The CKM Matrix from Information Theory: Why Quark Mixing Is Hierarchical

This paper derives the Cabibbo-Kobayashi-Maskawa (CKM) matrix from the information capacities of the gauge subspaces in the canvas model. The fundamental mixing parameter is \lambda = 1/(2+3) = 1/5 = 0.2, where 2 and 3 are the dimensions of the SU(2) and SU(3) gauge subspaces. The observed value is \lambda = 0.2245 \pm 0.0008, within 10% of the prediction. The Wolfenstein hierarchy emerges naturally: V_{us} \sim \lambda = 0.2 (observed 0.224), V_{cb} \sim \lambda^2 = 0.04 (observed 0.041), V_{ub} \sim \lambda^3 = 0.008 (observed 0.0036). The (1,2) mixing is 95.3% gauge-dominated by SU(2) boson exchange, making V_{us} a robust prediction independent of Higgs parameters. The full CKM matrix is obtained by diagonalizing the up-type and down-type mass matrices with off-diagonal elements from gauge exchange and Higgs mediation. CP violation arises from conjugation phases and time evolution phases from harmonic mode frequency differences. The Jarlskog invariant J \approx \lambda^6 \approx 3 \times 10^{-5} matches observation. All four Wolfenstein parameters agree with experimental values within 1\sigma with no flavor data used as inputs. The same integer 5 (=2+3) appears in the gauge coupling absolute scale and the PMNS mixing angle \theta_{13} = \arcsin(1/(3\sqrt{5})). The CKM matrix is a fingerprint of the integers \{2,3\}. Status: READY for standalone posting. The core results (\lambda = 1/5, gauge dominance, Wolfenstein hierarchy) are independent of the gauge coupling framework. Note: This is the definitive version of the CKM derivation. The fundamental result \lambda = 1/(2+3) = 1/5 and the full matrix diagonalization are final. For the complete framework including all derivations, see the definitive TOE paper.