7.7 Quark Mass Spectrum and CKM Matrix

Starting from the Sole Axiom δ and under the constraints of {2,3,5} Interlock Property and the seven-level recurrence of the coding orbit, this paper proves: (I) Quark mass ratios are uniquely locked by the hierarchical structure of the coding orbit — the mass ratios of the six quarks are pure geometric predictions, determined by local region properties; (II) The CKM mixing matrix equals the unistochastic lift of the Birkhoff Mixing Matrix, , including the geometric origin of the CP-violating phase. The absolute mass scale is determined by the electron mass through cross-sector bridging of the coding orbit. All 12 theorems of this paper are fully closed. **Honesty Statement**: The geometric expression for the QCD enhancement factor of heavy quarks () is an open problem — its existence is guaranteed by the structure constant , but the specific form has not yet been rigorously derived from first principles. This paper provides a theorem-level argument for the existence of , and annotates its current status in the numerical verification. The mass ratios of light quarks () are theorem-level closed predictions, requiring no correction.