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 (|Vᵤₛ|, 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 ξsym ≈ 0.5149, derived from the Schwinger-Dyson equation 18ξ⁴ = 1+ξ². 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 = ξsym 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 JCP ≈ 3.08 × 10⁻⁵ (an exact PDG match) and a falsifiable CP phase of δ = 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.