Entropic Stabilization of Fermion Generations and Mass Hierarchy in Noncommutative Unification

We demonstrate how the entropic stabilization of three spatial dimensions in noncommutative gravity-gauge unification naturally generates both the triplication of fermion generations and their observed mass hierarchy m1 : m2 : m3 ∼ 1 : 10^3 : 10^5. The mechanism emerges from Perelman-inspired entropy minimization constrained by topological invariants of the spatial hypersurface. Fermion masses maare shown to scale as ma ∝ exp−(a^2/2α) where a = 1, 2, 3 labels generations and α ≈ 0.90 is fixed by entropy extremization. This scaling law, rooted in theanisotropic curvature coupling of the noncommutative parameter θµν, resolves thegeneration puzzle without additional fields or fine-tuning. Testable predictions include cosmological mass evolution and modified gravitational wave spectra.