{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R339",
  "content_hash": null,
  "slug": "gtc-artifact-checker",
  "type": "artifact",
  "title": "Exhaustive graceful and alpha-labeling checker",
  "summary": "A dependency-free Python program that enumerates all trees up to a given size and searches for graceful and alpha-labelings, with both search heuristics switchable for comparison.",
  "relevance": "For Graceful tree conjecture, record gtc-artifact-checker (“Exhaustive graceful and alpha-labeling checker”) supplies evidence or a replay used to check the packet. The record states: A dependency-free Python program that enumerates all trees up to a given size and searches for graceful and alpha-labelings, with both search heuristics switchable for comparison.",
  "relevance_source": "recorded",
  "body": "Exact integer arithmetic, no third-party packages. Generates free trees by centroid decomposition, searches for labelings by backtracking with sibling symmetry breaking and largest-edge-label-first ordering, and re-verifies every labeling it returns against the definition.\n\nThe recorded run is --max-n 15, which checks 13,188 trees. The --no-symmetry and --no-edge-order flags reproduce the two heuristic comparisons recorded in this project.",
  "status": "reproduced",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "runs over every tree on at most 16 vertices",
    "bounds": {
      "n": {
        "max": 16
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "runnable",
    "kind": "program",
    "command": "python3 research/graceful-trees/checks.py --max-n 15",
    "source": "research/graceful-trees/checks.py",
    "citation": {
      "url": "https://arxiv.org/abs/1403.1564",
      "locator": "research/graceful-trees/checks.py"
    },
    "dependencies": "none",
    "runtime_seconds": 1962.101,
    "missing": [
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1403.1564",
    "locator": "research/graceful-trees/checks.py"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R353",
      "title": "Which search heuristic carries the exhaustive sweep",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R351",
      "title": "Independent exhaustive verification through n=15",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R347",
      "title": "The smallest tree with no alpha-labeling has seven vertices",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}