ICC XIII: Spectral Origin of Fermion Mass Hierarchy from Stochastic Copying Dynamics

We propose that the observed fermion mass hierarchy emerges from the spec tral statistics of a stochastic copying operator ˆ Lcopy on a 4D simplicial complex. The operator governs defect dynamics in the Information-Copying Cosmology (ICC) framework. We derive a universal scaling relation mf ∝ √ xf from renormalization group flow near the Anderson mobility edge, where xf = (λc − λf)/Λ2 mob is the dimensionless distance of the eigenvalue λf to the critical point λc. From the requirement of reproducing the fermion mass hierarchy we obtain µ ≈ −0.5 ± 0.3 for the spectral exponent µ defined by ρ(λ) ∼ (λc − λ)µ. The negative sign indicates eigenstate accumulation near the mobility edge, in contrast to standard Anderson localization. Numerical extraction on lattices L = 8,10,12 yields µ = −0.372(75),−0.427(60),−0.555(50) respectively. Finite-size scaling extrapolates to µ(∞) = −0.665, while averaging over random seeds gives µ = −0.487±0.040. Both results are consistent with the analytically required range. This confirms that the copying operator defines a new non-equilibrium universality class characterized by µ < 0, providing a geometric origin of flavor without free parameters beyond ∆ ≈ 0.10 from ICC XII.