{"id":"palomar/PALOMAR-2026-10-14-000008","url":"https://github.com/wstrinz/mobius-ramsey/tree/52284ddf3db595776b0d651c844fbeaf7b34a641","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-14-000008-v1.json","repo":"https://github.com/wstrinz/mobius-ramsey","tags":["math.CO","math.MG","msc:05D10","msc:52C10","msc:51B10","discrete-geometry","ramsey-theory","mobius-transformations"],"score":0,"title":"Möbius invariance of the Ramsey property for finite spherical sets","trust":"high","domain":"math.CO","source":"palomar","authors":["Will Strinz"],"reviews":0,"subject":"math.CO","summary":"Theorem C: for finitely many distinct points a of the unit sphere of R^d and any L in O(1,d) (L^T S L = S with S = diag(-1, 1, ..., 1)), the configuration a is Euclidean Ramsey if and only if its image under the Möbius map phi_L is Euclidean Ramsey. There is no affine-spanning hypothesis. Ramsey is OpenAI's definition from result 172 (for every r >= 2 there is D such that every r-colouring of R^D contains a monochromatic congruent copy). Corollaries, also proved: every Möbius image of a finite set of distinct unit-sphere points with real algebraic coordinates is Ramsey; and for distinct…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-14","reactions":{},"formalized":true}