{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R170",
  "content_hash": null,
  "slug": "cst101-attempt-literature-audit",
  "type": "attempt",
  "title": "The finite order-101 maximum was not located in the sources checked",
  "summary": "The literature gives exact formulas and asymptotic extremal results; the particular 42,376-orbit comparison appears to be a new finite computation.",
  "relevance": "For Most spanning trees in a 10-regular circulant on 101 vertices, record cst101-attempt-literature-audit (“The finite order-101 maximum was not located in the sources checked”) documents a concrete method, search boundary, or failed route. The record states: The literature gives exact formulas and asymptotic extremal results; the particular 42,376-orbit comparison appears to be a new finite computation.",
  "relevance_source": "recorded",
  "body": "Wang and Yang derive a spectral formula for spanning trees of circulant graphs. Zhang, Yong, and Golin develop Chebyshev formulas for fixed and varying jumps. Mednykh and Mednykh give further exact formulas, the square-form arithmetic theorem used as a check here, and Mahler-measure asymptotics.\n\nLonc, Parol, and Wojciechowski study the maximum number of spanning trees among \\(2k\\)-regular circulants as the number of vertices tends to infinity. Their result addresses asymptotic growth for fixed degree. The sources audited do not tabulate the exact order-101, degree-10 optimum or the two maximizing step-set representatives stated in this fixture.\n\nTargeted searches using the order, degree, winning step sets, and the 97-digit count found no matching publication. This is a focused prior-art check, so the originality of the finite result remains unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "published work on spanning-tree formulas and extremal spanning-tree counts for undirected circulant graphs, checked for the order-101 degree-10 finite maximum",
    "bounds": {
      "vertices": {
        "min": 101,
        "max": 101
      },
      "degree": {
        "min": 10,
        "max": 10
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://dblp.org/rec/journals/networks/LoncPW97",
      "locator": "Lonc, Parol, and Wojciechowski, Networks 30(1) (1997), 47-56; Wang and Yang 1984; Zhang, Yong, and Golin 2005; Mednykh and Mednykh 2019"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://dblp.org/rec/journals/networks/LoncPW97",
    "locator": "Lonc, Parol, and Wojciechowski, Networks 30(1) (1997), 47-56; Wang and Yang 1984; Zhang, Yong, and Golin 2005; Mednykh and Mednykh 2019"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R171",
      "title": "The exact maximum has 97 digits",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "outgoing"
    },
    {
      "slug": "circulant-spanning-trees-101-degree10",
      "title": "circulant spanning trees 101 degree10",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}