@article{moore-pyramid,
  author = {Moore, Kenneth},
  title = {A pyramid with a {Ramsey} base is {Ramsey}},
  journal = {arXiv preprint arXiv:2608.09649},
  year = {2026},
  eprint = {2608.09649},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2608.09649},
  url = {https://arxiv.org/abs/2608.09649v1},
  note = {Version 1, 10 August 2026}
}

@article{ilw-blocks,
  author = {Ivan, Maria-Romina and Leader, Imre and Walters, Mark},
  title = {Block sizes in the block sets conjecture},
  journal = {Forum of Mathematics, Sigma},
  volume = {14},
  pages = {e67},
  year = {2026},
  doi = {10.1017/fms.2026.10212},
  url = {https://arxiv.org/abs/2406.01459}
}

@article{behague-subsoluble,
  author = {Behague, Natalie},
  title = {Nearly all known {Euclidean Ramsey} sets are subsoluble},
  journal = {arXiv preprint arXiv:2510.15677},
  year = {2025},
  eprint = {2510.15677},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2510.15677},
  url = {https://arxiv.org/abs/2510.15677v3},
  note = {Version 3, 4 December 2025}
}

@article{ilw-prisms,
  author = {Ivan, Maria-Romina and Leader, Imre and Walters, Mark},
  title = {Generalised prisms and {Euclidean Ramsey} theory},
  journal = {arXiv preprint arXiv:2606.13472},
  year = {2026},
  eprint = {2606.13472},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2606.13472},
  url = {https://arxiv.org/abs/2606.13472v1},
  note = {Version 1, 11 June 2026}
}

@misc{stacks-completion,
  author = {{The Stacks Project Authors}},
  title = {The {Stacks} Project},
  year = {2026},
  url = {https://stacks.math.columbia.edu/tag/00MB},
  note = {Lemma 10.97.2, Tag 00MB; accessed 23 September 2026}
}

@article{egm-rss,
  author = {Erd{\H{o}}s, Paul and Graham, Ronald L. and Montgomery, Peter and Rothschild, Bruce L. and Spencer, Joel and Straus, Ernst G.},
  title = {Euclidean {Ramsey} theorems. {I}},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {14},
  number = {3},
  pages = {341--363},
  year = {1973},
  doi = {10.1016/0097-3165(73)90011-3},
  url = {https://www.cs.umd.edu/~gasarch/TOPICS/ERT/EGMRSSone.pdf}
}

@article{graham-survey,
  author = {Graham, Ronald L.},
  title = {Recent trends in {Euclidean Ramsey} theory},
  journal = {Discrete Mathematics},
  volume = {136},
  number = {1--3},
  pages = {119--127},
  year = {1994},
  doi = {10.1016/0012-365X(94)00110-5},
  url = {https://www.cs.umd.edu/~gasarch/TOPICS/ERT/GrahamTrends.pdf}
}

@article{lrw-transitive,
  author = {Leader, Imre and Russell, Paul A. and Walters, Mark},
  title = {Transitive sets in {Euclidean Ramsey} theory},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {119},
  number = {2},
  pages = {382--396},
  year = {2012},
  doi = {10.1016/j.jcta.2011.09.005},
  url = {https://arxiv.org/abs/1012.1350}
}

@article{lrw-kites,
  author = {Leader, Imre and Russell, Paul A. and Walters, Mark},
  title = {Transitive sets and cyclic quadrilaterals},
  journal = {Journal of Combinatorics},
  volume = {2},
  number = {3},
  pages = {457--462},
  year = {2011},
  doi = {10.4310/JOC.2011.v2.n3.a6},
  url = {https://arxiv.org/abs/1012.5468}
}

@article{hales-jewett,
  author = {Hales, A. W. and Jewett, R. I.},
  title = {Regularity and positional games},
  journal = {Transactions of the American Mathematical Society},
  volume = {106},
  number = {2},
  pages = {222--229},
  year = {1963},
  doi = {10.1090/S0002-9947-1963-0143712-1},
  url = {https://www.jstor.org/stable/1993764}
}

@article{shelah,
  author = {Shelah, Saharon},
  title = {Primitive recursive bounds for van der {Waerden} numbers},
  journal = {Journal of the American Mathematical Society},
  volume = {1},
  number = {3},
  pages = {683--697},
  year = {1988},
  doi = {10.2307/1990952},
  url = {https://shelah.logic.at/papers/329/}
}

@book{hindman-strauss,
  author = {Hindman, Neil and Strauss, Dona},
  title = {Algebra in the {Stone--\v{C}ech} Compactification: Theory and Applications},
  series = {de Gruyter Expositions in Mathematics},
  volume = {27},
  publisher = {Walter de Gruyter},
  address = {Berlin and New York},
  year = {1998},
  isbn = {3-11-015420-X},
  doi = {10.1515/9783110809220},
  url = {https://www.degruyterbrill.com/document/doi/10.1515/9783110809220/html}
}

