Mass Law for Lepton Mass Hierarchy: Rubik’s Tetrahedral Spinor Structure and Self-Similar Geometric Origin

We present a unified Rubik’s tetrahedral spinor geometry that accounts for the charged-lepton and neutrino mass hierarchies through discrete internal curvature. In this framework, fermion masses arise from activation of Hermitian bilinear curvature channels within a tetrahedral spinor manifold. The mass spectrum of the k-th generation follows a simple logarithmic mass law, ln⁡(m/m₁)=8 ln⁡k, or more precisely, with extra correction terms as ln⁡(m/m₁)=8 ln⁡k+ Ak² (k-1)+Bk³ (k-1). The mass law contains a fixed ladder coefficient of eight, corresponding to eight curvature channels, which can be visualized as a self-similar fractal Rubik’s tetrahedron, and reveals an invariant combination A_l+B_l=-9/4 (relative error < 10^-6%), consistent with quadratic spin contraction. In contrast, neutrino masses emerge from cyclic pseudo-temporal mixing of an internal triplet, producing a distinct invariant A_ν+B_ν=-4√3 (relative error0.003%). The √3 factor arises naturally from triplet normalization rather than parameter tuning. The two sectors thus reflect different curvature regimes within a common spinor structure. These results suggest that generational hierarchy encodes discrete geometric invariants, providing a curvature-based origin of lepton mass structure beyond phenomenological Yukawa parametrization.