{
  "generated": "2026-09-25T14:25:41Z",
  "sources": [
    {
      "key": "erdos_problems",
      "name": "Erdős problems dataset",
      "url": "https://raw.githubusercontent.com/teorth/erdosproblems/main/data/problems.yaml",
      "ok": true,
      "retrieved": "2026-09-25T14:25:26Z",
      "error": null,
      "records": 1221,
      "notes": []
    },
    {
      "key": "formal_conjectures",
      "name": "DeepMind Formal Conjectures",
      "url": "https://github.com/google-deepmind/formal-conjectures",
      "ok": true,
      "retrieved": "2026-09-25T14:25:26Z",
      "error": null,
      "records": 1403,
      "notes": [
        "17 collections",
        "571 statements cite an external proof"
      ]
    },
    {
      "key": "proof_artifacts",
      "name": "Cited Lean proof artifacts",
      "url": "",
      "ok": true,
      "retrieved": "2026-09-25T14:25:30Z",
      "error": null,
      "records": 714,
      "notes": [
        "690 reachable, 610 free of sorry and added axioms",
        "Static read only; artifacts are not compiled"
      ]
    },
    {
      "key": "alphaevolve",
      "name": "AlphaEvolve problem set",
      "url": "https://github.com/google-deepmind/alphaevolve_repository_of_problems",
      "ok": true,
      "retrieved": "2026-09-25T14:25:30Z",
      "error": null,
      "records": 68,
      "notes": [
        "19 constructions stand as the best known",
        "No numeric values published in machine-readable form"
      ]
    },
    {
      "key": "discoveries",
      "name": "Recorded discoveries",
      "url": "",
      "ok": true,
      "retrieved": "2026-09-25T14:25:30Z",
      "error": null,
      "records": 8,
      "notes": [
        "3 records currently held by a machine",
        "4 results recorded against statements",
        "5 announcements in the disclosure ledger"
      ]
    },
    {
      "key": "registries",
      "name": "Other registries",
      "url": "",
      "ok": true,
      "retrieved": "2026-09-25T14:25:33Z",
      "error": null,
      "records": 1059,
      "notes": [
        "palomar: 318 entries",
        "vibemathed: 741 entries"
      ]
    },
    {
      "key": "formalizations",
      "name": "Declared formalisations",
      "url": "https://github.com/mathlib-initiative/formalization.yaml",
      "ok": true,
      "retrieved": "2026-09-25T14:25:40Z",
      "error": null,
      "records": 567,
      "notes": [
        "567 declarations read from 348 repositories",
        "142 snapshot copies and 11 superseded versions set aside",
        "6 files could not be parsed as YAML"
      ]
    },
    {
      "key": "erdos_ai_wiki",
      "name": "Erdős problems AI wiki (retired)",
      "url": "https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems",
      "ok": true,
      "retrieved": "2026-09-25T14:25:40Z",
      "error": null,
      "records": 538,
      "notes": [
        "Source retired; latest data Jun 30, 2026",
        "No outcome column at source in sections 2(b), 2(c), 2(d)"
      ]
    },
    {
      "key": "news",
      "name": "Field activity feeds",
      "url": "",
      "ok": true,
      "retrieved": "2026-09-25T14:25:41Z",
      "error": null,
      "records": 68,
      "notes": [
        "7 of 7 feeds read",
        "0 items name a statement"
      ]
    },
    {
      "key": "submissions",
      "name": "Submissions",
      "url": "",
      "ok": true,
      "retrieved": "2026-09-25T14:25:41Z",
      "error": null,
      "records": 0,
      "notes": [
        "0 accepted, 0 in quarantine"
      ]
    }
  ],
  "rubric": {
    "autonomy": {
      "A3": "Autonomous. The system produced the result without significant human mathematical involvement.",
      "A2": "Directed. The system produced the result while building on literature or framing supplied to it.",
      "A1": "Collaborative. A human and a system worked the problem together, or the system played a supporting role.",
      "A0": "Human. No machine contribution to the mathematics.",
      "A?": "Not established. Declared by whoever submitted the work and not verifiable from the record."
    },
    "verification": {
      "V0": "Claimed. No public artifact, or the claim is marked unverified at source.",
      "V1": "Informal. A public write-up exists and has had community scrutiny.",
      "V2": "Artifact reported. A proof or a constructed object is published, but nobody independent of its authors has rebuilt it.",
      "V3": "Machine-checked. The artifact was rebuilt at a pinned commit by someone other than its authors — qed.bot, or a registry that publishes the check — and it holds: a proof that elaborates on the standard axioms alone, or an object that meets the problem's own constraints."
    },
    "fidelity": {
      "F3": "Anchored. The proof is checked for exact statement identity against a statement written independently of it, held here from a separate statement corpus.",
      "F2": "Declared. The authors record how the formal statement corresponds to the claim — a comparator challenge, an alignment table or written divergences — or a statement corpus cites the proof against its own statement.",
      "F1": "Unaudited. A formal artifact exists, but nothing records that its statement says what the claim says.",
      "F0": "None. No formal statement is attached to the result."
