{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1062",
  "content_hash": null,
  "slug": "fermat-catalan-conjecture-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited 2024 paper treats the Fermat-Catalan statement as an unresolved conjecture. 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 the set of primitive solutions satisfying the exponent condition is finite, or construct and verify infinitely many distinct primitive solutions.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited 2024 paper treats the Fermat-Catalan statement as an unresolved conjecture. 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 the set of primitive solutions satisfying the exponent condition is finite, or construct and verify infinitely many distinct primitive solutions.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2410.21552",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2410.21552",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1061",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1526",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    },
    {
      "slug": "fermat-catalan-conjecture",
      "title": "fermat catalan conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}