{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R105",
  "content_hash": null,
  "slug": "casf4-attempt-selected-witness-insertion",
  "type": "attempt",
  "title": "Every length-eight orbit blocks one-letter insertion",
  "summary": "Complete enumeration finds zero valid one-letter insertion edges from any of the 16 length-eight orbits to a length-nine circular word; selected witnesses at 14 later lengths are also insertion dead ends.",
  "relevance": "For Eventual existence of four-letter circular abelian-square-free words, record casf4-attempt-selected-witness-insertion (“Every length-eight orbit blocks one-letter insertion”) documents a concrete method, search boundary, or failed route. The record states: Complete enumeration finds zero valid one-letter insertion edges from any of the 16 length-eight orbits to a length-nine circular word; selected witnesses at 14 later lengths are also insertion dead ends.",
  "relevance_source": "recorded",
  "body": "The replay built the complete insertion graph on every alphabet-permutation orbit through length 16. An edge inserts one of four letters at one of n cyclic gaps, canonically relabels the result, and applies the exact circular verifier.\n\nThe length-eight layer has 16 valid orbits. Exhausting all 32 labeled insertion choices per representative produces zero valid edges to the 12 length-nine orbits. Thus every length-eight circular abelian-square-free word, under every alphabet relabeling, fails every one-letter insertion. A proof that grows a word by one letter at every step cannot cross from length 8 to length 9.\n\nThe same replay tested the selected DFS witness at each n through 36. For every n=8,...,36, all four fixed-seam appends fail. At n in\n`{8,17,18,19,21,24,25,26,27,28,29,33,34,35,36}`,\nall 4n cyclic-gap insertions fail. The later failures apply to the selected witnesses. At n=8 the conclusion covers every witness orbit.",
  "status": "failed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "complete one-letter insertion graph on all circular-word orbits through n=16, plus selected-witness tests through n=36",
    "bounds": {
      "complete_graph_n": {
        "min": 1,
        "max": 16
      },
      "selected_witness_n": {
        "min": 1,
        "max": 36
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Original exhaustive local-move audit executed and replayed 2026-07-28; see casf4-artifact-exact-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Original exhaustive local-move audit executed and replayed 2026-07-28; see casf4-artifact-exact-replay"
  },
  "models": [],
  "relations": [
    {
      "slug": "R100",
      "title": "Exact witness, count, and insertion-graph replay",
      "object_type": "artifact",
      "relation": "uses",
      "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"
    }
  ]
}