{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R102",
  "content_hash": null,
  "slug": "casf4-attempt-dated-status-audit",
  "type": "attempt",
  "title": "The 2026-07-28 source audit found no later resolution",
  "summary": "The exact cycle-coloring conjecture, both avoidance conventions, arXiv revisions, the journal article, and the indexed citing literature were checked; no proof or counterexample to eventual circular existence was located.",
  "relevance": "For Eventual existence of four-letter circular abelian-square-free words, record casf4-attempt-dated-status-audit (“The 2026-07-28 source audit found no later resolution”) documents a concrete method, search boundary, or failed route. The record states: The exact cycle-coloring conjecture, both avoidance conventions, arXiv revisions, the journal article, and the indexed citing literature were checked; no proof or counterexample to eventual circular existence was located.",
  "relevance_source": "recorded",
  "body": "The exact formulation is Wilson and Wood's conjecture that the anagram-free chromatic number of cycles is at most four with finitely many exceptions. A color word around C_n is an anagram-free coloring exactly when every circular factor of even length at most n has unequal Parikh vectors in its two halves.\n\nThe audit checked Wilson and Wood's journal PDF and arXiv:1607.01117, Peltomäki and Whiteland arXiv:2006.06307v1 and v2, the open journal manuscript, Crossref metadata, Semantic Scholar and OpenAlex citation lists, the 2023 survey arXiv:2207.09937v2, and the later citing papers arXiv:2008.08125, arXiv:2112.05347, and arXiv:2509.20773. The later citations use the 2020 article as general background and do not discuss the cycle conjecture. Exact web searches used the phrases `anagram-free chromatic number cycles`, `circular abelian-square-free`, `four-letter word circularly`, and the article title.\n\nTheoremDB orient resolved problem 2820 exactly and returned zero attached research records. Problem-directory searches for `circular abelian square`, `abelian square free`, and `cyclic abelian` found only this target. Research-memory search returned no overlapping attempt. Citation indexes can omit manuscripts and unindexed work. This dated audit is an inconclusive literature search and supplies no mathematical evidence of openness.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "dated source and duplicate audit for the eventual four-color anagram-free cycle conjecture",
    "family": "primary sources, arXiv revisions, journal versions, citation-index results, and exact TheoremDB matches checked on 2026-07-28"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.37236/6267",
      "locator": "Wilson and Wood, Anagram-Free Graph Colouring, Electronic Journal of Combinatorics 25(2) (2018), page 17; later-state audit completed 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.37236/6267",
    "locator": "Wilson and Wood, Anagram-Free Graph Colouring, Electronic Journal of Combinatorics 25(2) (2018), page 17; later-state audit completed 2026-07-28"
  },
  "relations": [
    {
      "slug": "R108",
      "title": "The source reports no cyclic counterexample below length 150",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R1814",
      "title": "The 2026-07-28 source audit found no later resolution",
      "object_type": "attempt",
      "relation": "supersedes",
      "direction": "incoming"
    },
    {
      "slug": "circular-abelian-square-free-four-eventual",
      "title": "circular abelian square free four eventual",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}