Gauge Dominance in the CKM Matrix: Why Quark Mixing Is Insensitive to Higgs Overlaps

This paper demonstrates that the dominant Cabibbo angle V_{us} \approx 0.225 in the CKM matrix is controlled almost entirely by SU(2) gauge boson exchange, making it robust under changes in the Higgs geometric overlaps. The CKM matrix describes quark flavor mixing. In the canvas model, the off-diagonal mass matrix elements that generate mixing arise from two sources: SU(2) gauge boson exchange between generations in the (1,2) plane, and Higgs-mediated couplings between all generations. The Higgs contribution to the (1,2) off-diagonal coupling is only \sim 5\% of the gauge contribution. Why this matters: The down-type Higgs direction was recently re-derived from first-principles mass ratios, changing the geometric overlaps by up to an order of magnitude. Despite this, the CKM (1,2) mixing changes by only \sim 10-20\%. The gauge coupling g_{12} = g_2/2 is independent of the Higgs overlaps. The gauge coupling itself is fixed by the primitives: g_2(M_P) = \sqrt{8\pi\alpha_0} from Postulate P8, with \alpha_0 = 1/\ln(I_{\text{max}}) from the horizon information bound. The renormalization group evolution to the electroweak scale yields g_2 \approx 0.65. The SU(2) algebra gives the generation coupling |\langle \vec{c}^{(1)}|T^+|\vec{c}^{(2)}\rangle| = 1/2. The nonlinear UWE dynamics provide an enhancement factor of \sim 5.6 from the peak-to-RMS ratio and the mode coupling. Together, these determine the off-diagonal coupling \xi_{12} \approx 1.8 with no free parameters. The (2,3) and (1,3) CKM elements are generated by Higgs mediation. These are smaller (V_{cb} \sim 0.04, V_{ub} \sim 0.004) and depend on the geometric overlaps. Their precise values require the full numerical diagonalization of the 3 \times 3 mass matrices with the updated down-type parameters, which is left for future work. The gauge dominance of the (1,2) sector is the central result of this paper. It explains why the CKM matrix is hierarchical while the mass spectrum spans six orders of magnitude: the physics that determines masses is distinct from the physics that determines mixing. The canvas model naturally separates mass generation from flavor mixing, preserving the independence of Yukawa couplings and the CKM matrix while deriving both from a common set of primitives. Keywords: CKM matrix, quark mixing, gauge dominance, SU(2) gauge boson exchange, Higgs-mediated couplings, canvas model, flavor physics, Wolfenstein parameter