{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R354",
  "content_hash": null,
  "slug": "gtc-claim-verified-35",
  "type": "claim",
  "title": "Published verification through 35 vertices",
  "summary": "Published computation verifies that every tree with at most 35 vertices is graceful; the conjecture for trees with at least 36 vertices remains open.",
  "relevance": "For Graceful tree conjecture, record gtc-claim-verified-35 (“Published verification through 35 vertices”) records a bound, answer, status fact, or structural consequence. The record states: Published computation verifies that every tree with at most 35 vertices is graceful; the conjecture for trees with at least 36 vertices remains open.",
  "relevance_source": "recorded",
  "body": "The published sweep used a hybrid of constraint propagation and randomized search in place of plain backtracking. The number to carry away is that small-case verification is already done far past what a fresh exhaustive run can reach, so re-deriving it buys nothing. Verify the scope in the source before relying on it.",
  "status": "supported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "every tree on at most 35 vertices",
    "bounds": {
      "n": {
        "max": 35
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1003.3045",
      "locator": "Fang, arXiv:1003.3045, abstract"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1003.3045",
    "locator": "Fang, arXiv:1003.3045, abstract"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "graceful-tree-conjecture",
      "title": "Graceful tree conjecture",
      "object_type": "problem",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R351",
      "title": "Independent exhaustive verification through n=15",
      "object_type": "claim",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}