Abstract

We present a compact, data-anchored framework that, from four inputs (the electron mass me, the 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 CP phases with propagated uncertainties. The mixing structure follows fixed selection rules; an allowed ∆ℓ = 2 contribution lifts |Vub|  to its observed scale without introducing new tunable parameters. 

In the lepton sector, the minimal construction yields δPMNS ≃ 0 with a strongly suppressed Jarlskog, |JCP|  ≃ 6.2 × 10−6. A Takagi-consistent, non-commuting complex term confined to the neutral sector then realizes an experiment-scale 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 pipeline accompanies the analysis.

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.