{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R133",
  "content_hash": null,
  "slug": "cds-claim-exact-maxima-through-fourteen",
  "type": "claim",
  "title": "Exact maxima for every alphabet through length fourteen",
  "summary": "Independent exhaustive programs give maxima 0,1,1,2,3,4,4,6,6,9,8,10,11,13 at lengths 1 through 14.",
  "relevance": "For The three-halves bound for distinct squares in circular words, record cds-claim-exact-maxima-through-fourteen (“Exact maxima for every alphabet through length fourteen”) records a bound, answer, status fact, or structural consequence. The record states: Independent exhaustive programs give maxima 0,1,1,2,3,4,4,6,6,9,8,10,11,13 at lengths 1 through 14.",
  "relevance_source": "recorded",
  "body": "Every length-n word is globally equivalent under alphabet renaming to one restricted-growth string, so the Bell-number layer covers arbitrary finite alphabets without fixing an alphabet size. Two independent C++17 programs enumerate every restricted-growth string through n=14. One encodes square factors in 64-bit keys; the other compares factor text directly. Their normalized outputs agree byte for byte.\n\nFor n=1,...,14, the exact maxima are\n[0,1,1,2,3,4,4,6,6,9,8,10,11,13].\nThe corresponding maxima restricted to primitive words are\n[0,0,1,2,3,3,4,6,6,7,8,10,11,11].\nFor nonprimitive words they are undefined at n=1 and then\n[1,1,2,2,4,3,6,4,9,5,9,6,13].\nA separate Python enumerator canonicalized alphabet renaming, rotation, and reversal through n=12 and returned the same total maxima. Every unrestricted maximum through n=14 has a binary witness. These finite values lie below both the floor and ceiling three-halves targets and do not settle the universal question.",
  "status": "supported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "every finite word of lengths 1 through 14, modulo global alphabet renaming",
    "bounds": {
      "word_length": {
        "min": 1,
        "max": 14
      },
      "alphabet_size": {
        "min": 1,
        "max": 14
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "locator": "Two independent exhaustive C++17 restricted-growth enumerations executed 2026-07-28, with a symmetry-reduced Python cross-check through n=12"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Two independent exhaustive C++17 restricted-growth enumerations executed 2026-07-28, with a symmetry-reduced Python cross-check through n=12"
  },
  "models": [],
  "relations": [
    {
      "slug": "R127",
      "title": "Packed-factor restricted-growth replay",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R126",
      "title": "Direct-factor independent restricted-growth replay",
      "object_type": "artifact",
      "relation": "evidences",
      "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"
    }
  ]
}