{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R178",
  "content_hash": null,
  "slug": "cwc1766-artifact-chee-113-code",
  "type": "artifact",
  "title": "Replay of Chee's 113-word code",
  "summary": "Standard-library Python checks all 6,328 pairs of the published supports.",
  "relevance": "For Exact size of a length-17 constant-weight code, record cwc1766-artifact-chee-113-code (“Replay of Chee's 113-word code”) supplies evidence or a replay used to check the packet. The record states: Standard-library Python checks all 6,328 pairs of the published supports.",
  "relevance_source": "recorded",
  "body": "The artifact transcribes the supports in Section 2 of Chee's paper. It checks the number of supports, coordinate range, block size, uniqueness, and every unordered pair. The largest intersection is three, so the minimum Hamming distance is six. The elementary four-subset packing argument is included as a comparison: every four-subset occurs in at most one block, giving \\(A(17,6,6)\\leq\\lfloor\\binom{17}{4}/\\binom{6}{4}\\rfloor=158\\). The published classification bound 124 is stronger.\n\nThe canonical report digest is `6191fb13e590386109d135e9e0758214aa9f5e427d9e9db2b23b71c285c8d18a`.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "all 113 supports in Chee's published length-17 constant-weight code",
    "bounds": {
      "coordinates": {
        "min": 17,
        "max": 17
      },
      "blocks": {
        "min": 113,
        "max": 113
      },
      "block_size": {
        "min": 6,
        "max": 6
      },
      "pair_checks": {
        "min": 6328,
        "max": 6328
      }
    },
    "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://arxiv.org/abs/0712.2619",
      "locator": "Yeow Meng Chee, A New Lower Bound for A(17,6,6), Ars Combinatoria 83 (2007), 361-363, Section 2"
    },
    "inline_source": [
      "from hashlib import sha256",
      "from itertools import combinations",
      "from json import dumps",
      "from math import comb",
      "raw='0 1 2 3 6 15;0 1 2 4 11 16;0 1 2 7 8 9;0 1 2 10 12 13;0 1 3 4 8 10;0 1 3 5 7 12;0 1 3 9 13 16;0 1 4 6 7 13;0 1 5 6 10 16;0 1 5 8 11 13;0 1 6 9 11 12;0 1 7 10 11 15;0 1 8 12 14 15;0 2 3 4 9 12;0 2 3 5 8 16;0 2 3 7 11 13;0 2 4 5 7 10;0 2 4 8 13 15;0 2 5 6 9 13;0 2 5 11 14 15;0 2 6 7 12 16;0 2 6 8 10 11;0 3 4 5 6 11;0 3 4 7 14 16;0 3 5 10 13 15;0 3 6 7 9 10;0 3 6 8 12 13;0 3 8 9 11 15;0 3 10 11 12 14;0 4 5 12 13 14;0 4 6 8 9 16;0 4 6 10 12 15;0 4 7 8 11 12;0 4 9 10 11 13;0 5 6 7 8 15;0 5 8 9 10 14;0 5 9 12 15 16;0 6 11 13 14 16;0 7 8 10 13 16;0 7 9 13 14 15;1 2 3 4 5 13;1 2 3 7 10 14;1 2 3 8 11 12;1 2 4 6 9 10;1 2 4 7 12 15;1 2 5 6 7 11;1 2 5 8 10 15;1 2 5 12 14 16;1 2 6 8 13 16;1 2 9 11 13 15;1 3 4 6 12 16;1 3 4 7 9 11;1 3 5 6 8 14;1 3 5 11 15 16;1 3 6 10 11 13;1 3 7 8 13 15;1 3 9 10 12 15;1 4 5 7 8 16;1 4 5 9 14 15;1 4 5 10 11 12;1 4 6 8 11 15;1 4 8 9 12 13;1 4 10 13 14 16;1 5 6 12 13 15;1 5 7 9 10 13;1 6 7 8 10 12;1 6 7 9 15 16;1 7 11 12 13 16;1 8 9 10 11 16;2 3 4 6 7 8;2 3 4 10 11 15;2 3 5 6 10 12;2 3 5 7 9 15;2 3 6 9 11 16;2 3 8 9 10 13;2 3 12 13 15 16;2 4 5 6 15 16;2 4 5 8 9 11;2 4 6 11 12 13;2 4 7 9 13 16;2 4 8 10 12 14;2 5 7 8 12 13;2 5 10 11 13 16;2 6 7 10 13 15;2 6 8 9 12 15;2 7 8 11 15 16;2 7 9 10 11 12;2 9 10 14 15 16;3 4 5 8 12 15;3 4 5 9 10 16;3 4 6 13 14 15;3 4 7 10 12 13;3 4 8 11 13 16;3 5 6 7 13 16;3 5 7 8 10 11;3 5 9 11 12 13;3 6 7 11 12 15;3 6 8 10 15 16;3 7 8 9 12 16;4 5 6 7 9 12;4 5 6 8 10 13;4 5 7 11 13 15;4 6 7 10 11 14;4 7 8 9 10 15;4 11 12 14 15 16;5 6 8 11 12 16;5 6 9 10 11 15;5 7 9 11 14 16;5 7 10 12 14 15;5 8 13 14 15 16;6 7 8 9 11 13;6 9 10 12 13 16;8 10 11 12 13 15'",
      "blocks=[tuple(map(int,item.split())) for item in raw.split(';')]",
      "assert len(blocks)==113 and len(set(blocks))==113",
      "assert all(len(block)==6 and tuple(sorted(block))==block and block[0]>=0 and block[-1]<17 for block in blocks)",
      "intersections=[len(set(a)&set(b)) for a,b in combinations(blocks,2)]",
      "assert len(intersections)==comb(113,2)==6328",
      "assert max(intersections)==3",
      "minimum_distance=min(2*(6-value) for value in intersections)",
      "assert minimum_distance==6",
      "packing_bound=comb(17,4)//comb(6,4)",
      "assert packing_bound==158",
      "canonical='\\n'.join(' '.join(map(str,block)) for block in blocks)+'\\n'",
      "code_sha=sha256(canonical.encode()).hexdigest()",
      "report={'blocks':len(blocks),'coordinates':17,'weight':6,'pair_checks':len(intersections),'maximum_intersection':max(intersections),'minimum_hamming_distance':minimum_distance,'elementary_four_subset_packing_bound':packing_bound,'code_sha256':code_sha}",
      "payload=dumps(report,sort_keys=True,separators=(',',':'))",
      "assert sha256(payload.encode()).hexdigest()=='6191fb13e590386109d135e9e0758214aa9f5e427d9e9db2b23b71c285c8d18a'",
      "print(payload)"
    ],
    "missing": [
      "command",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/0712.2619",
    "locator": "Yeow Meng Chee, A New Lower Bound for A(17,6,6), Ars Combinatoria 83 (2007), 361-363, Section 2"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R180",
      "title": "The certified interval is 113 through 124",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "constant-weight-code-17-6-6",
      "title": "constant weight code 17 6 6",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}