Quark Mass Hierarchies, CKM Mixing, and CP Violation from Spectral Seam Geometry (IGPS VII)

This paper provides a first-principles derivation of the Standard Model quark flavor sector—encompassing the CKM matrix, quark mass hierarchies, and CP violation—entirely from the spectral geometry of a Z₃ seam defect in SU (3) ₁ WZW theory. Remarkably, this framework requires zero free parameters beyond three empirical anchors (|Vₔₒ|, mᵤ, and md). It rigorously explains why flavor mixing, mass generation, and CP violation appear independent in the Standard Model via the TGA Algebra Decomposition Theorem. Key Highlights: The Master Equation: The framework is governed by a unique self-consistency parameter ₒₘ₌ 0. 5149, derived from the Schwinger-Dyson equation 18⁴ = 1+². It successfully reproduces 10 of 11 CKM observables to within 5% of PDG values. Predictive Mass Spectra: Quark mass hierarchies are determined by rigorous WZW spectral exponents (pᵤ = ₒₘ₌ and pd = 3/4), accurately predicting the masses of the c, s, t, and b quarks. Topological CP Violation: CP violation emerges naturally from Z₃ Wilson loop holonomy. This predicts J₂₏ 3. 08 10^-5 (an exact PDG match) and a falsifiable CP phase of = 110. 53^. Standard Model Embedding: The IGPS framework is formally derived from the SM Yukawa Lagrangian via a BPS domain wall, non-Abelian bosonization, and the Goddard-Kent-Olive (GKO) coset construction.