
    "problem_number": 3342,
    "slug": "erdos-problem-945",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:07:26+00:00",
    "updated_at": "2026-08-12T06:07:36+00:00"
  },
  "P9016": {
    "problem_number": 9016,
    "slug": "open-fc-858c5f3850c71645c9b5-erdos-945",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:08+00:00",
    "updated_at": "2026-08-17T19:45:11+00:00"
  },
  "P9306": {
    "problem_number": 9306,
    "slug": "open-fc-c06bc0c12ddd9faaf4bb-erdos-126-variants-islittleo",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:46+00:00",
    "updated_at": "2026-08-17T19:50:48+00:00"
  },
  "P3556": {
    "problem_number": 3556,
    "slug": "sphere-packing-upper-bounds-cohn-elkies",
    "resolution_state": "review_pending",
    "solution_state": "review_pending",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolution_under_review",
        "label": "Claimed checked, not independently verified",
        "tone": "review-pending",
        "reason": "A complete answer passed an evidence check and awaits independent verification.",
        "transitionRule": "A complete answer passed an evidence check and awaits independent verification."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Claimed checked, not independently verified. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-13T04:50:19+00:00",
    "updated_at": "2026-08-18T06:09:36+00:00"
  },
  "P8694": {
    "problem_number": 8694,
    "slug": "open-fc-3a2902d1fb3794be3c57-erdos-342-parts-iii",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:05:09+00:00",
    "updated_at": "2026-08-17T19:05:22+00:00"
  },
  "P9026": {
    "problem_number": 9026,
    "slug": "open-fc-8d87dad9b7be05a39bf4-erdos-517",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:45:27+00:00",
    "updated_at": "2026-08-17T19:45:29+00:00"
  },
  "P11578": {
    "problem_number": 11578,
    "slug": "vanishing-momentum-sums-in-the-twice-prime-xx-chain",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:35:08+00:00",
    "updated_at": "2026-08-30T04:35:16+00:00"
  },
  "P11568": {
    "problem_number": 11568,
    "slug": "vector-sum-classification-of-thomson-minimizers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T04:33:39+00:00",
    "updated_at": "2026-08-30T04:33:52+00:00"
  },
  "P3536": {
    "problem_number": 3536,
    "slug": "kourovka-21-139-virtual-freeness-or-surface-structure-from-bounded-betti-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:12:40+00:00",
    "updated_at": "2026-08-12T08:12:41+00:00"
  },
  "P3508": {
    "problem_number": 3508,
    "slug": "kourovka-21-124-virtual-specialness-of-cat-0-free-by-cyclic-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:10:07+00:00",
    "updated_at": "2026-08-12T08:10:10+00:00"
  },
  "P8636": {
    "problem_number": 8636,
    "slug": "open-fc-46bb87abba6fe9a07c28-voronovskaja-theorem-bezier-bernstein-operators-variants-answer-smoothness",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:57+00:00",
    "updated_at": "2026-08-17T18:58:58+00:00"
  },
  "P9854": {
    "problem_number": 9854,
    "slug": "open-fc-4a66bd020d1571981b90-voronovskaja-theorem-bezier-bernstein-operators-variants-eventually-smooth",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:03:59+00:00",
    "updated_at": "2026-08-17T20:04:00+00:00"
  },
  "P9326": {
    "problem_number": 9326,
    "slug": "open-fc-ce8976025621cc594984-waldschmidt",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:50:54+00:00",
    "updated_at": "2026-08-17T19:50:55+00:00"
  },
  "P8934": {
    "problem_number": 8934,
    "slug": "open-fc-ee7a9b966d2846c07c4c-weak-hall-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:53+00:00",
    "updated_at": "2026-08-17T19:40:54+00:00"
  },
  "P9760": {
    "problem_number": 9760,
    "slug": "open-fc-c0e12112686f21f1952a-grimm-conjecture-weak",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:02:24+00:00",
    "updated_at": "2026-08-17T20:02:24+00:00"
  },
  "P2918": {
    "problem_number": 2918,
    "slug": "life-horizontal-line-weak-vanishing",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:47:50+00:00",
    "updated_at": "2026-08-01T12:16:56+00:00"
  },
  "P3496": {
    "problem_number": 3496,
    "slug": "kourovka-21-114-weakly-ab-maximal-finite-groups",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T08:07:56+00:00",
