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 without introducing new continuous parameters.

In the lepton sector, the minimal real construction yields δPMNS ≃ 0 with a strongly sup-

pressed Jarlskog invariant, |JCP|  ≃ 6.2 × 10−6. Allowing a Takagi-consistent, non-commuting

complex perturbation confined to the neutral sector then realizes an experimentally preferred

leptonic phase while preserving the PMNS magnitudes within correlated few-percent shifts (with

|Ue3| held fixed):  δPMNS ∈ [220◦, 280◦]  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.