The simplest possible parameterization of new physics that results in an ultraviolet complete gauge-Yukawa sector of the Standard Model is explored. To this end, an antiscreening contribution to the beta function of the Abelian hypercharge gauge coupling, and a flavor-universal, antiscreening contribution to the beta functions of the Yukawa couplings are added. These two free parameters give rise to an intricate web of Renormalization Group fixed points. Their predictive power extends to the quarks' flavor structure and mixing patterns. This results in a fixing of some of the free parameters and on constraints on others due to the properties of Renormalization Group fixed points and flow.