{
  "family_id": "329",
  "title": "A counterexample to metric-entropy duality",
  "discipline": "Functional analysis",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Counterexamples to the duality conjecture for metric entropy",
      "path": "preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf",
      "readme_path": "preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/329.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/329.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}