{
  "family_id": "347",
  "title": "Counterexamples to stable-Morse and strong Arnold fixed-point bounds",
  "discipline": "Differential geometry",
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    {
      "title": "Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two",
      "path": "preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-in-Dimension-Twenty-Two-October-5-2026/hamiltonian-fixed-points-below-stable-morse-number.pdf",
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    {
      "title": "Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number",
      "path": "preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026/sharp-cyclic-integral-floer-bound-below-stable-morse-number.pdf",
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      "readme_path": "preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "Hamiltonian Fixed Points Below the Stable Morse Number",
      "path": "preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-Number-October-5-2026/paper.pdf",
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    },
    {
      "title": "A nondegenerate counterexample to the Morse-number Arnold bound",
      "path": "preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/paper.pdf",
      "readme_path": "preprints/A-nondegenerate-counterexample-to-the-Morse-number-Arnold-bound-September-23-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "Three fixed points on the symplectic quadric threefold",
      "path": "preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/paper.pdf",
      "readme_path": "preprints/A-degenerate-counterexample-to-the-critical-number-Arnold-bound-September-23-2026/README.md",
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    }
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}