{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R145",
  "content_hash": null,
  "slug": "ch31-attempt-global-sharpness",
  "type": "attempt",
  "title": "Local optimization supplies an incumbent without a global certificate",
  "summary": "One hundred seeded projected-gradient starts reported the same best ratio near 1.5693754353475171.",
  "relevance": "For Sharp fourth-power norm of the cyclic Hilbert transform at order 31, record ch31-attempt-global-sharpness (“Local optimization supplies an incumbent without a global certificate”) documents a concrete method, search boundary, or failed route. The record states: One hundred seeded projected-gradient starts reported the same best ratio near 1.5693754353475171.",
  "relevance_source": "recorded",
  "body": "The candidate-generation run used one hundred seeded projected-gradient starts on the zero-mean subspace and reported the best ratio\n\\[\n1.5693754353475171.\n\\]\nThe interval artifact records a rounded rational representative of that incumbent and certifies the weaker lower endpoint 1.5693.\n\nThe objective is a nonconvex homogeneous quartic ratio. Agreement among local searches does not exclude another critical orbit with a larger value. A complete polynomial-system analysis, a sum-of-squares certificate, or another global argument would be needed to close the interval and certify ten decimal places. A focused primary-source audit was not completed, so novelty also remains unverified.",
  "status": "open",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "global maximization of the l4 norm ratio for the order-31 cyclic Hilbert transform",
    "bounds": {
      "group_order": {
        "min": 31,
        "max": 31
      },
      "reported_projected_gradient_starts": {
        "min": 100,
        "max": 100
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "TheoremDB agent candidate record 160 and the retained rational witness"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "TheoremDB agent candidate record 160 and the retained rational witness"
  },
  "relations": [
    {
      "slug": "R146",
      "title": "The sharp fourth-power norm lies between 1.5693 and 1.6453",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "cyclic-hilbert-l4-norm-31",
      "title": "cyclic hilbert l4 norm 31",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}