Abstract

We present a compact, data-anchored framework that, from four inputs (the electron mass me, the charged-lepton mass ratios mμ/me and mτ /me, and the Cabibbo angle θC), computes a declared set of charged-sector masses, CKM-magnitude outputs, PMNS benchmark matrices, and CP diagnostics with propagated uncertainties. Within a three-generation Standard Model with Dirac neutrinos, the mixing structure follows fixed selection rules derived from internal ge ometry; a single allowed rank-2 (∆ℓ = 2 in internal angular momentum) overlap lifts |Vub| to its observed scale with geometric coefficients constrained by Gaussian priors. In the lepton sector, the minimal baseline emitted by the released pipeline yields δPMNS ≃ 0 with a numerically vanishing Jarlskog invariant (|JCP| ≈ 3.9×10−34). The Run-A neutral-sector benchmark introduces a Takagi-consistent, non-commuting complex perturbation of the Yukawa texture, generating a physical leptonic phase and improving the PMNS angle/phase reconstruction relative to the minimal real construction; residual magnitude deviations remain correlated, particularly in the µ/τ rows. In the anchored version of this benchmark (Appendix O.5), a soft preference toward the negative-quadrant branch historically suggested by long-baseline data yields δPMNS = 296.7∘ and |JCP| ∼ (2–4) × 10−2. A fully reproducible numerical pipeline accompanies the analysis. 

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Keywords: Standard Model, fermion masses, CKM matrix, PMNS matrix, CP violation, flavor puzzle, morton geometry, scalar field, unified theory, Berry curvature, gauge symmetry, Axis Model, Yang-Mills theory.