{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1538",
  "content_hash": null,
  "slug": "finite-group-power-semigroup-embeddability-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Every semigroup is a divisor of a power semigroup over a periodic group, and the divisor version over finite groups is decidable.",
  "relevance": "Locates the present research frontier immediately below Embeddability into a finite-group power semigroup.",
  "relevance_source": "recorded",
  "body": "Every semigroup is a divisor of a power semigroup over a periodic group, and the divisor version over finite groups is decidable.\n\nThis leaves the following boundary unresolved: Give a terminating correct algorithm for direct embeddability, or prove that no such algorithm exists. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.48550/arXiv.2604.04763",
      "locator": "S. Bershadsky, S. Kublanovsky, and G. Mashevitzky, “The Lyapin’s notebook: a collection of unsolved problems in Semigroup Theory,” arXiv:2604.04763 (2026). Problem 1.3 and its immediately following status paragraph"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.48550/arXiv.2604.04763",
    "locator": "S. Bershadsky, S. Kublanovsky, and G. Mashevitzky, “The Lyapin’s notebook: a collection of unsolved problems in Semigroup Theory,” arXiv:2604.04763 (2026). Problem 1.3 and its immediately following status paragraph"
  },
  "relations": [
    {
      "slug": "R1539",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "finite-group-power-semigroup-embeddability",
      "title": "finite group power semigroup embeddability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}