{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R94",
  "content_hash": null,
  "slug": "ca3153-claim-nist-80-row-array",
  "type": "claim",
  "title": "The completed NIST 80-row array covers every interaction",
  "summary": "Exhaustive enumeration verifies all 12,285 interaction requirements in an explicit completion of NIST's IPOG-F array.",
  "relevance": "For Exact value of CAN(3,15,3), record ca3153-claim-nist-80-row-array (“The completed NIST 80-row array covers every interaction”) records a bound, answer, status fact, or structural consequence. The record states: Exhaustive enumeration verifies all 12,285 interaction requirements in an explicit completion of NIST's IPOG-F array.",
  "relevance_source": "recorded",
  "body": "NIST publishes an 80-row IPOG-F array for these parameters. Its file contains 65 don't-care cells marked with hyphens. Replacing every don't-care cell by zero gives an ordinary array over \\(\\{0,1,2\\}\\). This completion preserves every interaction already witnessed by a specified cell and supplies a compact explicit certificate.\n\nThe executable record checks the shape and alphabet, then enumerates all \\(\\binom{15}{3}=455\\) column triples. Each of their 27 ordered ternary interactions occurs at least once. Across the 12,285 requirements, the minimum multiplicity is one and the maximum is eleven. The canonical completed array has SHA-256 digest `ed0f7e38bdb4c43d87b6cba972fe940ba0c3123f3a2c31f95cf3c4cd66bb100b`.\n\nThis proves the independently reproduced bound \\(\\operatorname{CAN}(3,15,3)\\le80\\). The sharper 57-row bound in the interval record rests on the cited primary report because its deposited witness was unavailable during this audit.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "all 455 triples of columns and all 27 ternary interactions in each triple for the completed NIST 80 by 15 array",
    "bounds": {
      "rows": {
        "min": 80,
        "max": 80
      },
      "columns": {
        "min": 15,
        "max": 15
      },
      "column_triples": {
        "min": 455,
        "max": 455
      },
      "interactions": {
        "min": 12285,
        "max": 12285
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://math.nist.gov/coveringarrays/ipof/cas/t%3D3/v%3D3/ca.3.3%5E15.txt.zip",
      "locator": "NIST Covering Array Tables, file ca.3.3^15.txt; 65 don't-care cells completed with zero and replayed in ca3153-artifact-coverage-verifier"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://math.nist.gov/coveringarrays/ipof/cas/t%3D3/v%3D3/ca.3.3%5E15.txt.zip",
    "locator": "NIST Covering Array Tables, file ca.3.3^15.txt; 65 don't-care cells completed with zero and replayed in ca3153-artifact-coverage-verifier"
  },
  "models": [],
  "relations": [
    {
      "slug": "R93",
      "title": "Exhaustive verifier for the NIST array",
      "object_type": "artifact",
      "relation": "verifies",
      "direction": "incoming"
    },
    {
      "slug": "R95",
      "title": "The checked published interval is 27 through 57",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "covering-array-3-15-3",
      "title": "covering array 3 15 3",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}