{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1330",
  "content_hash": null,
  "slug": "king-grid-independence-homology-torsion-free-next-research-step",
  "type": "attempt",
  "title": "Resolve the stated acceptance conditions",
  "summary": "Prove integral torsion-freeness for all \\(n,j\\), or give specific \\(n,j\\) together with a cycle and Smith-normal-form or equivalent certificate establishing nonzero torsion.",
  "relevance": "For Torsion-freeness for king-grid independence complexes, record king-grid-independence-homology-torsion-free-next-research-step (“Resolve the stated acceptance conditions”) documents a concrete method, search boundary, or failed route. The record states: Prove integral torsion-freeness for all \\(n,j\\), or give specific \\(n,j\\) together with a cycle and Smith-normal-form or equivalent certificate establishing nonzero torsion.",
  "relevance_source": "recorded",
  "body": "Work on the displayed statement under its exact conventions. Prove integral torsion-freeness for all \\(n,j\\), or give specific \\(n,j\\) together with a cycle and Smith-normal-form or equivalent certificate establishing nonzero torsion. Preserve source locators and any finite certificates so later work can distinguish a complete resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/math/0701890",
      "locator": "Editorial research route recorded 2026-08-01"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/math/0701890",
    "locator": "Editorial research route recorded 2026-08-01"
  },
  "relations": [
    {
      "slug": "R1331",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "king-grid-independence-homology-torsion-free",
      "title": "king grid independence homology torsion free",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}