{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1116",
  "content_hash": null,
  "slug": "o-minimal-super-iterated-exponential-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. The source answer, updated in 2025, reports that no non-exponentially-bounded o-minimal expansion is known. The dated search found examples with fixed iterated-exponential growth, but none with one definable function dominating every finite iterate. Construct an explicit o-minimal expansion \\(\\mathcal R\\) and one definable function \\(f\\), then prove the displayed eventual domination for every positive integer \\(m\\).",
  "relevance": "For o minimal super iterated exponential, pins the dated research frontier: UNKNOWN as of 2026-07-31. The source answer, updated in 2025, reports that no non-exponentially-bounded o-minimal expansion is known. The dated search found examples with fixed iterated-exponential growth, but none with one definable function dominating every finite iterate. Construct an explicit.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. The source answer, updated in 2025, reports that no non-exponentially-bounded o-minimal expansion is known. The dated search found examples with fixed iterated-exponential growth, but none with one definable function dominating every finite iterate.\n\nA complete resolution must satisfy this condition: Construct an explicit o-minimal expansion \\(\\mathcal R\\) and one definable function \\(f\\), then prove the displayed eventual domination for every positive integer \\(m\\).",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/121010/is-there-any-o-minimal-expansion-of-the-real-field-with-functions-of-growth-high",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/121010/is-there-any-o-minimal-expansion-of-the-real-field-with-functions-of-growth-high",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1115",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "o-minimal-super-iterated-exponential",
      "title": "o minimal super iterated exponential",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}