{
  "family_id": "052",
  "title": "Tangent splittings and product decompositions",
  "discipline": "Algebraic and complex geometry",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Universal-cover splitting for compact Kähler manifolds",
      "path": "preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf",
      "readme_path": "preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Integrability of split tangent bundles on rationally connected manifolds",
      "path": "preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/main.pdf",
      "readme_path": "preprints/Integrability-of-split-tangent-bundles-on-rationally-connected-manifolds-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/052.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/052.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}