{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R109",
  "content_hash": null,
  "slug": "casf4-claim-witnesses-one-through-thirty-six",
  "type": "claim",
  "title": "Exact circular witnesses cover every length through 36",
  "summary": "A deterministic restricted-growth search found one four-letter circular abelian-square-free word at each length 1 through 36, and a separate direct verifier checked every cyclic start and half-length.",
  "relevance": "For Eventual existence of four-letter circular abelian-square-free words, record casf4-claim-witnesses-one-through-thirty-six (“Exact circular witnesses cover every length through 36”) records a bound, answer, status fact, or structural consequence. The record states: A deterministic restricted-growth search found one four-letter circular abelian-square-free word at each length 1 through 36, and a separate direct verifier checked every cyclic start and half-length.",
  "relevance_source": "recorded",
  "body": "For every n in 1,...,36, the replay artifact contains an explicit word w_n over {0,1,2,3}. It tests every start s modulo n and every integer h with 1 <= h <= floor(n/2). The test compares the four-component Parikh vectors of w_n[s:s+h] and w_n[s+h:s+2h], with indices read modulo n.\n\nThe witness table has SHA-256 `53a8546a80f5700a254e23bfdbb005539a4b596848401919f92f8046b1f30054` under the artifact's canonical JSON encoding. The bounded result covers each integer length in the stated range. It supplies no construction for lengths above 36 and leaves eventual existence open.",
  "status": "observed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "one exact circular abelian-square-free witness for every integer length n from 1 through 36",
    "bounds": {
      "n": {
        "min": 1,
        "max": 36
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "locator": "Original exact computation and replay executed 2026-07-28; see casf4-artifact-exact-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Original exact computation and replay executed 2026-07-28; see casf4-artifact-exact-replay"
  },
  "models": [],
  "relations": [
    {
      "slug": "R104",
      "title": "Restricted-growth backtracking produced the bounded witness table",
      "object_type": "attempt",
      "relation": "produced",
      "direction": "incoming"
    },
    {
      "slug": "R100",
      "title": "Exact witness, count, and insertion-graph replay",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "circular-abelian-square-free-four-eventual",
      "title": "circular abelian square free four eventual",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}