{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R93",
  "content_hash": null,
  "slug": "ca3153-artifact-coverage-verifier",
  "type": "artifact",
  "title": "Exhaustive verifier for the NIST array",
  "summary": "Standard-library Python decodes the explicit array and verifies every ternary interaction in every triple of columns.",
  "relevance": "For Exact value of CAN(3,15,3), record ca3153-artifact-coverage-verifier (“Exhaustive verifier for the NIST array”) supplies evidence or a replay used to check the packet. The record states: Standard-library Python decodes the explicit array and verifies every ternary interaction in every triple of columns.",
  "relevance_source": "recorded",
  "body": "The compressed payload contains 80 lines of 15 ternary digits, with one row per line and a final newline. The program binds the payload to its digest, checks every entry, and enumerates the full coverage condition. It also verifies the complete multiplicity distribution and the incidence identity \\(80\\binom{15}{3}=36400\\).\n\nThe four-line standard output has SHA-256 digest `821bdc633a47f7300160b992df72caad902c15d2dc87723219e55ec3bbe1280a`.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "the complete 80-row ternary array and every strength-three coverage requirement on its 15 columns",
    "bounds": {
      "rows": {
        "min": 80,
        "max": 80
      },
      "columns": {
        "min": 15,
        "max": 15
      },
      "requirements": {
        "min": 12285,
        "max": 12285
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "inline_python_computation",
    "entrypoint": "save code as check.py and run python3 check.py",
    "runtime": "CPython 3, standard library only",
    "citation": {
      "url": "https://math.nist.gov/coveringarrays/ipof/cas/t%3D3/v%3D3/ca.3.3%5E15.txt.zip",
      "locator": "Inline CPython standard-library replay of the zero-completed NIST array, executed 2026-07-25"
    },
    "outputs": "rows=80 columns=15 alphabet=3\ncolumn_triples=455 interactions=12285 missing=0\ncoverage=1:1287,2:3368,3:3948,4:2412,5:886,6:274,7:77,8:29,9:1,10:2,11:1 incidences=36400\narray_sha256=ed0f7e38bdb4c43d87b6cba972fe940ba0c3123f3a2c31f95cf3c4cd66bb100b\n",
    "inline_source": "from base64 import b64decode\nfrom collections import Counter\nfrom hashlib import sha256\nfrom itertools import combinations\nfrom math import comb\nfrom zlib import decompress\n\npayload = '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'\nraw = decompress(b64decode(payload))\nassert sha256(raw).hexdigest() == 'ed0f7e38bdb4c43d87b6cba972fe940ba0c3123f3a2c31f95cf3c4cd66bb100b'\nlines = raw.decode().splitlines()\narray = [[int(ch) for ch in line] for line in lines]\nassert len(array) == 80 and all(len(row) == 15 for row in array)\nassert {entry for row in array for entry in row} == {0, 1, 2}\ncoverage = []\nmissing = []\nfor columns in combinations(range(15), 3):\n    counts = Counter(tuple(row[column] for column in columns) for row in array)\n    for interaction in ((a, b, c) for a in range(3) for b in range(3) for c in range(3)):\n        multiplicity = counts[interaction]\n        coverage.append(multiplicity)\n        if multiplicity == 0:\n            missing.append((columns, interaction))\ndistribution = Counter(coverage)\nassert len(coverage) == comb(15, 3) * 27 == 12285\nassert not missing and min(coverage) == 1 and max(coverage) == 11\nassert distribution == {1: 1287, 2: 3368, 3: 3948, 4: 2412, 5: 886, 6: 274, 7: 77, 8: 29, 9: 1, 10: 2, 11: 1}\nassert sum(coverage) == 80 * comb(15, 3) == 36400\nprint('rows=80 columns=15 alphabet=3')\nprint('column_triples=455 interactions=12285 missing=0')\nprint('coverage=' + ','.join(f'{key}:{distribution[key]}' for key in sorted(distribution)) + f' incidences={sum(coverage)}')\nprint('array_sha256=' + sha256(raw).hexdigest())\n",
    "missing": [
      "command"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://math.nist.gov/coveringarrays/ipof/cas/t%3D3/v%3D3/ca.3.3%5E15.txt.zip",
    "locator": "Inline CPython standard-library replay of the zero-completed NIST array, executed 2026-07-25"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R94",
      "title": "The completed NIST 80-row array covers every interaction",
      "object_type": "claim",
      "relation": "verifies",
      "direction": "outgoing"
    },
    {
      "slug": "covering-array-3-15-3",
      "title": "covering array 3 15 3",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}