{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R356",
  "content_hash": null,
  "slug": "gtc-formalization-statement",
  "type": "formalization",
  "title": "Draft Lean statement of the graceful tree conjecture",
  "summary": "The conjecture as a Lean proposition over finite trees, using the drafted gracefulness predicate.",
  "relevance": "For Graceful tree conjecture, record gtc-formalization-statement (“Draft Lean statement of the graceful tree conjecture”) states a machine-checkable theorem or proof obligation. The record states: The conjecture as a Lean proposition over finite trees, using the drafted gracefulness predicate.",
  "relevance_source": "recorded",
  "body": "Depends on the gracefulness definition in this project, and takes its hypothesis from Mathlib's SimpleGraph.IsTree. Not compiled and not proved; recorded so that a formalization effort starts from a statement someone has already argued about.",
  "status": "draft",
  "evidence_grade": "unverified_formalization",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "formalization",
    "citation": {
      "url": "https://arxiv.org/abs/1403.1564",
      "locator": "draft for this project"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": "theorem graceful_tree_conjecture {V : Type*} [Fintype V] [DecidableEq V]\n    (G : SimpleGraph V) [DecidableRel G.Adj] (h : G.IsTree) :\n    ∃ l : V → ℕ, IsGraceful G l := by\n  sorry",
  "source": {
    "url": "https://arxiv.org/abs/1403.1564",
    "locator": "draft for this project"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "graceful-tree-conjecture",
      "title": "Graceful tree conjecture",
      "object_type": "problem",
      "relation": "formalizes",
      "direction": "outgoing"
    },
    {
      "slug": "R355",
      "title": "Draft Lean definition of a graceful labeling",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "outgoing"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}