Finite-Capacity Vacuum Coherence: A Unified Closure of W Mass, Z-Pole Observables, Higgs Rigidity, Yukawa Hierarchies, and the Fine-Structure Constant

This work introduces a finite-capacity vacuum framework (QUOT/VCI) providing a unified geometric closure of key electroweak precision observables. Starting from a single coherence operator, the construction reproduces: the W-boson mass from a universal vacuum relaxation time, the full Z-pole sextet {M_Z, Γ_Z, sin²θ_eff, σ_h⁰, R_ℓ, R_b} via node curvature, the Higgs resonance as a transverse rigidity mode, fermion Yukawa hierarchies from discrete topological coherence paths, the muon as the first oscillatory eigenmode of a minimal coherence filter, and the fine-structure constant α as a vacuum transfer impedance. No additional normalization parameters are introduced. All quantities emerge from the same curvature-controlled architecture. The framework closes W, Z, Higgs, Yukawas, and α within a single coherent structure, achieving agreement with experimental values up to 10⁻⁶ precision for α. 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 provides a complementary structural solution to electroweak precision physics, offering a unified geometric interpretation of masses, couplings, and constants that previously required independent inputs.