{
  "family_id": "095",
  "title": "Hyperbolicity cones without semidefinite lifts",
  "discipline": "Convex and metric geometry",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Hyperbolicity Cones Without Semidefinite Lifts",
      "path": "preprints/Hyperbolicity-Cones-Without-Semidefinite-Lifts-October-5-2026/nonliftable-hyperbolicity.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hyperbolicity-Cones-Without-Semidefinite-Lifts-October-5-2026/nonliftable-hyperbolicity.pdf",
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    },
    {
      "title": "A nonspectrahedral hyperbolicity cone",
      "path": "preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf",
      "readme_path": "preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone",
      "path": "preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone.pdf",
      "readme_path": "preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
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  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/095.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}