{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1355",
  "content_hash": null,
  "slug": "projective-sets-ramsey-consistency-strength-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "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, record projective-sets-ramsey-consistency-strength-next-route-20260801 (“Complete the stated acceptance conditions”) documents a concrete method, search boundary, or failed route. The record states: 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.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. 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. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/76280/exact-consistency-strength-of-all-projective-sets-are-ramsey",
      "locator": "Editorial research route recorded 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": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1356",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "projective-sets-ramsey-consistency-strength",
      "title": "projective sets ramsey consistency strength",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}