Topological Origin of the Quark Mixing Hierarchy and CP Violation in a Discrete Information Space

We extend the 8-bit discrete lattice framework of Standard Model fermions to the calcu- lation of inter-generational quark mixing. By projecting a loop-level topological transition operator onto the physical 9-state left-handed quark basis, we derive the unrenormalized electroweak transition matrices. To map the discrete microstates to macroscopic observ- ables, we construct the SU (3) colour singlet using a standard Euclidean Boltzmann weight (wc ∝ e−δ·HWc ), corresponding to the information cost of the colour bits on the Boolean hypercube. Without introducing continuous fitted parameters, this discrete geometry yields: (1) a structural GIM mechanism where tree-level flavour-changing neutral currents vanish; (2) CP violation originating strictly from the down-type quark sector due to spatial routing asymmetries triggered by the I3 = 1 isospin bit; and (3) a hierarchical CKM matrix exhibit- ing Standard Model Wolfenstein power counting (λ, λ2, λ3). The calculated bare Cabibbo angle (|Vus| ≈ 0.237) and Jarlskog invariant (J ≈ 4.3 × 10−5) show strong structural agree- ment with global fits. We discuss the residual O(2) variances in the 1 → 3 and 2 → 3 matrix elements as expected consequences of missing Renormalisation Group running from the top-quark mass pole, referencing recent ATLAS and PDG constraints.