2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129498We present a new proof of Reidemeister and Singer's Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound on the minimal genus of a common stabilization in terms of the number of negative slope inflection points and type-two cusps in a Rubinstein-Scharlemann graphic for the two splittings.24 pages, 10 figuresGeometric Topology57Mtext