We extend the $IT^3$ paradigm to a universal spectral-Diophantine framework that generates predictions and strict mathematical bounds for the complete spectrum of the Standard Model (over 25 fundamental parameters and states). By unifying the topological winding functional with effective Diophantine approximation bounds, spectral zeta-function residues, symplectic capacity cutoffs, and Random Matrix Theory (RMT) statistical tolerances via the adjacent gap ratio, we derive parameter-free formulas for all fermion masses, gauge bosons, mixing angles, and cosmological scales. Lower bounds emerge from effective Diophantine approximation ensuring topological stability ($M_X > 0$) ; upper bounds are fixed by Gromov's non-squeezing theorem and topological saturation thresholds. Integer coefficients are rigorously derived as residues of the spectral zeta-function $\zeta_{\Delta}(s)$ at $s=3/2$. The framework yields falsifiable predictions for the entire quark and lepton sectors, a sterile neutrino state at 7.4 keV, the QCD axion window, CKM phase boundaries, and an absolute resonance desert above 173.5 GeV, with all bounds derived strictly from the geometry of $T^3(1,\sqrt{2},\sqrt{3})$ without phenomenological fitting.