{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R330",
  "content_hash": null,
  "slug": "gmstg8-attempt-literature-audit",
  "type": "attempt",
  "title": "Primary-source audit found bounds and a neighboring finite enumeration",
  "summary": "The sources define the relaxation, supply the general upper bound, and settle the eight-city 1,2 subclass; none reports this graph-metric maximum.",
  "relevance": "For Largest subtour-LP gap among eight-vertex graph metrics, record gmstg8-attempt-literature-audit (“Primary-source audit found bounds and a neighboring finite enumeration”) documents a concrete method, search boundary, or failed route. The record states: The sources define the relaxation, supply the general upper bound, and settle the eight-city 1,2 subclass; none reports this graph-metric maximum.",
  "relevance_source": "recorded",
  "body": "Held and Karp's 1970 paper develops the classical LP lower-bound framework for symmetric TSP. Karlin, Klein, and Oveis Gharan give the current general metric bound used here. Qian, Schalekamp, Williamson, and van Zuylen report an isomorph-free computation for eight-city 1,2-TSP instances.\n\nThe 1,2 computation does not settle this question. Graphs of diameter three or greater produce shortest-path distances above two, while an arbitrary 1,2 cost matrix need not equal the shortest-path metric of its cost-one graph. A focused search for `graphic TSP`, `subtour LP`, `eight vertices`, `graph metric`, and `integrality gap enumeration` found no source stating the maximum over connected eight-vertex graph metrics.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1287/opre.18.6.1138",
      "locator": "Michael Held and Richard M. Karp, The Traveling-Salesman Problem and Minimum Spanning Trees, Operations Research 18(6), 1970; related sources listed in metadata"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1287/opre.18.6.1138",
    "locator": "Michael Held and Richard M. Karp, The Traveling-Salesman Problem and Minimum Spanning Trees, Operations Research 18(6), 1970; related sources listed in metadata"
  },
  "relations": [
    {
      "slug": "R331",
      "title": "The certified interval is 1 to slightly below 3/2",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "graph-metric-subtour-gap-eight",
      "title": "graph metric subtour gap eight",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}