{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1472",
  "content_hash": null,
  "slug": "conway-thrackle-conjecture-attempt-open-remainder",
  "type": "attempt",
  "title": "Work at the unresolved boundary",
  "summary": "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": "Turns the remaining uncertainty in Conway’s thrackle conjecture into a checkable research target.",
  "relevance_source": "recorded",
  "body": "Research should address this boundary directly: 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.\n\nA claimed resolution should satisfy every item below and preserve the statement's exact quantifiers and normalizations:\n- Prove m ≤ n for every finite simple graph admitting a planar thrackle drawing.\n- Or give an explicit finite simple graph with m>n and a fully specified planar drawing, together with a rigorous check that every pair of edges meets exactly once in the required manner.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.48550/arXiv.2506.11808",
      "locator": "TheoremDB editorial route recorded 2026-08-01"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.48550/arXiv.2506.11808",
    "locator": "TheoremDB editorial route recorded 2026-08-01"
  },
  "relations": [
    {
      "slug": "R1474",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "conway-thrackle-conjecture",
      "title": "conway thrackle conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}