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 $\mathbb{Z}_3$ seam defect in $\mathrm{SU}(3)_1$ WZW theory.

Remarkably, this framework requires zero free parameters beyond three empirical anchors ($|V_{us}|$, $m_u$, and $m_d$). 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 $\xi_{\text{sym}} \approx 0.5149$, derived from the Schwinger-Dyson equation $18\xi^4 = 1+\xi^2$. 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 ($p_u = \xi_{\text{sym}}$ and $p_d = 3/4$), accurately predicting the masses of the $c, s, t,$ and $b$ quarks.

• Topological CP Violation: CP violation emerges naturally from $\mathbb{Z}_3$ Wilson loop holonomy. This predicts $J_{CP} \approx 3.08 \times 10^{-5}$ (an exact PDG match) and a falsifiable CP phase of $\delta = 110.53^\circ$.

• 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.