{
  "family_id": "049",
  "title": "A stable-coordinate counterexample in four variables",
  "discipline": "Algebraic and complex geometry",
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  "papers": [
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      "title": "A stable coordinate that is not a coordinate in four variables",
      "path": "preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-stable-coordinate-that-is-not-a-coordinate-in-four-variables-October-5-2026/stable-coordinate-four-variables.pdf",
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    },
    {
      "title": "An explicit noncoordinate polynomial with affine three-space zero fibre",
      "path": "preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf",
      "readme_path": "preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/README.md",
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    }
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