{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1112",
  "content_hash": null,
  "slug": "nonexistence-of-odd-perfect-numbers-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited American Mathematical Society article says that the existence of an odd perfect number is unknown. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review. Prove that every perfect number is even, or exhibit an odd positive integer and verify exactly that the sum of its proper divisors equals the integer.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited American Mathematical Society article says that the existence of an odd perfect number is unknown. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review.\n\nA complete resolution must satisfy this condition: Prove that every perfect number is even, or exhibit an odd positive integer and verify exactly that the sum of its proper divisors equals the integer.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathvoices.ams.org/mathmedia/tonys-take-october-2024/",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathvoices.ams.org/mathmedia/tonys-take-october-2024/",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1111",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1668",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "nonexistence-of-odd-perfect-numbers",
      "title": "nonexistence of odd perfect numbers",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}