{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R419",
  "content_hash": null,
  "slug": "ising6-attempt-literature-and-sector-audit",
  "type": "attempt",
  "title": "Literature gives the general framework, while the exact 6 by 6 value remains unlocated",
  "summary": "The checked sources cover spectral-gap comparison and high-temperature torus dynamics. The audit found no published characteristic polynomial or exact gap for this parameter choice.",
  "relevance": "For Exact heat-bath spectral gap on the six by six Ising torus, record ising6-attempt-literature-and-sector-audit (“Literature gives the general framework, while the exact 6 by 6 value remains unlocated”) documents a concrete method, search boundary, or failed route. The record states: The checked sources cover spectral-gap comparison and high-temperature torus dynamics.",
  "relevance_source": "recorded",
  "body": "Holley and Stroock develop functional inequalities and perturbation methods for stochastic Ising models. Martinelli's Saint-Flour lectures give a broad account of reversible Glauber dynamics, finite-volume spectral gaps, and temperature regimes. Lubetzky and Sly study heat-bath Glauber dynamics on square tori throughout the strong-spatial-mixing regime and relate finite-torus gaps to the infinite-volume gap.\n\nThese sources support the chain convention and the use of Poincare comparison. They do not tabulate the second eigenvalue for \\(C_6\\mathbin{\\square}C_6\\) at \\(\\beta=(\\log2)/2\\). Targeted searches for the exact size, the five rational conditional probabilities, and a finite-volume characteristic polynomial also found no such certificate. This is a status audit rather than a proof of novelty.\n\nA full resolution needs a decomposition of the transition operator under spin flip and the automorphism group of the torus, followed by an exact characteristic polynomial or rational eigenvalue enclosures for every block. The present one-dimensional Ritz calculation covers one invariant trial subspace and supplies the upper endpoint recorded here.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "primary and standard references located for heat-bath Glauber dynamics, finite-volume spectral gaps, perturbation comparison, and high-temperature Ising dynamics on square tori",
    "bounds": {
      "publication_year": {
        "min": 1987,
        "max": 2013
      },
      "exact_target_side_length": {
        "min": 6,
        "max": 6
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s00222-012-0404-5",
      "locator": "Richard Holley and Daniel Stroock, Logarithmic Sobolev Inequalities and Stochastic Ising Models, Journal of Statistical Physics 46 (1987), 1159-1194, DOI 10.1007/BF01011161; Fabio Martinelli, Lectures on Glauber Dynamics for Discrete Spin Models, Lecture Notes in Mathematics 1717 (1999), 93-191, DOI 10.1007/978-3-540-48115-7_2; Eyal Lubetzky and Allan Sly, Cutoff for the Ising Model on the Lattice, Inventiones Mathematicae 191 (2013), 719-755, DOI 10.1007/s00222-012-0404-5"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00222-012-0404-5",
    "locator": "Richard Holley and Daniel Stroock, Logarithmic Sobolev Inequalities and Stochastic Ising Models, Journal of Statistical Physics 46 (1987), 1159-1194, DOI 10.1007/BF01011161; Fabio Martinelli, Lectures on Glauber Dynamics for Discrete Spin Models, Lecture Notes in Mathematics 1717 (1999), 93-191, DOI 10.1007/978-3-540-48115-7_2; Eyal Lubetzky and Allan Sly, Cutoff for the Ising Model on the Lattice, Inventiones Mathematicae 191 (2013), 719-755, DOI 10.1007/s00222-012-0404-5"
  },
  "relations": [
    {
      "slug": "R420",
      "title": "A certified rational interval for the six-torus heat-bath gap",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "ising-six-torus-heat-bath-gap",
      "title": "ising six torus heat bath gap",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}