@article{James1974,
  author = {James, Robert C.},
  title = {A separable somewhat reflexive {Banach} space with nonseparable dual},
  journal = {Bulletin of the American Mathematical Society},
  volume = {80},
  number = {4},
  year = {1974},
  pages = {738--743},
  doi = {10.1090/S0002-9904-1974-13580-9}
}

@article{Girardi,
  author = {Girardi, Maria},
  title = {The dual of the {James} tree space is asymptotically uniformly convex},
  journal = {Studia Mathematica},
  volume = {147},
  number = {2},
  pages = {119--130},
  year = {2001},
  doi = {10.4064/sm147-2-2}
}

@article{BaudierEtAl2017,
 author={Baudier, Florent and Causey, Ryan and Dilworth, Stephen and Kutzarova, Denka and Randrianarivony, Nirina L. and Schlumprecht, Thomas and Zhang, Sheng},
 title={On the geometry of the countably branching diamond graphs},
 journal={Journal of Functional Analysis}, volume={273}, number={10}, pages={3150--3199}, year={2017},
 doi={10.1016/j.jfa.2017.05.013}, eprint={1612.01984}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/1612.01984v1},
 note={Theorem locators refer to arXiv v1, 6 December 2016}
}

@misc{Perreau2021,
  author = {Perreau, Yo{\"e}l},
  title = {On the embeddability of countably branching bundle graphs into dual spaces},
  year = {2021},
  eprint = {2104.10494},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  doi = {10.48550/arXiv.2104.10494},
  url = {https://arxiv.org/abs/2104.10494v1},
  note = {Version 1, 21 April 2021}
}

@book{BaudierLancien2025,
  author = {Baudier, Florent P. and Lancien, Gilles},
  title = {Asymptotic and nonlinear geometries of {Banach} spaces and their interactions},
  series = {Cours Sp{\'e}cialis{\'e}s},
  volume = {33},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  year = {2026},
  isbn = {978-2-37905-225-5},
  eprint = {2512.00817},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2512.00817v1},
  note = {Problem and page locators refer to arXiv:2512.00817v1, 30 November 2025}
}

@misc{BassetLancienProchazka2026,
  author = {Basset, Estelle and Lancien, Gilles and Proch{\'a}zka, Anton{\'i}n},
  title = {On metric characterizations of tree and fragmentability indices of {Banach} spaces},
  year = {2026},
  eprint = {2605.28311},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  doi = {10.48550/arXiv.2605.28311},
  url = {https://arxiv.org/abs/2605.28311v1},
  note = {Version 1, 27 May 2026}
}


@article{AbrahamsenEtAl2022,
  author = {Abrahamsen, Trond A. and Lima, Vegard and Martiny, Andr\'e and Perreau, Yo\"el},
  title = {Asymptotic geometry and {Delta}-points},
  journal = {Banach Journal of Mathematical Analysis},
  volume = {16},
  year = {2022},
  eid = {57},
  pagetotal = {33},
  doi = {10.1007/s43037-022-00210-9},
  eprint = {2203.14528},
  archivePrefix = {arXiv}
}

@article{DKRRZ2016,
  author = {Dilworth, S. J. and Kutzarova, Denka and Randrianarivony, N. Lovasoa and Revalski, J. P. and Zhivkov, N. V.},
  title = {Lenses and asymptotic midpoint uniform convexity},
  journal = {Journal of Mathematical Analysis and Applications},
  volume = {436},
  number = {2},
  pages = {810--821},
  year = {2016},
  doi = {10.1016/j.jmaa.2015.11.061},
  url = {https://denka.web.illinois.edu/AMUC_els4.pdf},
  note = {Author-manuscript locators refer to the version dated 8 October 2015}
}

@article{KW2004,
  author = {Kadets, Vladimir and Werner, Dirk},
  title = {A {Banach} space with the {Schur} and the {Daugavet} property},
  journal = {Proceedings of the American Mathematical Society},
  volume = {132},
  number = {6},
  pages = {1765--1773},
  year = {2004},
  doi = {10.1090/S0002-9939-03-07278-2},
  eprint = {math/0301182},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  url = {https://arxiv.org/abs/math/0301182v1},
  note = {Preprint version: arXiv:math/0301182v1, 17 January 2003}
}

@misc{Baudier2026,
  author = {Baudier, Florent P.},
  title = {The {Kadets--Werner} modification of {Bourgain--Rosenthal} space is asymptotically midpoint uniformly convex},
  year = {2026},
  eprint = {2609.21283},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  doi = {10.48550/arXiv.2609.21283},
  url = {https://arxiv.org/abs/2609.21283v1},
  note = {Version 1, 18 September 2026}
}