    "updated_at": "2026-08-12T08:08:09+00:00"
  },
  "P9490": {
    "problem_number": 9490,
    "slug": "open-fc-9348779cd769cf7edf63-existsweaklyfirstcountablecompactnotfirstcountable",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:54:25+00:00",
    "updated_at": "2026-08-17T19:54:25+00:00"
  },
  "P8626": {
    "problem_number": 8626,
    "slug": "open-fc-893936223471ff825c1c-erdos-891-variants-weisenberg",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:58:40+00:00",
    "updated_at": "2026-08-17T18:58:49+00:00"
  },
  "P9860": {
    "problem_number": 9860,
    "slug": "open-fc-50b76ce1bd53544fe7ad-conjecture314",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:02+00:00",
    "updated_at": "2026-08-17T20:04:02+00:00"
  },
  "P11360": {
    "problem_number": 11360,
    "slug": "fourth-super-root-of-two-arithmetic-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:37:10+00:00",
    "updated_at": "2026-08-29T18:51:48+00:00"
  },
  "P11196": {
    "problem_number": 11196,
    "slug": "square-knight-domination-asymptotic-density",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T22:48:34+00:00",
    "updated_at": "2026-08-29T18:48:59+00:00"
  },
  "P11560": {
    "problem_number": 11560,
    "slug": "exact-density-of-three-x-minus-one-obstruction-residues",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T02:05:22+00:00",
    "updated_at": "2026-08-29T18:54:40+00:00"
  },
  "P11256": {
    "problem_number": 11256,
    "slug": "exact-fifth-weak-schur-number",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-28T23:06:22+00:00",
    "updated_at": "2026-08-29T18:50:02+00:00"
  },
  "P12597": {
    "problem_number": 12597,
    "slug": "when-do-patterned-odd-digit-multiples-fail-to-exist",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T21:54:37+00:00",
    "updated_at": "2026-09-02T21:54:44+00:00"
  },
  "P12331": {
    "problem_number": 12331,
    "slug": "when-does-a-normalized-binomial-period-contain-another-factor-of-n",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:39:40+00:00",
    "updated_at": "2026-09-01T19:39:45+00:00"
  },
  "P12691": {
    "problem_number": 12691,
    "slug": "when-does-multiplication-by-11-preserve-a-decimal-palindrome",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:17:08+00:00",
    "updated_at": "2026-09-02T22:17:46+00:00"
  },
  "P11732": {
    "problem_number": 11732,
    "slug": "when-is-a-cubic-lattice-ball-manhattan-optimal",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T11:23:24+00:00",
    "updated_at": "2026-08-30T11:24:41+00:00"
  },
  "P11382": {
    "problem_number": 11382,
    "slug": "double-divisor-sum-prime-output-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:43:17+00:00",
    "updated_at": "2026-08-29T18:52:06+00:00"
  },
  "P12763": {
    "problem_number": 12763,
    "slug": "which-a038348-index-counts-terms-in-gamma-derivatives",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:47:45+00:00",
    "updated_at": "2026-09-02T22:48:16+00:00"
  },
  "P11380": {
    "problem_number": 11380,
    "slug": "squarefree-binomial-two-to-n-minus-one-classification",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T00:42:53+00:00",
    "updated_at": "2026-08-29T18:52:03+00:00"
  },
  "P12717": {
    "problem_number": 12717,
    "slug": "which-even-gaps-recur-before-prime-squares",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:28:12+00:00",
    "updated_at": "2026-09-02T22:28:45+00:00"
  },
  "P12111": {
    "problem_number": 12111,
    "slug": "which-generalized-gcd-recurrences-become-quasi-periodic",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-01T19:12:51+00:00",
    "updated_at": "2026-09-01T19:12:56+00:00"
  },
  "P11526": {
    "problem_number": 11526,
    "slug": "catalan-clique-covers-of-johnson-graphs",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:46:14+00:00",
    "updated_at": "2026-08-29T18:54:16+00:00"
  },
  "P3148": {
    "problem_number": 3148,
    "slug": "whitehead-asphericity",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-02T12:47:11+00:00",
    "updated_at": "2026-08-02T12:57:31+00:00"
  },
  "P8790": {
    "problem_number": 8790,
    "slug": "open-fc-6e94d73de0d2cc604f70-wichmann-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:20:59+00:00",