    },
    "disclosure": {
      "D3": "Checkable. Every result announced is identified, and each carries a machine-checkable artifact.",
      "D2": "Written up. The results are identified and written up, but not all carry a machine-checkable artifact.",
      "D1": "Named. The results are identified but not written up.",
      "D0": "Withheld. Results are claimed without being identified."
    },
    "automation": {
      "autonomous": "The system worked without human direction.",
      "agent": "An agent did the work under human direction.",
      "copilot": "A person did the work with machine assistance.",
      "manual": "A person did the work.",
      "other": "Described by the project in its own terms."
    },
    "outcomes": {
      "full": "Full resolution",
      "partial": "Partial progress",
      "incorrect": "Incorrect work",
      "candidate": "Unverified candidate",
      "unstated": "No outcome recorded at source"
    },
    "record_outcomes": {
      "record": "Best known value",
      "matched": "Equalled the best known value",
      "superseded": "Held the record, since beaten",
      "below": "Did not reach the best known value",
      "unstated": "No standing recorded at source"
    },
    "check_methods": {
      "lean": "qed.bot rebuilt the proof and inspected every theorem's axioms.",
      "evaluator": "qed.bot rebuilt the object and tested it against the problem's own constraints.",
      "palomar": "Palomar rebuilt the project at a pinned commit and registered it; the register cites that check rather than repeating it."
    },
    "relations": {
      "references": "cites, in its source text",
      "derives-from": "whose proof imports the proof of",
      "part-of": "is one component of",
      "variant-of": "is a modified form of"
    }
  },
  "stats": {
    "statements_registered": 6,
    "statements_rebuilt_here": 19,
    "registry_checks": 13,
    "theorems_registered": 57,
    "formal_record_lags": [],
    "targets": 72,
    "target_collections": 4,
    "records_held_by_machine": 3,
    "targets_verified": 4,
    "record_claims": 72,
    "records_standing": 22,
    "records_matched": 13,
    "evaluations": 3,
    "evaluations_verified": 3,
    "statements": 1841,
    "collections": 18,
    "by_collection": {
      "Erdős": 1221,
      "OEIS": 227,
      "Wikipedia": 160,
      "Written on the Wall II": 55,
      "Green's open problems": 52,
      "arXiv": 37,
      "Papers": 34,
      "MathOverflow": 13,
      "Books": 11,
      "Other": 8,
      "Millennium": 7,
      "Kourovka notebook": 6,
      "Open quantum problems": 3,
      "Hilbert": 2,
      "Subsets": 2,
      "Litt's problems": 1,
      "Mathlib": 1,
      "Optimization constants": 1
    },
    "formalised": 1396,
    "open_in_formal_record": 439,
    "relations": 71,
    "claims": 613,
    "primary_claims": 257,
    "secondary_claims": 284,
    "statements_with_claims": 479,
    "autonomous_full": 34,
    "human_collaborations": 132,
    "systems": 73,
    "by_outcome": {
      "full": 91,
      "candidate": 43,
      "partial": 106,
      "incorrect": 17
    },
    "by_outcome_secondary": {
      "full": 222,
      "partial": 57,
      "unstated": 3,
      "incorrect": 2
    },
    "by_autonomy": {
      "A1": 416,
      "A2": 110,
      "A3": 87
    },
    "by_verification": {
      "V2": 67,
      "V3": 24,
      "V0": 45,
      "V1": 477
    },
    "statements_with_artifacts": 571,
    "artifacts": 717,
    "artifacts_reachable": 693,
    "artifacts_unreachable": 24,
    "artifacts_flagged": 80,
    "checks_attempted": 35,
    "checks_verified": 19,
    "checks_failed": 16,
    "checks_nonstandard": 1,
    "by_verdict": {
      "verified": 19,
      "not self-contained": 14,
      "nonstandard axioms": 1,
      "dependencies unavailable": 1
    },
    "nonstandard_axioms_found": [
      "Lean.ofReduceBool",
      "Lean.trustCompiler"
    ],
    "statements_verified": 25,
    "theorems_verified": 1787,
    "prize_total": 61790,
    "prize_open": 34195,
    "benchmarks": {
      "fc-open": 439,
      "fc-all": 1396,
      "erdos-prize-open": 47
    },
    "top_systems": [
      [
        "Aristotle",
        198
      ],
      [
        "AlphaEvolve",
        77
      ],
      [
        "GPT-5.5 Pro",
        72
      ],
      [
        "GPT-5.4 Pro",
        45
      ],
      [
        "GPT",
        43
      ],
      [
        "GPT-5.2 Pro",
        30
      ],
      [
        "Codex",
        29
      ],
      [
        "GPT-5.2 Thinking",
        28
      ],
      [
        "ChatGPT Deep research",
        26
      ],
      [
        "GPT-5",
        24
      ],
      [
