{
  "family_id": "331",
  "title": "Reflexive midpoint convexity and diamond distortion",
  "discipline": "Functional analysis",
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      "title": "Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space",
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      "title": "Distortion of countably branching diamonds from midpoint and tree energies",
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    {
      "title": "Exact asymptotic moduli in a Daugavet subspace of L1",
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    {
      "title": "Midpoint convexity from bounded tree potentials and path costs",
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      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026/manuscript.pdf",
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    {
      "title": "Independent products in real L1: asymptotic midpoint convexity without AUC renormings",
      "path": "preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026/manuscript.pdf",
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    {
      "title": "Midpoint convexity from two recursive potentials",
      "path": "preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf",
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