@article{Cartan1927,
  author  = {Cartan, {\'E}lie},
  title   = {Sur la possibilit{\'e} de plonger un espace riemannien donn{\'e} dans un espace euclidien},
  journal = {Annales de la Soci{\'e}t{\'e} Polonaise de Math{\'e}matique},
  volume  = {6},
  year    = {1927},
  pages   = {1--7},
  url     = {https://mccuan.math.gatech.edu/courses/6455/Cartan1927.pdf},

  note = {Volume year 1927; volume imprint 1928. \url{https://mccuan.math.gatech.edu/courses/6455/Cartan1927.pdf}},
}

@incollection{Choquet1958,
  author    = {Choquet, Gustave},
  title     = {Les travaux de {Nash} et {Kuiper} sur le plongement isom{\'e}trique des {$C^1$}-vari{\'e}t{\'e}s riemanniennes dans l'espace euclidien},
  booktitle = {S{\'e}minaire Bourbaki, 1956--1958},
  volume    = {4},
  year      = {1958},
  pages     = {139--149},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},

  note = {Expos{\'e} no. 147, May 1957. \url{https://www.numdam.org/item/SB_1956-1958__4__139_0/}},
  url       = {https://www.numdam.org/item/SB_1956-1958__4__139_0/}
}

@book{GromovPDR1986,
  author = {Gromov, Mikhael},
  title = {Partial Differential Relations},
  series = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3)},
  volume = {9},
  publisher = {Springer-Verlag},
  address = {Berlin--Heidelberg},
  year = {1986},
  doi = {10.1007/978-3-662-02267-2},
  note = {\url{https://doi.org/10.1007/978-3-662-02267-2}}
}

@article{Gromov2000,
  author  = {Misha Gromov},
  title   = {Spaces and questions},
  journal = {Geometric and Functional Analysis},
  volume  = {Special Volume, Part I},
  year    = {2000},
  pages   = {118--161},
  url     = {https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/SpacesandQuestions.pdf},
  note    = {Author manuscript, November 1999:
             \url{https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/SpacesandQuestions.pdf}}
}

@misc{Gromov2015,
  author       = {Misha Gromov},
  title        = {Geometric, Algebraic and Analytic Descendants of {Nash}
                  Isometric Embedding Theorems},
  howpublished = {Author manuscript, October 9, 2015},
  year         = {2015},
  url          = {https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/nash-copy-Oct9.pdf},
  note         = {\url{https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/nash-copy-Oct9.pdf}}
}

@article{Hamilton1982,
  author  = {Hamilton, Richard S.},
  title   = {The inverse function theorem of {Nash} and {Moser}},
  journal = {Bulletin of the American Mathematical Society (New Series)},
  volume  = {7},
  number  = {1},
  year    = {1982},
  pages   = {65--222},
  doi     = {10.1090/S0273-0979-1982-15004-2},
  url     = {https://www.ams.org/journals/bull/1982-07-01/S0273-0979-1982-15004-2/},
  note = {\url{https://doi.org/10.1090/S0273-0979-1982-15004-2}}
}

@article{Janet1926,
  author  = {Janet, Maurice},
  title   = {Sur la possibilit{\'e} de plonger un espace riemannien donn{\'e} dans un espace euclidien},
  journal = {Annales de la Soci{\'e}t{\'e} Polonaise de Math{\'e}matique},
  volume  = {5},
  year    = {1926},
  pages   = {38--43},
  url     = {https://rcin.org.pl/dlibra/publication/31746/edition/15034},

  note = {Volume year 1926; catalog imprint 1927. \url{https://rcin.org.pl/dlibra/publication/31746/edition/15034}},
}

@article{Kallen1978,
  author  = {K{\"a}ll{\'e}n, Anders},
  title   = {Isometric embedding of a smooth compact manifold with a metric of low regularity},
  journal = {Arkiv f{\"o}r Matematik},
  volume  = {16},
  number  = {1},
  year    = {1978},
  pages   = {29--50},
  doi     = {10.1007/BF02385981},
  url     = {https://archive.ymsc.tsinghua.edu.cn/pacm_download/116/7279-11512_2006_Article_BF02385981.pdf},
  note = {\url{https://doi.org/10.1007/BF02385981}}
}