        "GPT-5.4 Thinking",
        19
      ],
      [
        "Claude",
        18
      ]
    ],
    "news_items": 68,
    "news_linked": 0,
    "reconciliation": {
      "external_entries": 1059,
      "external_by_registry": {
        "vibemathed": 741,
        "palomar": 318
      },
      "external_placed": 153,
      "external_unplaced": 906,
      "comparable": 125,
      "held_here_too": 114,
      "between_others_only": 11,
      "agreeing": 30,
      "conflicting": 40,
      "conflicts_by_axis": {
        "autonomy": 39,
        "contested": 1
      },
      "gaps": 80,
      "they_hold_more": 61,
      "we_hold_more": 10,
      "leads": 6,
      "lead_repos": [
        "allengrahamhart/formalconjectures-bench",
        "ericlisg/erdos-593-1177-lean",
        "ericlisg/erdos731",
        "ericlisg/erdos768-lean",
        "shouqiaow/erdos",
        "sprite143/erdos-106-counterexample"
      ],
      "our_claimed_nodes": 479,
      "ours_alone": 365,
      "lead_probe": {
        "probed": 6,
        "with_lean": 5,
        "without_lean": 1,
        "empty_repos": [
          "sprite143/erdos-106-counterexample"
        ]
      }
    },
    "formal": {
      "declarations": 567,
      "repositories": 348,
      "joined": 38,
      "containers": 3,
      "nodes_declared": 51,
      "joins": {
        "artifact": 29,
        "names": 13,
        "anchor": 12
      },
      "palomar_registrations": 318,
      "palomar_declared": 249,
      "nodes_registered": 6,
      "nodes_named_by_registrations": 6,
      "checked": 251,
      "checked_here": 2,
      "checked_by_palomar": 249,
      "unchecked": 316,
      "contradicted": 0,
      "confirmed": 2,
      "comparator": 269,
      "alignment": 399,
      "divergences": 402,
      "assume_literature": 19,
      "literature_dependencies": 94,
      "nonstandard_declared": 3,
      "declared_unproved": 22,
      "thin_wrappers": 11,
      "original": 88,
      "incomplete": 2,
      "self_assessed": 348,
      "by_method": {
        "agent": 497,
        "autonomous": 47,
        "other": 13,
        "manual": 8,
        "not stated": 2
      },
      "by_review": {
        "self-assessed": 339,
        "agent-reviewed": 112,
        "other": 59,
        "author-verified": 47,
        "unchecked": 6,
        "not stated": 3,
        "peer-reviewed": 1
      },
      "top_models": [
        [
          "Claude Opus 5 (Anthropic)",
          43
        ],
        [
          "claude-opus-5",
          34
        ],
        [
          "claude-fable-5",
          29
        ],
        [
          "AxiomProver",
          18
        ],
        [
          "GPT-5 Codex",
          17
        ],
        [
          "OpenAI Codex",
          15
        ],
        [
          "claude-fable-5-1",
          14
        ],
        [
          "claude-opus-4-8",
          14
        ],
        [
          "Claude (Anthropic)",
          12
        ],
        [
          "GPT-5.6 Sol",
          11
        ]
      ],
      "discovery": {
        "listed": 1072,
        "seeds": 598,
        "dropped_history": 142,
        "dropped_name": 14,
        "superseded": 11,
        "located": 731,
        "absent": {
          "cited": 138,
          "palomar": 21
        },
        "unparseable": [
          "sneed-and-feed/lean-theorems-3/palomar/cauchy_davenport/formalization.yaml",
          "sneed-and-feed/lean-theorems-3/palomar/expander_mixing/formalization.yaml",
          "sneed-and-feed/lean-theorems-3/palomar/roths_theorem/formalization.yaml",
          "sneed-and-feed/lean-theorems-3/palomar/ruzsa_freiman/formalization.yaml",
          "sneed-and-feed/lean-theorems-3/palomar/szemeredi_regularity/formalization.yaml",
          "sneed-and-feed/lean-theorems-3/palomar/tanner_expansion/formalization.yaml"
        ],
        "read": 567,
        "incomplete": 2,
        "repositories": 348,
        "searched": false
      }
    },
    "fidelity": {
      "by_grade": {
        "F0": 237,
        "F2": 223,
        "F1": 13,
        "F3": 3,
        "object": 3
      },
      "flags": {
        "declares divergences from its source": 8,
        "reviewed by its authors only": 7,
        "reviewed by an agent": 3,
        "source authors not contacted": 2,
        "declares 8 unproved goals": 1,
        "a thin wrapper around another repository": 1,
        "its anchor link points at a path the corpus has since renamed": 1
      }
    },
    "disclosure": {
      "announcements": 5,
      "by_grade": {
        "D0": 1,
        "D3": 4
      },
      "claimed": 114,
      "identified": 14,
      "checkable": 14,
      "withheld": 100
    }
  }
}