{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1520",
  "content_hash": null,
  "slug": "eventual-categoricity-aecs-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The conjecture holds for important tame or universal settings and under strong large-cardinal assumptions. Unresolved remainder: The general ZFC theorem for arbitrary AECs remains open.",
  "relevance": "Documents why Shelah's eventual categoricity conjecture for AECs was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, 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- Shelah eventual categoricity conjecture AEC open 2026\n- eventual categoricity abstract elementary classes large cardinals 2024\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The conjecture holds for important tame or universal settings and under strong large-cardinal assumptions. Unresolved remainder: The general ZFC theorem for arbitrary AECs remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://shelah.logic.at/papers/842/",
      "locator": "S. Shelah and S. Vasey, Categoricity and multidimensional diagrams, Sh:842 (2024). eventual categoricity theorem under strongly compact cardinals"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://shelah.logic.at/papers/842/",
    "locator": "S. Shelah and S. Vasey, Categoricity and multidimensional diagrams, Sh:842 (2024). eventual categoricity theorem under strongly compact cardinals"
  },
  "relations": [
    {
      "slug": "R1523",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "eventual-categoricity-aecs",
      "title": "eventual categoricity aecs",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}