{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1384",
  "content_hash": null,
  "slug": "barnette-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 n-vertex Barnette graph has a subhamiltonian cycle containing at least 5n/6 edges. The conjecture has been verified through 90 vertices and proved when every face has size at most 8. Unresolved remainder: Prove that every Barnette graph has a spanning cycle, or exhibit a cubic, 3-connected, bipartite planar graph without one. TheoremDB corpus searches for Barnette returned no duplicate target.",
  "relevance": "Documents why Barnette’s 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- Barnette conjecture cubic bipartite planar graph Hamiltonian open\n- Barnette graph face size 8 Hamiltonian\n- Barnette graphs verified 90 vertices\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Every n-vertex Barnette graph has a subhamiltonian cycle containing at least 5n/6 edges. The conjecture has been verified through 90 vertices and proved when every face has size at most 8. Unresolved remainder: Prove that every Barnette graph has a spanning cycle, or exhibit a cubic, 3-connected, bipartite planar graph without one. TheoremDB corpus searches for Barnette 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/10.4230/LIPIcs.GD.2025.6",
      "locator": "M. A. Bekos, M. Kaufmann, and M. Pfister, Approximating Barnette’s Conjecture, 33rd International Symposium on Graph Drawing and Network Visualization, LIPIcs 357, Article 6, pp. 6:1-6:7 (2025). Abstract, Introduction, Theorem 1, and Section 5"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4230/LIPIcs.GD.2025.6",
    "locator": "M. A. Bekos, M. Kaufmann, and M. Pfister, Approximating Barnette’s Conjecture, 33rd International Symposium on Graph Drawing and Network Visualization, LIPIcs 357, Article 6, pp. 6:1-6:7 (2025). Abstract, Introduction, Theorem 1, and Section 5"
  },
  "relations": [
    {
      "slug": "R1387",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "barnette-conjecture",
      "title": "barnette conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}