2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221525We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for $\ell_2$ in the context of the Urysohn space $\Ur$. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.19 pagesMetric GeometryCombinatorics22F05text