@article{Kuiper1955,
  author  = {Kuiper, N. H.},
  title   = {On {$C^1$}-isometric imbeddings. {I}},
  journal = {Nederl. Akad. Wetensch. Proc. Ser. A},
  volume  = {58},
  year    = {1955},
  pages   = {545--556},
  note    = {Also Indagationes Mathematicae 17 (1955)}
}

@misc{Lewicka2026v3,
  author        = {Lewicka, Marta},
  title         = {Full flexibility of isometric immersions of metrics with low {H\"older} regularity in {Poznyak} theorem's dimension},
  year          = {2026},
  archivePrefix = {arXiv},
  eprint        = {2511.16305v3},
  primaryClass  = {math.DG},
  url           = {https://arxiv.org/abs/2511.16305v3},

  note = {Version 3, submitted August 14, 2026; manuscript dated August 17, 2026. \url{https://arxiv.org/abs/2511.16305v3}},
}

@article{Moser1966,
  author  = {Moser, J{\"u}rgen},
  title   = {A rapidly convergent iteration method and non-linear partial differential equations---{I}},
  journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze},
  series  = {3},
  volume  = {20},
  number  = {2},
  year    = {1966},
  pages   = {265--315},
  url     = {https://numdam.org/item/ASNSP_1966_3_20_2_265_0/},
  note = {\url{https://numdam.org/item/ASNSP_1966_3_20_2_265_0/}}
}

@article{Nash1954,
  author  = {Nash, John},
  title   = {{$C^1$}-isometric imbeddings},
  journal = {Annals of Mathematics. Second Series},
  volume  = {60},
  number  = {3},
  year    = {1954},
  pages   = {383--396},
  doi     = {10.2307/1969840},
  url     = {https://doi.org/10.2307/1969840},
  note = {\url{https://doi.org/10.2307/1969840}}
}

@article{Nash1956,
  author  = {John Nash},
  title   = {The Imbedding Problem for {Riemannian} Manifolds},
  journal = {Annals of Mathematics. Second Series},
  volume  = {63},
  number  = {1},
  year    = {1956},
  pages   = {20--63},
  doi     = {10.2307/1969989},
  url     = {https://sites.math.rutgers.edu/~feehan/teaching/math866/nash.pdf},
  note    = {\url{https://doi.org/10.2307/1969989}}
}

@misc{OpenAILocalObstruction2026,
  author = {{OpenAI}},
  title = {{A Smooth Metric with No Local Isometric Immersion into Three-Space}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026/paper.pdf}{OAI:A-Smooth-Metric-with-No-Local-Isometric-Immersion-into-Three-Space-September-24-2026}},
  year = {2026}
}

@article{Poznyak1973,
  author = {Poznyak, E. G.},
  title = {Isometric immersions of two-dimensional {Riemannian} metrics in euclidean space},
  journal = {Russian Mathematical Surveys},
  volume = {28},
  number = {4},
  year = {1973},
  pages = {47--77},
  doi = {10.1070/RM1973v028n04ABEH001591},
  note = {\url{https://doi.org/10.1070/RM1973v028n04ABEH001591}}
}

@article{Sard1942,
  author = {Sard, Arthur},
  title = {The measure of the critical values of differentiable maps},
  journal = {Bulletin of the American Mathematical Society},
  volume = {48},
  number = {12},
  year = {1942},
  pages = {883--890},
  doi = {10.1090/S0002-9904-1942-07811-6},
  url = {https://doi.org/10.1090/S0002-9904-1942-07811-6},
  note = {\url{https://doi.org/10.1090/S0002-9904-1942-07811-6}}
}

@article{Whitney1944,
  author  = {Hassler Whitney},
  title   = {The Singularities of a Smooth {$n$}-Manifold in {$(2n-1)$}-Space},
  journal = {Annals of Mathematics. Second Series},
  volume  = {45},
  number  = {2},
  year    = {1944},
  pages   = {247--293},
  doi     = {10.2307/1969266},
  url     = {https://webhomes.maths.ed.ac.uk/~v1ranick/papers/singular.pdf},
  note    = {\url{https://doi.org/10.2307/1969266}}
}