{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R359",
  "content_hash": null,
  "slug": "h65537-attempt-literature-audit",
  "type": "attempt",
  "title": "The finite-field literature gives statistical context",
  "summary": "Two primary papers treat reversible Hénon reductions and their cycle model; the audit found no p=65537 decomposition for this map.",
  "relevance": "For Largest cycle of a Hénon permutation over the 65537 field, record h65537-attempt-literature-audit (“The finite-field literature gives statistical context”) documents a concrete method, search boundary, or failed route. The record states: Two primary papers treat reversible Hénon reductions and their cycle model; the audit found no p=65537 decomposition for this map.",
  "relevance_source": "recorded",
  "body": "Roberts and Vivaldi's 2005 paper studies time-reversal symmetry in polynomial automorphisms over finite fields, including area-preserving Hénon maps and their cycle statistics. Their 2009 paper develops the associated random-involution model and its universal limiting distribution.\n\nThe displayed reversing identity puts this problem in that setting. The two papers discuss asymptotic behavior and computations at other moduli. The focused formula, title, and citation audit found no published complete decomposition for \\(y^2+1-x\\) at \\(p=65537\\). This fixture therefore records 294,672 as a certified lower bound and leaves the finite maximum unresolved.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "published finite-field cycle results relevant to H(x,y)=(y,y^2+1-x) at p=65537",
    "bounds": {
      "prime": {
        "min": 65537,
        "max": 65537
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1088/0951-7715/18/5/015",
      "locator": "Roberts and Vivaldi, Nonlinearity 18 (2005), 2171-2192; Roberts and Vivaldi, Nonlinearity 22 (2009), 1965-1982"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1088/0951-7715/18/5/015",
    "locator": "Roberts and Vivaldi, Nonlinearity 18 (2005), 2171-2192; Roberts and Vivaldi, Nonlinearity 22 (2009), 1965-1982"
  },
  "models": [],
  "relations": [
    {
      "slug": "R361",
      "title": "The map is a reversible area-preserving Hénon map",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R360",
      "title": "A certified cycle has length 294,672",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "henon-65537-max-cycle",
      "title": "henon 65537 max cycle",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}