{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1591",
  "content_hash": null,
  "slug": "hilberts-sixteenth-problem-second-part-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: Buzzi and Novaes refute a recent claimed quadratic formula by comparing it with established lower-growth constructions. Their note leaves the finiteness of H(n) open. Exact unresolved remainder: Prove a finite uniform upper bound H(n) for every degree n, or give one fixed degree with polynomial vector fields having arbitrarily many limit cycles.",
  "relevance": "For Hilbert's sixteenth problem, second part, 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: Buzzi and Novaes refute a recent claimed quadratic formula by comparing it with established lower-growth constructions. Their note leaves the finiteness of H(n) open.\n\nExact unresolved remainder: Prove a finite uniform upper bound H(n) for every degree n, or give one fixed degree with polynomial vector fields having arbitrarily many limit cycles.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2411.09594",
      "locator": "abstract and analysis of the claimed quadratic formula"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2411.09594",
    "locator": "abstract and analysis of the claimed quadratic formula"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1078",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "hilberts-sixteenth-problem-second-part",
      "title": "hilberts sixteenth problem second part",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}