{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1471",
  "content_hash": null,
  "slug": "conway-thrackle-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: Every planar thrackle satisfies m ≤ 1.393(n-1). The conjectured coefficient 1 is proved for straight-line thrackles and several other restricted drawing classes. Unresolved remainder: Reduce the general coefficient to 1, or construct a planar thrackle with more edges than vertices. A recent higher-genus counterexample concerns a different conjecture and explicitly leaves the planar target open. TheoremDB corpus searches for thrackle returned no duplicate target.",
  "relevance": "Documents why Conway’s thrackle conjecture 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- Conway thrackle conjecture open 2026\n- Conway thrackle best known bound 1.393\n- thrackle straight line conjecture theorem\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Every planar thrackle satisfies m ≤ 1.393(n-1). The conjectured coefficient 1 is proved for straight-line thrackles and several other restricted drawing classes. Unresolved remainder: Reduce the general coefficient to 1, or construct a planar thrackle with more edges than vertices. A recent higher-genus counterexample concerns a different conjecture and explicitly leaves the planar target open. TheoremDB corpus searches for thrackle returned no duplicate target.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.48550/arXiv.2506.11808",
      "locator": "C. Hernández-Vélez, J. Kynčl, and G. Salazar, Thrackles on nonplanar surfaces, arXiv:2506.11808, version dated March 22, 2026. Abstract and Introduction, especially the current planar status paragraph"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.48550/arXiv.2506.11808",
    "locator": "C. Hernández-Vélez, J. Kynčl, and G. Salazar, Thrackles on nonplanar surfaces, arXiv:2506.11808, version dated March 22, 2026. Abstract and Introduction, especially the current planar status paragraph"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1474",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "conway-thrackle-conjecture",
      "title": "conway thrackle conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}