{
  "family_id": "350",
  "title": "Yau’s nodal bounds: surfaces and higher dimensions",
  "discipline": "Differential geometry",
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      "title": "Sharp nodal length on smooth surfaces",
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      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Sharp-nodal-length-on-smooth-surfaces-September-23-2026/paper.pdf",
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    {
      "title": "Smooth counterexamples to Yau's nodal upper bound in dimensions three and four",
      "path": "preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf",
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    },
    {
      "title": "Power-law violations of Yau's nodal upper bound",
      "path": "preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Power-law-violations-of-Yaus-nodal-upper-bound-September-23-2026/paper.pdf",
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