{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1716",
  "content_hash": null,
  "slug": "projective-sets-ramsey-consistency-strength-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The MathOverflow answers give upper and lower consistency bounds and say the exact strength is open. Later checked problem lists continue to ask for the missing comparison, but the audit did not locate a definitive current survey. Exact unresolved remainder: Prove both relative-consistency directions between \\(\\mathsf{ZFC}\\) plus projective Ramsey regularity and a precisely stated standard large-cardinal theory, thereby fixing the exact consistency strength. For the named subquestion, prove equiconsistency with one inaccessible cardinal or give strictly sharper matching upper and lower bounds that refute that calibration.",
  "relevance": "For Consistency strength of projective Ramsey regularity, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The MathOverflow answers give upper and lower consistency bounds and say the exact strength is open. Later checked problem lists continue to ask for the missing comparison, but the audit did not locate a definitive current survey.\n\nExact unresolved remainder: Prove both relative-consistency directions between \\(\\mathsf{ZFC}\\) plus projective Ramsey regularity and a precisely stated standard large-cardinal theory, thereby fixing the exact consistency strength. For the named subquestion, prove equiconsistency with one inaccessible cardinal or give strictly sharper matching upper and lower bounds that refute that calibration.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/76280/exact-consistency-strength-of-all-projective-sets-are-ramsey",
      "locator": "Full question, answers, and visible comments concerning Consistency strength of projective Ramsey regularity; checked 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/76280/exact-consistency-strength-of-all-projective-sets-are-ramsey",
    "locator": "Full question, answers, and visible comments concerning Consistency strength of projective Ramsey regularity; checked 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1356",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "projective-sets-ramsey-consistency-strength",
      "title": "projective sets ramsey consistency strength",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}