The CKM Hierarchy as Quantum Error-Correction Failure on the Octahedral Information Lattice

We show that the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing hierarchy arises naturally from the error-correction structure of the [8,4,4] code on the Q3 face-adjacency graph of the regular octahedron. We prove an exact Z2 theorem: the generation-0 bit (G0) is strictly conserved by the single-particle walk operator on the infinite three-dimensional lattice, partitioning the three fermion generations into two sectors {1,2}(G0 = 0) and {3} (G0 = 1). Cabibbo mixing (Vus) arises within the G0 = 0 sector through single-void virtual excursions across the electroweak constraint boundary. Third-generation mixing (Vcb, Vub) is forbidden at the single-particle level but activated by correlated two-particle tunnelling through the code’s invalid subspace, with an activation threshold at exactly twice the spec- tral gap (2∆ = 4 lattice units). In the resonance window, the lattice produces Vub/Vcb ≈0.1, matching the experimental ratio 0.093 with zero fitted parameters. The CKM hierarchy is thus identified with the error-correction hierarchy of the vacuum’s quantum code: Vus from single-void correctable errors, Vcb from two-void correlated errors, and Vub from compound correlated-plus-rotated errors. This framework predicts that CKM universality holds for Vus but is structurally violated for Vcb, offering a geometric origin for the long-standing tension between inclusive and exclusive determinations of |Vcb|from B-meson decays.