{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R400",
  "content_hash": null,
  "slug": "hs16-attempt-literature-audit",
  "type": "attempt",
  "title": "Primary literature supports the model, transfer, and zero-free disk",
  "summary": "The located sources supply the hard-square setting, compatible-mask transfer, and universal disk bound. None reports the finite 16 by 16 nearest zero.",
  "relevance": "For Nearest hard-square partition-function zero for the sixteen grid, record hs16-attempt-literature-audit (“Primary literature supports the model, transfer, and zero-free disk”) documents a concrete method, search boundary, or failed route. The record states: The located sources supply the hard-square setting, compatible-mask transfer, and universal disk bound.",
  "relevance_source": "recorded",
  "body": "Baxter, Enting, and Tsang study the hard-square lattice gas and its activity expansion on the square lattice. Calkin and Wilf assemble grid independent sets with compatible row or column masks and evaluate the total at activity one. Adding the monomial weight \\(z^{|m|}\\) gives the coefficient transfer used here.\n\nScott and Sokal connect the hard-core partition function with the Lovász local lemma and present the Shearer-Dobrushin nonvanishing criterion. For maximum degree four, its uniform specialization supplies the disk \\(|z|<27/256\\).\n\nFocused searches covered the exact graph name, finite hard-square partition zeros, independence-polynomial zeros for square grids, and the cited papers' references. No primary source located in this audit gives the nearest zero of \\(P_{16}\\mathbin{\\square}P_{16}\\). Publication novelty and the exact least-modulus value remain unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/BF01012867",
      "locator": "R. J. Baxter, I. G. Enting, and S. K. Tsang, Hard-square lattice gas, Journal of Statistical Physics 22(4) (1980), 465-489; Neil J. Calkin and Herbert S. Wilf, The Number of Independent Sets in a Grid Graph, SIAM Journal on Discrete Mathematics 11(1) (1998), 54-60; Alexander D. Scott and Alan D. Sokal, The repulsive lattice gas, the independent-set polynomial, and the Lovasz local lemma, Journal of Statistical Physics 118 (2005), 1151-1261"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/BF01012867",
    "locator": "R. J. Baxter, I. G. Enting, and S. K. Tsang, Hard-square lattice gas, Journal of Statistical Physics 22(4) (1980), 465-489; Neil J. Calkin and Herbert S. Wilf, The Number of Independent Sets in a Grid Graph, SIAM Journal on Discrete Mathematics 11(1) (1998), 54-60; Alexander D. Scott and Alan D. Sokal, The repulsive lattice gas, the independent-set polynomial, and the Lovasz local lemma, Journal of Statistical Physics 118 (2005), 1151-1261"
  },
  "relations": [
    {
      "slug": "R401",
      "title": "A certified radius bracket and an isolated real zero for the sixteen grid",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "hard-square-sixteen-zero-radius",
      "title": "hard square sixteen zero radius",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}