Mass, Mixing, and the Golden Ratio: The CKM Hierarchy and Generation Mass Spectrum as Error-Correction Phenomena on the Octahedral Lattice

We derive the quark mixing hierarchy and generation mass spectrum from the error- correction structure of the [8,4,4] code on the Q3 face-adjacency graph of the regular octa- hedron. 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 sectors {1,2}(G0 = 0) and {3}(G0 = 1). This single topological lock produces three consequences. First, Cabibbo mixing (Vus) arises within the G0 = 0 sector through single-void virtual excursions across the electroweak constraint boundary, while third-generation mixing (Vcb, Vub) requires correlated two-particle tunnelling through the code’s invalid subspace, activat- ing at the double spectral gap 2∆ = 4. In the resonance window, the ratio |Vub|/|Vcb|≈0.1 matches the experimental value 0.093 with zero fitted parameters. Second, the generation mass hierarchy follows the Boltzmann-weighted thermodynamic cost of propagating a frustrated codeword through the error-correcting vacuum: M= exp(φF/2), where F is the codeword’s frustration count on Q3 and φ = (√5−1)/2 is the reciprocal of the golden ratio. This exponent is confirmed by high-precision scanning of the two-particle CKM resonance region in the full 65,536-dimensional virtual space. Third, the golden ratio ϕ= (1+√5)/2 appears as the leading eigenvalue of the P4 colour flux tube (the spectral bound governing quark confinement), while its reciprocal φ = 1/ϕ governs the mass hierarchy. The identity κ×ϕ= φ×ϕ = 1 unifies the generation mass spectrum with the colour confinement string tension as dual aspects of a single geometric fixed point of the walk operator on Q3. The framework predicts that CKM universality holds for Vus but is structurally violated for Vcb, offering a geometric origin for the persistent∼3σ “Vcb puzzle.” v2.0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger); see the paper's status note for the specific corrections, supersessions, or upgrades.