Möbius invariance of the Ramsey property for finite spherical sets
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-10-14-000008
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-14-000008/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-14-000008/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'