A Minimal Scaling Model for Fermions Mass Hierarchy

This paper introduces a discrete scaling model for the hierarchy of fermion masses, grounded in geometric contraction and interaction-induced feedback. By analyzing the lepton sector and applying a minimal model with exponential scaling, the approach predicts a discrete mass spectrum governed by a geometric constant K=2−1K = \sqrt{2} - 1K=2−1, with a fixed interaction strength ϵ≈K9\epsilon \approx K^9ϵ≈K9. The model successfully explains the observed lepton hierarchy, predicts new states in the 10–30 GeV range, and provides a simple yet powerful framework for understanding fermion mass generation. This phenomenological model offers insight into the nature of mass hierarchies, emphasizing the role of scaling, interaction feedback, and stability.