2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203403We argue that the best way to determine horizontal symmetry is from neutrino mixing, and proceed to show that the only finite group capable of yielding the tri-bimaximal mixing for all Yukawa couplings is $S_4$, or any group containing it. The method used is largely group theoretical, but it can be implemented by dynamical schemes in which the Higgs expectation values introduced to break $S_4$ spontaneously are uniquely determined up to an unknown scale for each.version to appear in Phys. Rev. Letts.: one reference added and some slight rephrasing of sentencesHigh Energy Physics - Phenomenologytext