{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1536",
  "content_hash": null,
  "slug": "finite-group-power-semigroup-embeddability-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact formulation, named variants, 2025–2026 updates, and repository-wide semantic duplicates were checked on 2026-08-01. The source collection still marks the stated remainder open. Living-database status remains subject to later literature not indexed there.",
  "relevance": "Documents why Embeddability into a finite-group power semigroup was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across source collection and its cited primary literature, Crossref/arXiv or MathSciNet stable records, TheoremDB published, prospecting, formal-conjecture, packet, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- \"Lyapin notebook\" \"Problem 1.3\"\n- \"Embeddability into a finite-group power semigroup\"\n- site:arxiv.org semigroup \"power semigroup\" open problem\n\nThe exact formulation, named variants, 2025–2026 updates, and repository-wide semantic duplicates were checked on 2026-08-01. The source collection still marks the stated remainder open. Living-database status remains subject to later literature not indexed there.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "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": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "finite-group-power-semigroup-embeddability",
      "title": "finite group power semigroup embeddability",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}