Charged-Fermion Mass Phenomenology and the Pati–Salam Mass Plane: Sp(18) Normalization and a USp(6) Mass Construction

The pattern of charged-fermion masses suggests a connection between the shapes of quark and lepton spectra. This revised and expanded study examines the resulting Pati–Salam mass plane in complementary $\mathrm{Sp}(18)$ and $\mathrm{USp}(6)$ constructions. It relates the logarithmic plane to a specified source geometry and develops an economical $N=1$ supersymmetric $\mathrm{USp}(6)$ realization. In a common-profile embedding, a single route-odd normalization coefficient controls the component normal to the plane. Exact finite matrix identities show how the relation is modified by noncommuting kinetic terms and by the middle singular value. Three candidate composite operators $P_0A^jL_0$, $j=0,1,2$, have charges compatible with the restricted family-source texture; one active right-handed ten-plet pair then yields a charged-mass determinant relation.In a local radiative example, heavy-threshold gauge transport, full-matrix Standard-Model evolution below 10 TeV, and the retained gluino, bino and colorless-Higgsino mass and kinetic corrections give $m_s(M_Z)=53.12642$ MeV for the finite boundary $c_{K6}=3/4$. The other eight charged masses and CKM mixing, including its CP invariant, are reproduced using the existing down-soft sector. The same canonical tree messenger block gives $H_\ell/H_d=1.540962$ and a squared-splitting ratio of $2.375000$. The choice of $c_{K6}$ was informed by the known strange-mass range. Taking that mass as a ninth input instead calibrates $c_{K6}=0.727266026$; neither procedure derives the coefficient from strong dynamics.The $\mathrm{Sp}(18)$ analysis retains conditional current–scalar matching identities and local vacuum tests for its own specified action. An analytic bound below $0.018\%$ controls the family-direction dependence of a separate canonical $\mathrm{USp}(6)$ flavon kernel, while a reduced high-scale charged-source system provides independently checked evolution and matching identities. Local vacuum and selected flavor tests are available in specified reference configurations; the complete pole spectrum and baryon amplitudes require further matching. These results define a concrete effective mass benchmark, conditional heavy-mass tests and a source-normalization target for a microscopic completion.