{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R130",
  "content_hash": null,
  "slug": "cds-attempt-short-square-half-charge",
  "type": "attempt",
  "title": "The short-square half-length charge fails at twelve",
  "summary": "A binary word of length 12 has nine distinct squares of total length at most 6, exceeding the proposed ceiling of 6.",
  "relevance": "For The three-halves bound for distinct squares in circular words, record cds-attempt-short-square-half-charge (“The short-square half-length charge fails at twelve”) documents a concrete method, search boundary, or failed route. The record states: A binary word of length 12 has nine distinct squares of total length at most 6, exceeding the proposed ceiling of 6.",
  "relevance_source": "recorded",
  "body": "A tempting split would bound squares of total length at most n/2 by ceil(n/2), then charge the remaining long squares separately. Exact binary enumeration refutes the short part at n=12. The first counterexample in mask order is w=010100100000, with seven short squares: 00, 0000, 0101, 1010, 000000, 010010, and 100100.\n\nThe exact binary maximum at n=12 is nine, attained by w=011011010010. Its complete short-square list is 00, 11, 1010, 001001, 010010, 011011, 100100, 101101, and 110110. Each listed word has total length at most six. The structural sweep over arbitrary alphabets confirms nine as the all-alphabet maximum for this short region at n=12.",
  "status": "failed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all binary words of length 12, with every square factor of total length at most 6 exhaustively listed",
    "bounds": {
      "word_length": {
        "min": 12,
        "max": 12
      },
      "alphabet_size": {
        "min": 2,
        "max": 2
      },
      "square_total_length": {
        "min": 2,
        "max": 6
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Exhaustive binary and restricted-growth computations executed independently on 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exhaustive binary and restricted-growth computations executed independently on 2026-07-28"
  },
  "models": [],
  "relations": [
    {
      "slug": "R125",
      "title": "Packed binary enumeration through length twenty-six",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R124",
      "title": "Direct-string independent binary replay",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R129",
      "title": "Strengthen the primitive Rauzy split case",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "circular-distinct-squares-three-halves",
      "title": "circular distinct squares three halves",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}