{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R162",
  "content_hash": null,
  "slug": "cset11-attempt-literature-and-search-audit",
  "type": "attempt",
  "title": "The literature supplies the framework and universal bound, with no exact n=11 table located",
  "summary": "Kalai's theory identifies these complexes as rational 2-hypertrees; later work treats their enumeration and torsion growth, while the exact eleven-vertex maximum remains unlocated.",
  "relevance": "For Largest first-homology torsion from forty-five triangles on eleven vertices, record cset11-attempt-literature-and-search-audit (“The literature supplies the framework and universal bound, with no exact n=11 table located”) documents a concrete method, search boundary, or failed route. The record states: Kalai's theory identifies these complexes as rational 2-hypertrees; later work treats their enumeration and torsion growth, while the exact eleven-vertex maximum remains unlocated.",
  "relevance_source": "recorded",
  "body": "Kalai introduced rationally acyclic simplicial complexes and proved the torsion-weighted higher-dimensional version of Cayley's formula. In the present parameters, a full-rank selection of 45 triangle-boundary columns is a rational 2-hypertree. The same paper gives the universal torsion bound used above.\n\nLinial and Peled restate the boundary-basis characterization and Kalai's torsion-weighted enumeration, then study unweighted enumeration and random constructions. Their work does not give a table of maximum torsion by vertex count. Newman studies the inverse problem of realizing prescribed torsion on few vertices. His concluding Question 3 asks for the largest torsion group realizable at fixed \\(n\\) and \\(d\\), and says the problem appears difficult even for small parameters.\n\nThe audit searched the exact parameter phrase, combinations of `11 vertices`, `2-hypertree`, `maximum torsion`, and determinant formulations. It also checked the cited hypertree and small-complex papers. No primary source settling this exact 45-face optimization was located. The value 74 should therefore be treated as a reproducible incumbent rather than a published optimum.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "a focused status audit for maximum first-homology torsion among eleven-vertex rational 2-hypertrees",
    "bounds": {
      "vertices": {
        "min": 11,
        "max": 11
      },
      "dimension": {
        "min": 2,
        "max": 2
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1801.02423",
      "locator": "Nati Linial and Yuval Peled, Enumeration and randomized constructions of hypertrees, Definition 1.1 and Theorem 1.2; Andrew Newman, Small simplicial complexes with prescribed torsion in homology, Theorem 4 part 1 and Question 3"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1801.02423",
    "locator": "Nati Linial and Yuval Peled, Enumeration and randomized constructions of hypertrees, Definition 1.1 and Theorem 1.2; Andrew Newman, Small simplicial complexes with prescribed torsion in homology, Theorem 4 part 1 and Question 3"
  },
  "relations": [
    {
      "slug": "R163",
      "title": "The certified interval is 74 through 387,420,489",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "outgoing"
    },
    {
      "slug": "complete-skeleton-eleven-torsion",
      "title": "complete skeleton eleven torsion",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}