{
  "family_id": "056",
  "title": "Termination of projective and Kähler fourfold minimal model programs",
  "discipline": "Algebraic and complex geometry",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Termination of generalized log canonical flips on compact Kähler fourfolds",
      "path": "preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf",
      "readme_path": "preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Termination of generalized-canonical flips on compact Kähler fourfolds",
      "path": "preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/termination-generalized-terminal-flips-compact-kahler-fourfolds.pdf",
      "readme_path": "preprints/Termination-of-generalized-canonical-flips-on-compact-Kahler-fourfolds-October-6-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Termination for projective log canonical fourfolds with rational boundary",
      "path": "preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/paper.pdf",
      "readme_path": "preprints/Termination-for-projective-log-canonical-fourfolds-with-rational-boundary-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Finite ordinary minimal model programs on compact Kähler fourfolds",
      "path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
      "readme_path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-October-6-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Finite ordinary minimal model programs on compact Kähler fourfolds",
      "path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/paper.pdf",
      "readme_path": "preprints/Finite-ordinary-minimal-model-programs-on-compact-Kahler-fourfolds-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": null,
  "lean_scope_url": null,
  "verification_status": "no_family_scope_document",
  "review_status": "inventory_complete_deep_review_pending"
}