{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1526",
  "content_hash": null,
  "slug": "fermat-catalan-conjecture-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: The linked 2024 work formulates product variants and treats the classical primitive-solution finiteness statement as conjectural. Darmon and Granville prove finiteness when the exponent triple is fixed, while the union over varying exponents remains open. Exact unresolved remainder: Prove that only finitely many primitive solutions satisfy the reciprocal-exponent condition, or construct infinitely many distinct primitive solutions.",
  "relevance": "For Fermat-Catalan conjecture, 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: The linked 2024 work formulates product variants and treats the classical primitive-solution finiteness statement as conjectural. Darmon and Granville prove finiteness when the exponent triple is fixed, while the union over varying exponents remains open.\n\nExact unresolved remainder: Prove that only finitely many primitive solutions satisfy the reciprocal-exponent condition, or construct 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": "introduction, motivating conjectures, and formulation of product variants"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2410.21552",
    "locator": "introduction, motivating conjectures, and formulation of product variants"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1062",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "fermat-catalan-conjecture",
      "title": "fermat catalan conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}