{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1473",
  "content_hash": null,
  "slug": "conway-thrackle-conjecture-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "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.",
  "relevance": "Locates the present research frontier immediately below Conway’s thrackle conjecture.",
  "relevance_source": "recorded",
  "body": "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.\n\nThis leaves the following boundary unresolved: 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. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "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": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "conway-thrackle-conjecture",
      "title": "conway thrackle conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}