    "updated_at": "2026-08-17T19:21:05+00:00"
  },
  "P11472": {
    "problem_number": 11472,
    "slug": "composite-sum-square-spiral-eventually-visits-two",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-29T01:14:57+00:00",
    "updated_at": "2026-08-29T18:53:36+00:00"
  },
  "P11780": {
    "problem_number": 11780,
    "slug": "will-the-ulam-spiral-gcd-walk-ever-visit-37",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T12:34:32+00:00",
    "updated_at": "2026-08-30T12:36:57+00:00"
  },
  "P11951": {
    "problem_number": 11951,
    "slug": "will-the-visible-prime-ulam-walk-ever-visit-571",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-30T16:34:25+00:00",
    "updated_at": "2026-08-30T16:34:39+00:00"
  },
  "P3358": {
    "problem_number": 3358,
    "slug": "kourovka-21-91-willems-brauer-degree-bound",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-12T06:55:18+00:00",
    "updated_at": "2026-08-12T06:55:55+00:00"
  },
  "P2930": {
    "problem_number": 2930,
    "slug": "node-kayles-subcubic-trees",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:49:30+00:00",
    "updated_at": "2026-08-01T12:19:30+00:00"
  },
  "P3746": {
    "problem_number": 3746,
    "slug": "edmonds-karp-eight-max-augmentations",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:03+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P3760": {
    "problem_number": 3760,
    "slug": "union-find-sixteen-sixty-four-cost",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:51:35+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2706": {
    "problem_number": 2706,
    "slug": "nearest-neighbor-graph-metric-ten",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:58:22+00:00",
    "updated_at": "2026-08-01T02:26:14+00:00"
  },
  "P36": {
    "problem_number": 36,
    "slug": "yang-mills-existence-and-mass-gap",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Open. Not Lean-verified"
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:47+00:00",
    "updated_at": "2026-08-01T12:34:58+00:00"
  },
  "P8986": {
    "problem_number": 8986,
    "slug": "open-fc-6f57926b0007fd836bad-zagier-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:44:23+00:00",
    "updated_at": "2026-08-17T19:44:23+00:00"
  },
  "P11096": {
    "problem_number": 11096,
    "slug": "zariski-dense-monodromy-of-singular-hyperbolic-metrics-on-non-hyperbolic-riemann-surfaces",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-19T03:04:05+00:00",
    "updated_at": "2026-08-30T15:20:24.350519+00:00"
  },
  "P46": {
    "problem_number": 46,
    "slug": "zauners-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "source_backed",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-22T21:49:48+00:00",
    "updated_at": "2026-08-01T12:35:19+00:00"
  },
  "P9856": {
    "problem_number": 9856,
    "slug": "open-fc-4beef29ed15bb4ebe917-volume-frontier-mandelbrotset-eq-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:04:01+00:00",
    "updated_at": "2026-08-17T20:04:02+00:00"
  },
  "P9660": {
    "problem_number": 9660,
    "slug": "open-fc-5b76dceea7a1f1f993aa-volume-frontier-multibrotset-eq-zero",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T20:00:46+00:00",
    "updated_at": "2026-08-17T20:00:47+00:00"
  },
  "P2880": {
    "problem_number": 2880,
    "slug": "easily-bored-sequence-zero-density",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-07-27T20:42:47+00:00",
    "updated_at": "2026-08-01T11:36:13+00:00"
  },
  "P3706": {
    "problem_number": 3706,
    "slug": "square-ice-twelve-torus-zero-flux-count",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "editorial_review": "submitter_supplied",
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-08-15T16:46:28+00:00",
    "updated_at": "2026-08-22T17:00:00.689911+00:00"
  },
  "P2628": {
    "problem_number": 2628,
    "slug": "zero-sum-free-f7-sphere",
    "resolution_state": "resolved",
    "solution_state": "resolved",
    "solution_claimed": true,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "resolved",
        "label": "Resolved",
        "tone": "resolved",
        "reason": "The canonical record accepts a complete answer.",
        "transitionRule": "A complete answer has passed resolution review."
