{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1331",
  "content_hash": null,
  "slug": "king-grid-independence-homology-torsion-free-status-20260801",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-08-01. The checked grid-independence-complex literature does not give an integral torsion classification for the king graphs \\(K_n\\).",
  "relevance": "Fixes the dated literature boundary and identifies the exact statement that remains unresolved.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-08-01. The checked grid-independence-complex literature does not give an integral torsion classification for the king graphs \\(K_n\\).\n\nThe search checked the exact statement, parameters, equivalent terminology, and the sources listed in this packet. Database silence is treated only as bounded status evidence. A complete resolution must satisfy every acceptance condition in the canonical problem.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/math/0701890",
      "locator": "Integral homotopy methods for independence complexes of nearby square-grid families"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/math/0701890",
    "locator": "Integral homotopy methods for independence complexes of nearby square-grid families"
  },
  "relations": [
    {
      "slug": "R1330",
      "title": "Resolve the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "king-grid-independence-homology-torsion-free",
      "title": "king grid independence homology torsion free",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}