{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1611",
  "content_hash": null,
  "slug": "inverse-galois-problem-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: All finite solvable groups and many nonsolvable families are known to occur over Q, but the linked survey describes realization of every finite group over Q as unsolved. Exact unresolved remainder: Construct or prove a finite Galois extension of Q for every finite group, or exhibit a finite group and prove it cannot occur as such a Galois group.",
  "relevance": "For Inverse Galois problem, 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: All finite solvable groups and many nonsolvable families are known to occur over Q, but the linked survey describes realization of every finite group over Q as unsolved.\n\nExact unresolved remainder: Construct or prove a finite Galois extension of Q for every finite group, or exhibit a finite group and prove it cannot occur as such a Galois group.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1090/trans2/004/08",
      "locator": "main theorem constructing a Galois extension of Q for every finite solvable group"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1090/trans2/004/08",
    "locator": "main theorem constructing a Galois extension of Q for every finite solvable group"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1086",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "inverse-galois-problem",
      "title": "inverse galois problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}