{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R338",
  "content_hash": null,
  "slug": "gtc-artifact-alpha-free-trees",
  "type": "artifact",
  "title": "Trees with no alpha-labeling through n=15",
  "summary": "Edge lists and counts for every tree through n=15 that admits no alpha-labeling, with diameter and caterpillar flags.",
  "relevance": "For Graceful tree conjecture, record gtc-artifact-alpha-free-trees (“Trees with no alpha-labeling through n=15”) supplies evidence or a replay used to check the packet. The record states: Edge lists and counts for every tree through n=15 that admits no alpha-labeling, with diameter and caterpillar flags.",
  "relevance_source": "recorded",
  "body": "The checker emits the failing trees along with their diameter, maximum degree, and whether they are caterpillars. The set is the raw material for the characterization question, and the natural regression suite for any proposed alpha-labeling construction: a construction that claims these trees is wrong.",
  "status": "reproduced",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "complete for trees on 7 to 15 vertices",
    "bounds": {
      "n": {
        "max": 15,
        "min": 7
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "derived_dataset",
    "command": "python3 research/graceful-trees/checks.py --max-n 15 --json",
    "citation": {
      "url": "https://arxiv.org/abs/1403.1564",
      "locator": "research/graceful-trees/checks.py --max-n 15"
    },
    "missing": [
      "source",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1403.1564",
    "locator": "research/graceful-trees/checks.py --max-n 15"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R346",
      "title": "Trees with no alpha-labeling: the count doubles, the share peaks and falls",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}