{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R180",
  "content_hash": null,
  "slug": "cwc1766-claim-certified-interval-113-124",
  "type": "claim",
  "title": "The certified interval is 113 through 124",
  "summary": "A published 113-word code gives the lower endpoint, and a classification-based bound gives the upper endpoint.",
  "relevance": "For Exact size of a length-17 constant-weight code, record cwc1766-claim-certified-interval-113-124 (“The certified interval is 113 through 124”) records a bound, answer, status fact, or structural consequence. The record states: A published 113-word code gives the lower endpoint, and a classification-based bound gives the upper endpoint.",
  "relevance_source": "recorded",
  "body": "The strongest bounds found in the checked primary sources and coding-theory tables are\n\\[\n\\boxed{113\\leq A(17,6,6)\\leq124}.\n\\]\nChee published the 113 supports reproduced in this record. The executable artifact independently checks that every support has size six and that each distinct pair meets in at most three points. This proves the lower bound.\n\nThe upper endpoint comes from Östergård's computer-aided classification of binary constant-weight codes. Agrell's table attributes the entry \\(A(17,6,6)\\leq124\\) to Tables IX through XI and Theorem 3 of that paper. The classification certificate itself is not distributed with the table, so this record treats 124 as a sourced published bound rather than an independently replayed computation.\n\nThe exact value remains unresolved in the sources checked for this entry.",
  "status": "open",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "binary constant-weight codes of length 17, weight 6, and minimum Hamming distance at least 6",
    "bounds": {
      "length": {
        "min": 17,
        "max": 17
      },
      "weight": {
        "min": 6,
        "max": 6
      },
      "minimum_distance": {
        "min": 6,
        "max": 6
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://codes.se/bounds/cw.html",
      "locator": "Bounds on A(n,6,w), row n=17 and column w=6; superscript O points to P. R. J. Östergård, Classification of Binary Constant Weight Codes, IEEE Transactions on Information Theory 56 (2010), Tables IX-XI and Theorem 3"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://codes.se/bounds/cw.html",
    "locator": "Bounds on A(n,6,w), row n=17 and column w=6; superscript O points to P. R. J. Östergård, Classification of Binary Constant Weight Codes, IEEE Transactions on Information Theory 56 (2010), Tables IX-XI and Theorem 3"
  },
  "relations": [
    {
      "slug": "R178",
      "title": "Replay of Chee's 113-word code",
      "object_type": "artifact",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R179",
      "title": "Primary-source audit leaves an eleven-word gap",
      "object_type": "attempt",
      "relation": "contextualizes",
      "direction": "incoming"
    },
    {
      "slug": "constant-weight-code-17-6-6",
      "title": "constant weight code 17 6 6",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}