{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R712",
  "content_hash": null,
  "slug": "sdcm-artifact-witness-verifier",
  "type": "artifact",
  "title": "Exact verifier for the 24-win construction",
  "summary": "Standard-library Python checks the partition, evaluates every adjacent face pair, and checks the arithmetic that excludes count 26 under the published universal bound.",
  "relevance": "For Largest cyclic winning margin for six disjoint six-sided dice, record sdcm-artifact-witness-verifier (“Exact verifier for the 24-win construction”) supplies evidence or a replay used to check the packet. The record states: Standard-library Python checks the partition, evaluates every adjacent face pair, and checks the arithmetic that excludes count 26 under the published universal bound.",
  "relevance_source": "recorded",
  "body": "The six dice are stored as sorted integer lists. The verifier checks that their disjoint union is exactly \\(\\{1,\\ldots,36\\}\\). For each cyclic edge it evaluates all \\(6\\cdot6=36\\) ordered face pairs and counts the strict wins. The resulting vector is\n\\[\n[24,24,36,36,24,24].\n\\]\nIt also checks the exact integer inequality \\(2\\cdot13^2>18^2\\), which is the comparison \\(13/18>1/\\sqrt2\\) used after applying Komisarski's theorem. The compact report has SHA-256 digest `d60da0645a4d7bed2cf496969ce652c1ccaef7d9373a3921679ada3af063f5fa`.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "all 216 ordered face comparisons on the six cyclic edges of the displayed partition",
    "bounds": {
      "cyclic_edges": {
        "min": 6,
        "max": 6
      },
      "ordered_face_pairs_per_edge": {
        "min": 36,
        "max": 36
      },
      "total_ordered_face_pairs": {
        "min": 216,
        "max": 216
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "inline_python_computation",
    "entrypoint": "join source_lines with newline and run with python3",
    "runtime": "CPython 3, standard library only",
    "citation": {
      "url": "https://doi.org/10.1080/00029890.2021.1889921",
      "locator": "Self-contained Python standard-library verifier reproduced on 2026-07-25"
    },
    "inline_source": [
      "from hashlib import sha256",
      "from json import dumps",
      "DICE=[[3,4,5,32,33,34],[1,2,28,29,30,31],[22,23,24,25,26,27],[16,17,18,19,20,21],[10,11,12,13,14,15],[6,7,8,9,35,36]]",
      "assert all(len(die)==6 and die==sorted(die) and len(set(die))==6 for die in DICE)",
      "assert sorted(x for die in DICE for x in die)==list(range(1,37))",
      "def wins(left,right):",
      "    return sum(x>y for x in left for y in right)",
      "counts=[wins(DICE[i],DICE[(i+1)%6]) for i in range(6)]",
      "assert counts==[24,24,36,36,24,24]",
      "assert min(counts)==24",
      "# Exact comparison 13/18 > 1/sqrt(2).",
      "assert 2*13*13>18*18",
      "report={'dice':DICE,'cyclic_win_counts':counts,'minimum_win_count':min(counts),'lower_probability':'2/3','universal_strict_upper':'1/sqrt(2)','first_excluded_integer_count':26,'excluded_probability':'13/18'}",
      "payload=dumps(report,sort_keys=True,separators=(',',':'))",
      "assert sha256(payload.encode()).hexdigest()=='d60da0645a4d7bed2cf496969ce652c1ccaef7d9373a3921679ada3af063f5fa'",
      "print(payload)"
    ],
    "missing": [
      "command",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1080/00029890.2021.1889921",
    "locator": "Self-contained Python standard-library verifier reproduced on 2026-07-25"
  },
  "relations": [
    {
      "slug": "R714",
      "title": "The optimal cyclic win count is 24 or 25",
      "object_type": "claim",
      "relation": "verifies",
      "direction": "outgoing"
    },
    {
      "slug": "six-dice-cyclic-margin",
      "title": "six dice cyclic margin",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}