{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1421",
  "content_hash": null,
  "slug": "cabling-conjecture-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The conjecture holds for many classes, including strongly invertible and recent thin-knot regimes, with strong restrictions in general. Unresolved remainder: The classification for arbitrary knots in S³ remains open.",
  "relevance": "Documents why Cabling conjecture for reducible Dehn surgery was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- Cabling Conjecture still open 2025 reducible surgery\n- thin knots cabling conjecture 2025\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The conjecture holds for many classes, including strongly invertible and recent thin-knot regimes, with strong restrictions in general. Unresolved remainder: The classification for arbitrary knots in S³ remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1016/0040-9383(95)00016-X",
      "locator": "C. McA. Gordon and J. Luecke, “Reducible manifolds and Dehn surgery,” Topology 35(2) (1996), 385–409. main reducible-surgery theorems"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/0040-9383(95)00016-X",
    "locator": "C. McA. Gordon and J. Luecke, “Reducible manifolds and Dehn surgery,” Topology 35(2) (1996), 385–409. main reducible-surgery theorems"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1424",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "cabling-conjecture",
      "title": "cabling conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}