@article{Girardi2001,
  author = {Girardi, Maria},
  title = {The dual of the {James} tree space is asymptotically uniformly convex},
  journal = {Studia Mathematica},
  volume = {147},
  number = {2},
  year = {2001},
  pages = {119--130},
  doi = {10.4064/sm147-2-2},
  eprint = {math/0004166},
  archivePrefix = {arXiv}
}


@article{Banakh2000,
  author = {Banakh, Taras},
  title = {The topological classification of weak unit balls of {Banach} spaces},
  journal = {Dissertationes Mathematicae},
  volume = {387},
  pages = {7--35},
  year = {2000},
  url = {https://www.impan.pl/shop/publication/transaction/download/product/88099}
}

@article{LeeNaor2004,
  author = {Lee, James R. and Naor, Assaf},
  title = {Embedding the diamond graph in {$L_p$} and dimension reduction in {$L_1$}},
  journal = {Geometric and Functional Analysis},
  volume = {14},
  number = {4},
  pages = {745--747},
  year = {2004},
  doi = {10.1007/s00039-004-0473-8},
  eprint = {math/0407520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0407520v1},
  note = {Theorem and page locators refer to arXiv:math/0407520v1}
}

@article{JohnsonSchechtman2009,
  author = {Johnson, William B. and Schechtman, Gideon},
  title = {Diamond graphs and super-reflexivity},
  journal = {Journal of Topology and Analysis},
  volume = {1},
  number = {2},
  pages = {177--189},
  year = {2009},
  doi = {10.1142/S1793525309000114},
  url = {https://www.weizmann.ac.il/math/gideon/sites/math.gideon/files/uploads/diamond.pdf}
}

@article{Swift2018,
 author={Swift, Andrew}, title={A coding of bundle graphs and their embeddings into {Banach} spaces},
 journal={Mathematika}, volume={64}, number={3}, pages={847--874}, year={2018},
 doi={10.1112/S002557931800027X}, eprint={1710.00877}, archivePrefix={arXiv},
 url={https://arxiv.org/abs/1710.00877v1},
 note={Theorem locators refer to arXiv v1, 2 October 2017}
}

@article{GhoussoubMaurey1985,
  author = {Ghoussoub, Nassif and Maurey, Bernard},
  title = {{$G_\delta$}-embeddings in {Hilbert} space},
  journal = {Journal of Functional Analysis},
  volume = {61},
  number = {1},
  year = {1985},
  pages = {72--97},
  doi = {10.1016/0022-1236(85)90039-4}
}


@article{Malthaner2025,
 author={Malthaner, Ryan},
 title={On {Matou\v{s}ek}-like embedding obstructions of countably branching graphs},
 journal={Journal of Mathematical Analysis and Applications}, volume={543}, number={2},
 pages={128896}, year={2025}, doi={10.1016/j.jmaa.2024.128896},
 eprint={2310.03257}, archivePrefix={arXiv}, url={https://arxiv.org/abs/2310.03257v2},
 note={Part 1. Preprint theorem locators refer to v2, 8 October 2023; journal numbering differs}
}

@misc{SegmentLenses,
  author = {{OpenAI}},
  title = {{Midpoint lenses in segment spaces}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Midpoint-lenses-in-segment-spaces-September-27-2026/manuscript.pdf}{OAI:Midpoint-lenses-in-segment-spaces-September-27-2026}},
  year = {2026}
}
@misc{DiamondEnergies,
  author = {{OpenAI}},
  title = {{Distortion of countably branching diamonds from midpoint and tree energies}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026/manuscript.pdf}{OAI:Diamond-distortion-from-midpoint-and-tree-energies-September-27-2026}},
  year = {2026}
}
@misc{TreePotentials,
  author = {{OpenAI}},
  title = {{Midpoint convexity from bounded tree potentials and path costs}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026/manuscript.pdf}{OAI:Midpoint-convexity-from-bounded-tree-potentials-and-path-costs-September-27-2026}},
  year = {2026}
}
@misc{RecursivePotentials,
  author = {{OpenAI}},
  title = {{Midpoint convexity from two recursive potentials}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Midpoint-convexity-from-two-recursive-potentials-September-27-2026/manuscript.pdf}{OAI:Midpoint-convexity-from-two-recursive-potentials-September-27-2026}},
  year = {2026}
}