{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R343",
  "content_hash": null,
  "slug": "gtc-attempt-diameter-ladder",
  "type": "attempt",
  "title": "Push the diameter ladder from five to six",
  "summary": "Settle the diameter-six families that Superdock's construction leaves open, using the diameter-five proof as the base case.",
  "relevance": "For Graceful tree conjecture, record gtc-attempt-diameter-ladder (“Push the diameter ladder from five to six”) documents a concrete method, search boundary, or failed route. The record states: Settle the diameter-six families that Superdock's construction leaves open, using the diameter-five proof as the base case.",
  "relevance_source": "recorded",
  "body": "The most concrete open route. Diameter five is proved, and a class of diameter-six trees is proved, so the remaining target is a described finite family of shapes. The work is case analysis on the structure hanging off the central path.\n\nBefore starting: read the published diameter-six class and check which shapes it already covers. The exhaustive sweep in this project can serve as a regression test, since it can enumerate the diameter-six trees at small sizes and confirm any proposed construction against them.",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1403.1564",
      "locator": "Superdock, arXiv:1403.1564"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1403.1564",
    "locator": "Superdock, arXiv:1403.1564"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "gtc-problem-diameter-six",
      "title": "Gracefulness of diameter-six trees",
      "object_type": "problem",
      "relation": "attempts",
      "direction": "outgoing"
    },
    {
      "slug": "R350",
      "title": "Trees of diameter at most five are graceful",
      "object_type": "claim",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}