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  "family_id": "034",
  "title": "Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity",
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      "title": "Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity",
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      "title": "Uniform indices for semi-log-canonical log Calabi–Yau pairs",
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    {
      "title": "Conditional good minimal models for compact Kähler fourfolds",
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      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf",
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    {
      "title": "Log abundance in characteristic zero",
      "path": "preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf",
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    {
      "title": "Minimal metrics and interior injectivity for nef adjoints",
      "path": "preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Minimal-metrics-and-interior-injectivity-for-nef-adjoints-September-27-2026/paper.pdf",
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    {
      "title": "Fourfold nonvanishing by minimal metrics and moving jets",
      "path": "preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fourfold-nonvanishing-by-minimal-metrics-and-moving-jets-September-27-2026/paper.pdf",
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    },
    {
      "title": "Lifting sections from the reduced support of an adjoint",
      "path": "preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf",
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    {
      "title": "Schnell fiber spaces and good canonical models",
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    {
      "title": "Uniform log Iitaka fibrations and bounded moduli denominators",
      "path": "preprints/Uniform-log-Iitaka-fibrations-and-bounded-moduli-denominators-October-4-2026/uniform-log-iitaka.pdf",
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    {
      "title": "Uniform Pluricanonical Iitaka Fibrations",
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    {
      "title": "Relative denominators and effective systems for log Calabi-Yau fibrations",
      "path": "preprints/Relative-denominators-and-effective-systems-for-log-Calabi-Yau-fibrations-September-27-2026/paper.pdf",
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    {
      "title": "Arithmetic Stein-degree bounds for log Calabi–Yau pairs",
      "path": "preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf",
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    {
      "title": "Uniform effective log Iitaka fibrations for fourfolds",
      "path": "preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-effective-log-Iitaka-fibrations-for-fourfolds-September-26-2026/paper.pdf",
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    {
      "title": "Abundance after nonvanishing for compact Kähler fourfolds",
      "path": "preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf",
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