{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R157",
  "content_hash": null,
  "slug": "cpcrt-attempt-literature-identification",
  "type": "attempt",
  "title": "Focused literature search found neighboring classes",
  "summary": "The exact two-letter family was not located; surveys place it near one-cluster automata and automata with low-rank idempotent letters.",
  "relevance": "For Reset threshold of the cyclic pair-compression automaton, record cpcrt-attempt-literature-identification (“Focused literature search found neighboring classes”) documents a concrete method, search boundary, or failed route. The record states: The exact two-letter family was not located; surveys place it near one-cluster automata and automata with low-rank idempotent letters.",
  "relevance_source": "recorded",
  "body": "The letter \\(a\\) is a transitive cycle, making this a one-cluster automaton, while \\(b\\) is an idempotent of rank \\((n+1)/2\\) at odd orders. Volkov's survey collects reset-threshold results for one-cluster automata, simple idempotents, and low-rank letters. Volkov's 2019 paper constructs different slowly synchronizing families whose letters are low-rank idempotents. A focused search by the transition formulas and the value \\(n(n-1)/2\\) did not locate the present binary family. Novelty therefore remains unverified.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "published work on cyclic, one-cluster, and low-rank-idempotent synchronizing automata"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4213/rm10005e",
      "locator": "Mikhail V. Volkov, Synchronization of finite automata, Russian Mathematical Surveys 77:5 (2022), 819-891; Mikhail V. Volkov, Slowly synchronizing automata with idempotent letters of low rank, arXiv:1807.07048 and International Journal of Foundations of Computer Science 30 (2019), 1043-1063"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4213/rm10005e",
    "locator": "Mikhail V. Volkov, Synchronization of finite automata, Russian Mathematical Surveys 77:5 (2022), 819-891; Mikhail V. Volkov, Slowly synchronizing automata with idempotent letters of low rank, arXiv:1807.07048 and International Journal of Foundations of Computer Science 30 (2019), 1043-1063"
  },
  "models": [],
  "relations": [
    {
      "slug": "R159",
      "title": "The candidate odd threshold is n(n-1)/2",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "cyclic-pair-compression-reset-threshold",
      "title": "cyclic pair compression reset threshold",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}