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 the remaining fermion masses, the CKM and PMNS matrices, and the associated CP phases with propagated uncertainties. Within a three-generation Standard Model with Dirac neutrinos, the mixing structure follows fixed selection rules derived from internal geometry; 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). In the anchored benchmark Run A (App. O.5), one finds δPMNS = 296.68∘and |JCP| = 3.04 × 10−2. Allowing a Takagi-consistent, non-commuting complex perturbation confined to the neutral sector introduces a physical leptonic phase and enhances CP violation while preserving the PMNS magnitudes within correlated few-percent shifts (with |Ue3| held fixed). In the anchored benchmark (App. O.5), a soft preference toward the experimentally hinted quadrant near δPMNS ∼ 280∘ 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.