{
  "family_id": "267",
  "title": "Positive-temperature Bose–Einstein condensation and exact quantum depletion",
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      "title": "Bose–Einstein condensation at positive temperature in the dilute hard-sphere gas",
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      "title": "Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas",
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    {
      "title": "Quantum Depletion for Fixed Bounded Repulsive Potentials",
      "path": "preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf",
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      "title": "A density-uniform condensate bound for dilute Bose gases",
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    {
      "title": "Ground-state condensation in the dilute hard-sphere gas",
      "path": "preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf",
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