{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R104",
  "content_hash": null,
  "slug": "casf4-attempt-restricted-growth-search",
  "type": "attempt",
  "title": "Restricted-growth backtracking produced the bounded witness table",
  "summary": "A deterministic search fixed alphabet-name symmetry, pruned every newly completed linear abelian square, and tested seam-crossing factors at complete length; it reached one witness at every n through 36.",
  "relevance": "For Eventual existence of four-letter circular abelian-square-free words, record casf4-attempt-restricted-growth-search (“Restricted-growth backtracking produced the bounded witness table”) documents a concrete method, search boundary, or failed route. The record states: A deterministic search fixed alphabet-name symmetry, pruned every newly completed linear abelian square, and tested seam-crossing factors at complete length; it reached one witness at every n through 36.",
  "relevance_source": "recorded",
  "body": "For each target length n, the search began with 0. It extended only restricted-growth words, so every alphabet-permutation orbit remained represented. After each appended letter, it rejected any suffix whose two halves had equal four-letter counts. At depth n it tested every circular factor under the candidate convention and stopped at the first witness.\n\nThe runs for n=1,...,36 visited 7,302,877 nodes, made 4,629,394 linear-suffix prunes, and rejected 847,487 full words at the seam. Their summed measured runtime was 478.900 seconds. Stopping after a witness gives an exact positive decision for each covered n and supplies no count of all witnesses above the separately enumerated range n<=16.",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "deterministic first-witness search at every integer target length n from 1 through 36",
    "bounds": {
      "n": {
        "min": 1,
        "max": 36
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Original deterministic search executed 2026-07-28; witnesses replayed by casf4-artifact-exact-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Original deterministic search executed 2026-07-28; witnesses replayed by casf4-artifact-exact-replay"
  },
  "relations": [
    {
      "slug": "R109",
      "title": "Exact circular witnesses cover every length through 36",
      "object_type": "claim",
      "relation": "produced",
      "direction": "outgoing"
    },
    {
      "slug": "R101",
      "title": "Build a certified boundary-profile splice system",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "circular-abelian-square-free-four-eventual",
      "title": "circular abelian square free four eventual",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}