{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R444",
  "content_hash": null,
  "slug": "lee7-attempt-torus-grid-literature-audit",
  "type": "attempt",
  "title": "The exact parameter pair is covered by a 2025 torus-grid theorem",
  "summary": "The peer-reviewed torus-grid paper uses the same metric and closed Rips convention and proves the requested homotopy equivalence as a small-scale case.",
  "relevance": "For Homotopy type of a Lee-metric Rips complex on the 7 by 7 torus, record lee7-attempt-torus-grid-literature-audit (“The exact parameter pair is covered by a 2025 torus-grid theorem”) documents a concrete method, search boundary, or failed route. The record states: The peer-reviewed torus-grid paper uses the same metric and closed Rips convention and proves the requested homotopy equivalence as a small-scale case.",
  "relevance_source": "recorded",
  "body": "A focused search for Lee-metric, torus-grid, graph-power, and Vietoris-Rips formulations located a direct source. Adams, Adetowubo, Barriga-Acosta, Feng, and Sterling define \\(T_{n,n}\\) on \\(\\{0,\\ldots,n-1\\}^2\\) with the same circular \\(l^1\\) metric. Their closed Rips complex contains each finite set of diameter at most \\(k\\), which is the clique complex in the candidate statement.\n\nTheir Theorem 5.8 covers every \\(k\\geq2\\) and \\(n>3k\\), including \\((n,k)=(7,2)\\). The abstract states the equivalent small-scale range \\(n\\geq7\\) and \\(2\\leq k\\leq(n-1)/3\\). The article appeared in Mediterranean Journal of Mathematics in 2025. John Sterling's 2025 Auburn thesis gives an extended exposition of the same project, with the corresponding result as Theorem 4.2 on pages 26 and 27.\n\nThe candidate's open-status claim is therefore outdated. This parameter pair has a published affirmative classification.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "literature search for the homotopy type of the 7 by 7 l1 torus-grid Rips complex at scale 2",
    "bounds": {
      "side_length": {
        "min": 7,
        "max": 7
      },
      "lee_threshold": {
        "min": 2,
        "max": 2
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s00009-025-02945-9",
      "locator": "Adams et al., Vietoris-Rips Complexes of Torus Grids, Mediterranean Journal of Mathematics 22, 173 (2025), DOI 10.1007/s00009-025-02945-9, abstract and Theorem 5.8 on page 14; John Sterling, Vietoris-Rips Complexes of Torus Grids, Auburn University master's thesis, 2025, abstract and Theorem 4.2 on pages 26-27"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00009-025-02945-9",
    "locator": "Adams et al., Vietoris-Rips Complexes of Torus Grids, Mediterranean Journal of Mathematics 22, 173 (2025), DOI 10.1007/s00009-025-02945-9, abstract and Theorem 5.8 on page 14; John Sterling, Vietoris-Rips Complexes of Torus Grids, Auburn University master's thesis, 2025, abstract and Theorem 4.2 on pages 26-27"
  },
  "relations": [
    {
      "slug": "R445",
      "title": "The complex is homotopy equivalent to the 2-torus",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "lee-rips-torus-7-homotopy",
      "title": "lee rips torus 7 homotopy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}