{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1061",
  "content_hash": null,
  "slug": "fermat-catalan-conjecture-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "Prove that the set of primitive solutions satisfying the exponent condition is finite, or construct and verify infinitely many distinct primitive solutions.",
  "relevance": "For Fermat-Catalan conjecture, record fermat-catalan-conjecture-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: Prove that the set of primitive solutions satisfying the exponent condition is finite, or construct and verify infinitely many distinct primitive solutions.",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. Prove that the set of primitive solutions satisfying the exponent condition is finite, or construct and verify infinitely many distinct primitive solutions. Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2410.21552",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2410.21552",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1062",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "fermat-catalan-conjecture",
      "title": "fermat catalan conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}