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}

@article{Landau1941a,
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}

@article{LeeHuangYang1957,
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@article{Leggett1970,
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@article{Leggett1973,
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}

@article{Leggett1998,
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@article{Leggett1999,
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}

@book{Leggett2006,
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  publisher = {Oxford University Press},
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  doi = {10.1093/acprof:oso/9780198526438.001.0001},
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}

@book{LehmannCasella1998,
  author = {Lehmann, E. L. and Casella, George},
  title = {{Theory of Point Estimation}},
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}

@article{Levy1940,
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@incollection{Levy1951,
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  editor = {Neyman, Jerzy},
  title = {{Wiener}'s Random Function, and Other {Laplacian} Random Functions},
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}

@article{LiebRuskai1973,
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}

@article{LiebRuskai1973a,
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}

@article{LiebSeiringer2002,
  author = {Lieb, Elliott H. and Seiringer, Robert},
  title = {{Proof of Bose-Einstein Condensation for Dilute Trapped Gases}},
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  pages = {170409},
  year = {2002},
  doi = {10.1103/PhysRevLett.88.170409},
  eprint = {math-ph/0112032},
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  url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.88.170409}
}

@article{LiebSeiringer2006,
  author = {Lieb, Elliott H. and Seiringer, Robert},
  title = {{Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases}},
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  year = {2006},
  doi = {10.1007/s00220-006-1524-9},
  eprint = {math-ph/0504042},
  archiveprefix = {arXiv},
  url = {https://arxiv.org/abs/math-ph/0504042}
}

@book{LiebSeiringerSolovejYngvason2005,
  author = {Lieb, Elliott H. and Seiringer, Robert and Solovej, Jan Philip and Yngvason, Jakob},
  title = {{The Mathematics of the Bose Gas and its Condensation}},
  series = {Oberwolfach Seminars},
  volume = {34},
  publisher = {Birkh{\"a}user},
  year = {2005},
  doi = {10.1007/b137508},
  eprint = {cond-mat/0610117},
  archiveprefix = {arXiv},
  url = {https://link.springer.com/book/10.1007/b137508}
}

@article{LiebSeiringerYngvason2000,
  author = {Lieb, Elliott H. and Seiringer, Robert and Yngvason, Jakob},
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@article{LiebSeiringerYngvason2002,
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@article{LiebYngvason1998,
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@article{LiggettSchonmannStacey1997,
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@article{London1938,
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@book{LyonsPeres2016,
  author = {Lyons, Russell and Peres, Yuval},
  title = {{Probability on Trees and Networks}},
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}

@article{NamNapiorkowskiRicaudTriay2022,
  author = {Nam, Phan Th{\`a}nh and Napi{\'o}rkowski, Marcin and Ricaud, Julien and Triay, Arnaud},
  title = {{Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime}},
  journal = {Analysis \& PDE},
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  doi = {10.2140/apde.2022.15.1585},
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  archiveprefix = {arXiv},
  url = {https://arxiv.org/abs/2001.04364}
}

@misc{OpenAI2026B,
  author = {{OpenAI}},
  title = {{A density-uniform condensate bound for dilute Bose gases}},
  year = {2026},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}},
  note = {September 27, 2026; pinned commit 1581d4cbdd69a0faf34b2089614fe2a814316a6a},
  url = {https://github.com/openai/math/blob/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/A-density-uniform-condensate-bound-for-dilute-Bose-gases-September-27-2026/paper.pdf}
}

@misc{OpenAI2026BEC,
  author = {{OpenAI}},
  title = {{Bose--Einstein condensation at positive temperature in the dilute hard-sphere gas}},
  year = {2026},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}},
  note = {October 5, 2026; pinned commit 1581d4cbdd69a0faf34b2089614fe2a814316a6a},
  url = {https://github.com/openai/math/blob/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/Bose-Einstein-condensation-at-positive-temperature-in-the-dilute-hard-sphere-gas-October-5-2026/positive-temperature-hard-spheres.pdf}
}

@misc{OpenAI2026DepletionHS,
  author = {{OpenAI}},
  title = {{Quantum Depletion and Momentum Distribution in the Dilute Hard-Sphere Bose Gas}},
  year = {2026},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}},
  note = {October 5, 2026; pinned commit 1581d4cbdd69a0faf34b2089614fe2a814316a6a},
  url = {https://github.com/openai/math/blob/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/Quantum-Depletion-and-Momentum-Distribution-in-the-Dilute-Hard-Sphere-Bose-Gas-October-5-2026/Quantum-Depletion-in-the-Dilute-Hard-Sphere-Bose-Gas.pdf}
}

@misc{OpenAI2026DepletionSoft,
  author = {{OpenAI}},
  title = {{Quantum Depletion for Fixed Bounded Repulsive Potentials}},
  year = {2026},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}},
  note = {October 5, 2026; pinned commit 1581d4cbdd69a0faf34b2089614fe2a814316a6a},
  url = {https://github.com/openai/math/blob/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf}
}

@misc{OpenAI2026HS,
  author = {{OpenAI}},
  title = {{Ground-state condensation in the dilute hard-sphere gas}},
  year = {2026},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}},
  note = {September 24, 2026; pinned commit 1581d4cbdd69a0faf34b2089614fe2a814316a6a},
  url = {https://github.com/openai/math/blob/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/Ground-state-condensation-in-the-dilute-hard-sphere-gas-September-24-2026/paper.pdf}
}

@article{PaleyZygmund1932a,
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@article{Peierls1936,
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@article{PenroseOnsager1956,
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@misc{PeresSly2014,
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@article{PilatiGiorginiProkofev2008,
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@book{PitaevskiiStringari2016,
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@book{RevuzYor1999,
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@book{Schatten1960,
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@article{Seiringer2002,
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@article{Seiringer2008,
  author = {Seiringer, Robert},
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  eprint = {math-ph/0608069},
  archiveprefix = {arXiv},
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}

@article{Seiringer2011,
  author = {Seiringer, Robert},
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  doi = {10.1007/s00220-011-1261-6},
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  archiveprefix = {arXiv},
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@article{SeiringerUeltschi2009,
  author = {Seiringer, Robert and Ueltschi, Daniel},
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  doi = {10.1103/PhysRevB.80.014502},
  eprint = {0904.0050},
  archiveprefix = {arXiv},
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@article{Simon1976,
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@book{Simon2005,
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@book{Simon2005b,
  author = {Simon, Barry},
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@article{SindzingreKleinCeperley1989,
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@article{Stratonovich1966,
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@article{Stringari1996,
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@article{Suto1993,
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