      },
      "lean": {
        "state": "pending",
        "verified": false,
        "kernelAccepted": false,
        "label": "Not Lean-verified",
        "reason": "Formalization work is attached, and signed verification has not been established."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": true,
        "hasFormalization": true,
        "solutionRecord": null
      },
      "proofMessage": "A Lean formalization is attached. Signed verification is pending.",
      "summary": "Resolved. Not Lean-verified"
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-07-26T00:57:51+00:00",
    "updated_at": "2026-08-01T02:27:04+00:00"
  },
  "P9382": {
    "problem_number": 9382,
    "slug": "open-fc-f8efc0cd4c108941e9b2-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:51:17+00:00",
    "updated_at": "2026-08-17T19:51:18+00:00"
  },
  "P8922": {
    "problem_number": 8922,
    "slug": "open-fc-e5d3a039287cc073104a-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:40:36+00:00",
    "updated_at": "2026-08-17T19:40:37+00:00"
  },
  "P9090": {
    "problem_number": 9090,
    "slug": "open-fc-be4a0d61c1324f6687da-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:21+00:00",
    "updated_at": "2026-08-17T19:47:22+00:00"
  },
  "P9144": {
    "problem_number": 9144,
    "slug": "open-fc-e88ab50dcd65c182e04a-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:47:48+00:00",
    "updated_at": "2026-08-17T19:47:48+00:00"
  },
  "P8412": {
    "problem_number": 8412,
    "slug": "open-fc-2b7cad7010548d9b326e-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T18:50:14+00:00",
    "updated_at": "2026-08-17T18:50:24+00:00"
  },
  "P8742": {
    "problem_number": 8742,
    "slug": "open-fc-50ef9fab7360a5ac0474-conjecture",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": false,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "No proof or formalization has been recorded.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-17T19:12:28+00:00",
    "updated_at": "2026-08-17T19:12:45+00:00"
  },
  "P11160": {
    "problem_number": 11160,
    "slug": "sun-prime-difference-matrix-determinant",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_assessed"
    },
    "statement_integrity": null,
    "created_at": "2026-08-26T02:43:19+00:00",
    "updated_at": "2026-08-29T18:48:27+00:00"
  },
  "P12705": {
    "problem_number": 12705,
    "slug": "zumkeller-sparsely-totient-numbers",
    "resolution_state": "open",
    "solution_state": "none",
    "solution_claimed": false,
    "lean_verified": false,
    "public_status": {
      "schema": "theoremdb-public-problem-status-v1",
      "resolution": {
        "state": "open",
        "label": "Open",
        "tone": "open",
        "reason": "No complete answer has passed resolution review.",
        "transitionRule": "No complete answer has passed resolution review."
      },
      "lean": {
        "state": "none",
        "verified": false,
        "kernelAccepted": false,
        "label": "",
        "reason": "No signed Lean verification is attached to this problem or its selected resolution."
      },
      "evidence": {
        "hasRecordedWork": true,
        "hasInformalProof": false,
        "hasFormalization": false,
        "solutionRecord": null
      },
      "proofMessage": "Research work is recorded. A complete resolution has not passed review.",
      "summary": "Open. No signed Lean verification is attached to this problem or its selected resolution."
    },
    "display_standard": {
      "formal_correspondence": "not_applicable"
    },
    "statement_integrity": null,
    "created_at": "2026-09-02T22:22:45+00:00",
    "updated_at": "2026-09-02T22:23:10+00:00"
  }
}