{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R103",
  "content_hash": null,
  "slug": "casf4-attempt-keranen-window-scan",
  "type": "attempt",
  "title": "A complete phi-squared window scan gives sparse extra witnesses",
  "summary": "Scanning every factor of the 7,225-letter word phi^2(0) found circular witnesses at 24 lengths in 36 through 100 and exhausted all windows without a witness at the other 41 lengths.",
  "relevance": "For Eventual existence of four-letter circular abelian-square-free words, record casf4-attempt-keranen-window-scan (“A complete phi-squared window scan gives sparse extra witnesses”) documents a concrete method, search boundary, or failed route. The record states: Scanning every factor of the 7,225-letter word phi^2(0) found circular witnesses at 24 lengths in 36 through 100 and exhausted all windows without a witness at the other 41 lengths.",
  "relevance_source": "recorded",
  "body": "The scan used the 85-uniform Keränen image printed in Peltomäki and Whiteland, Section 3:\n`phi(0)=0120232123203231301020103101213121021232021013010203212320231210212320232132303132120`.\nThe images phi(1), phi(2), and phi(3) were obtained by adding 1, 2, and 3 modulo 4 to every symbol. Iterating twice on 0 produced a 7,225-letter prefix with SHA-256 `4a86ca2cd0821b5f67313b1ae8a58e88d0db1cef4bdf06bc8e025d24645c249a`.\n\nFor each n=36,...,100, the scan checked factors from left to right. It stopped at the first circular witness. When no witness appeared, it exhausted all 7,226-n windows. Witnesses occurred at\n`{36,39,40,41,44,46,47,48,50,54,55,58,60,63,66,67,70,79,81,87,89,90,95,100}`.\nEvery explicit witness was replayed by the packet artifact. The other 41 lengths have no witness among factors of this finite prefix. That prefix-specific absence says nothing about all four-letter words.\n\nThe computation tested 296,943 windows in 455.913 seconds. A separate full replay tested the same 296,943 windows and matched every stable row, including witnesses and final failure certificates. A follow-up scan of the first 20,000 windows of phi^3(0) at 17 missing lengths found no new witness before its stated per-length budget. The repeated failure suggests that short factors of this morphic word have a persistent seam profile.",
  "status": "partial",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "first-witness or complete no-window scan in phi^2(0) for every n from 36 through 100",
    "bounds": {
      "n": {
        "min": 36,
        "max": 100
      },
      "prefix_length": {
        "min": 7225,
        "max": 7225
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1016/j.aam.2020.102095",
      "locator": "Peltomäki and Whiteland, Section 3, displayed definition of Keränen's morphism phi; original window scans executed 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.aam.2020.102095",
    "locator": "Peltomäki and Whiteland, Section 3, displayed definition of Keränen's morphism phi; original window scans executed 2026-07-28"
  },
  "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"
    }
  ]
}