{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1668",
  "content_hash": null,
  "slug": "nonexistence-of-odd-perfect-numbers-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Any odd perfect number exceeds 10^1500, has at least 101 prime factors counted with multiplicity, and obeys further severe factorization restrictions. Exact unresolved remainder: Prove that no odd positive integer N satisfies sigma(N)=2N.",
  "relevance": "For Nonexistence of odd perfect numbers, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Any odd perfect number exceeds 10^1500, has at least 101 prime factors counted with multiplicity, and obeys further severe factorization restrictions.\n\nExact unresolved remainder: Prove that no odd positive integer N satisfies sigma(N)=2N.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1090/S0025-5718-2012-02563-4",
      "locator": "Abstract and main theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1090/S0025-5718-2012-02563-4",
    "locator": "Abstract and main theorem"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1112",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "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"
    }
  ]
}