@article{frankl-rodl-triangles,
  author = {Frankl, Peter and R{\"o}dl, Vojt{\v{e}}ch},
  title = {All triangles are {Ramsey}},
  journal = {Transactions of the American Mathematical Society},
  volume = {297}, number = {2}, pages = {777--779}, year = {1986},
  doi = {10.1090/S0002-9947-1986-0854099-6},
  url = {https://www.renyi.hu/~pfrankl/1986-3.pdf}
}
@article{frankl-rodl-simplices,
  author = {Frankl, Peter and R{\"o}dl, Vojt{\v{e}}ch},
  title = {A partition property of simplices in {Euclidean} space},
  journal = {Journal of the American Mathematical Society},
  volume = {3}, number = {1}, pages = {1--7}, year = {1990},
  doi = {10.1090/S0894-0347-1990-1020148-2},
  url = {https://www.renyi.hu/~pfrankl/1990-3.pdf}
}
@article{kriz-permutation,
  author = {K{\v{r}}{\'i}{\v{z}}, Igor},
  title = {Permutation groups in {Euclidean Ramsey} theory},
  journal = {Proceedings of the American Mathematical Society},
  volume = {112}, number = {3}, pages = {899--907}, year = {1991},
  doi = {10.1090/S0002-9939-1991-1065087-9}
}
@article{kriz-trapezoids,
  author = {K{\v{r}}{\'i}{\v{z}}, Igor},
  title = {All trapezoids are {Ramsey}},
  journal = {Discrete Mathematics},
  volume = {108}, number = {1--3}, pages = {59--62}, year = {1992},
  doi = {10.1016/0012-365X(92)90660-8},
  url = {https://www.sciencedirect.com/science/article/pii/0012365X92906608}
}
@article{cantwell-polytopes,
  author = {Cantwell, Kristal},
  title = {All regular polytopes are {Ramsey}},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {114}, number = {3}, pages = {555--562}, year = {2007},
  doi = {10.1016/j.jcta.2006.08.001}
}
@article{karamanlis-tori,
  author = {Karamanlis, Miltiadis},
  title = {Simplices and regular polygonal tori in {Euclidean Ramsey} theory},
  journal = {The Electronic Journal of Combinatorics},
  volume = {29}, number = {3}, pages = {Paper No. 3.66}, year = {2022},
  doi = {10.37236/10944},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v29i3p66}
}
@article{eberhard-subtransitive,
  author = {Eberhard, Sean},
  title = {Almost all sets of {$d+2$} points on the {$(d-1)$}-sphere are not subtransitive},
  journal = {Mathematika}, volume = {59}, number = {2},
  pages = {267--268}, year = {2013},
  doi = {10.1112/S0025579313000053},
  url = {https://arxiv.org/abs/1212.1803}
}
@article{mirabi-extensions,
  author = {Mirabi, Mostafa},
  title = {One-point extensions of {Euclidean Ramsey} sets},
  journal = {arXiv preprint arXiv:2608.11736}, year = {2026},
  eprint = {2608.11736}, archivePrefix = {arXiv}, primaryClass = {math.CO},
  doi = {10.48550/arXiv.2608.11736},
  url = {https://arxiv.org/abs/2608.11736v1},
  note = {Version 1, 12 August 2026}
}
@article{palvolgyi-heptagon,
  author = {P{\'a}lv{\"o}lgyi, D{\"o}m{\"o}t{\"o}r},
  title = {A cyclic non-{Ramsey} heptagon},
  journal = {arXiv preprint arXiv:2609.23327}, year = {2026},
  eprint = {2609.23327}, archivePrefix = {arXiv}, primaryClass = {math.CO},
  url = {https://arxiv.org/abs/2609.23327v1},
  note = {Version 1, 20 September 2026}
}

@article{ellis-idempotent,
  author = {Ellis, Robert},
  title = {Distal transformation groups},
  journal = {Pacific Journal of Mathematics},
  volume = {8},
  number = {3},
  pages = {401--405},
  year = {1958},
  doi = {10.2140/pjm.1958.8.401},
  url = {https://msp.org/pjm/1958/8-3/pjm-v8-n3-p02-p.pdf}
}

@article{liouville1851,
  author = {Liouville, Joseph},
  title = {Sur des classes tr\`es-\'etendues de quantit\'es dont la valeur n'est ni alg\'ebrique, ni m\^eme r\'eductible \`a des irrationnelles alg\'ebriques},
  journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
  series = {1},
  volume = {16},
  pages = {133--142},
  year = {1851},
  url = {https://www.numdam.org/item/JMPA_1851_1_16__133_0/}
}


@article{palvolgyi-nearcircumsphere,
  author = {P{\'a}lv{\"o}lgyi, D{\"o}m{\"o}t{\"o}r},
  title = {A nearcircumsphere-{Ramsey} theorem for solvable transitive configurations},
  journal = {arXiv preprint arXiv:2608.10865},
  year = {2026},
  eprint = {2608.10865},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2608.10865},
  url = {https://arxiv.org/abs/2608.10865v2},
  note = {Version 2, 3 September 2026}
}

@article{shaw-pentagon,
  author = {Shaw, Benedict Randall},
  title = {The regular pentagon is canonically {Ramsey}},
  journal = {arXiv preprint arXiv:2608.19183},
  year = {2026},
  eprint = {2608.19183},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2608.19183},
  url = {https://arxiv.org/abs/2608.19183v1},
  note = {Version 1, 19 August 2026}
}

@article{rado-note,
  author = {Rado, Richard},
  title = {Note on combinatorial analysis},
  journal = {Proceedings of the London Mathematical Society},
  series = {2},
  volume = {48},
  pages = {122--160},
  year = {1945},
  doi = {10.1112/plms/s2-48.1.122},
  url = {https://www.cs.umd.edu/~gasarch/TOPICS/vdw/rado-gallai-english.pdf}
}