We present new advances in the minimal $SO(10)$ Higgs model where the $45\oplus126$ scalars drive spontaneous symmetry breaking down to the Standard model. A comprehensive analysis of all theoretical aspects of the model was performed extending previous results. Computational tools, including full one-loop mass corrections and one-loop scalar beta functions, were developed and allowed us to construct thorough viability constraints. Only two potentially realistic scenarios were identified, one of them seems to be preferred.