We present a topological–geometric framework, formulated as effective field theories with solitonic solutions, that unifiesmass scaling in leptons and baryons with very few global parameters. We show that a single power law emerges from soliton-based EFTs in leptons (vortices) and baryons (hopfions), with δ fixed by a coherence-window/RG mechanism (not fitted). The key ingredient is a universal offset—set by coherence-window and renormalization arguments, not by data fitting—that imprints the structure of the non-Abelian vacuum on both sectors. Calibrating with two anchors per sector, the scheme reproduces known masses and yields out-of-anchor predictions: the tau lepton at sub-percent level and light-baryon systematics at the ∼1% scale. The baryonic topological assignments are minimal and falsifiable. The approach is parsimonious and grounded in EFT and RG considerations. We conclude with proposed numerical/experimental tests and a set of relations designed to be refuted by additional data or variational simulations.