The microscopic origin of mass and coupling: coherence of the finite-capacity vacuum and the universal relaxation time T

This work introduces a Finite-Capacity Vacuum (QUOT/VCI) framework that provides a unified geometric closure for key electroweak precision observables. Grounded in a single coherence operator, the architecture reproduces:The W boson mass derived from a universal vacuum relaxation time;The complete Z-pole sextet $\{M_Z, \Gamma_Z, \sin^2\theta_{eff}, \sigma_h^0, R_l, R_b\}$ via node curvature;The Higgs resonance as a transverse rigidity mode;Fermion Yukawa hierarchies emerging from discrete topological coherence paths;The muon as the first oscillatory eigenmode of a minimum coherence filter;And the fine-structure constant $\alpha$ as the vacuum transfer impedance.No additional normalization parameters are introduced. All quantities arise from the same curvature-controlled architecture. The framework closes W, Z, Higgs, Yukawas, and $\alpha$ within a single coherent structure, achieving agreement with experimental values up to $10^{-6}$ precision for $\alpha$.Rather than proposing new particles, this approach reinterprets existing Standard Model parameters as stationary eigenvalues of a finite-capacity vacuum network. Charged lepton generations appear as coherence eigenmodes (electron: DC reference, muon: phase bridge, tau: rigidity limit), while color acts as chromatic friction.This manuscript offers a complementary structural solution to electroweak precision physics, providing a unified geometric interpretation of masses, couplings, and constants that previously required independent inputs.