{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R174",
  "content_hash": null,
  "slug": "cubic20ising-attempt-corpus-and-literature-audit",
  "type": "attempt",
  "title": "The exact target remains a finite 396,150-class computation",
  "summary": "Published generators settle the corpus size, while the checked Ising and matching papers provide context and a universal bound rather than the order-20 extremum.",
  "relevance": "For Most antiferromagnetic ground states in a 3-connected cubic graph on twenty vertices, record cubic20ising-attempt-corpus-and-literature-audit (“The exact target remains a finite 396,150-class computation”) documents a concrete method, search boundary, or failed route. The record states: Published generators settle the corpus size, while the checked Ising and matching papers provide context and a universal bound rather than the order-20 extremum.",
  "relevance_source": "recorded",
  "body": "McKay and Royle constructed the cubic graphs through 20 vertices. The current connectivity table, OEIS A204198, records exactly 396,150 strictly 3-connected cubic isomorphism classes on 20 vertices and points to the `C3` option of snarkhunter for reproduction. Brinkmann, Goedgebeur, and McKay describe the modern isomorph-free cubic-graph generator and report independent count checks against earlier generators.\n\nThe focused Ising search found work on ground-state degeneracy for signed lattice models and work relating antiferromagnetic Ising ground states to counting problems. Those sources do not state this finite extremum for uniform antiferromagnetic couplings on 3-connected cubic graphs of order 20. The matching-partition-function theorem supplies the general upper bound in this fixture.\n\nA complete resolution can stream the 396,150 graph6 representatives, verify 3-connectivity or request it from the generator, fix one spin, and compute the maximum-cut multiplicity for each class. The class count and a digest of the generated stream should accompany the final maximum. This fixture stops with the certified interval and explicit incumbent.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://oeis.org/A204198",
      "locator": "OEIS A204198; Brendan D. McKay and Gordon F. Royle, Constructing the Cubic Graphs on up to 20 Vertices, Ars Combinatoria 21A (1986), 129-140; Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, Generation of Cubic Graphs, DMTCS 13(2) (2011), 69-80"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A204198",
    "locator": "OEIS A204198; Brendan D. McKay and Gordon F. Royle, Constructing the Cubic Graphs on up to 20 Vertices, Ars Combinatoria 21A (1986), 129-140; Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, Generation of Cubic Graphs, DMTCS 13(2) (2011), 69-80"
  },
  "models": [],
  "relations": [
    {
      "slug": "R175",
      "title": "The certified interval is 36 through 254,658 ground states",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "outgoing"
    },
    {
      "slug": "cubic-graph-twenty-ising-degeneracy",
      "title": "cubic graph twenty ising degeneracy",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}