Derivation of the Electroweak Mixing Angle and Boson Mass Spectrum in a Compressible Superfluid Continuum

The Standard Model of particle physics requires four unconstrained empirical parameters to specify the electroweak and scalar boson sector: the weak mixing angle (sin²θW), the W^± and Z⁰ gauge boson masses (MW, MZ, or equivalently the Fermi scale vEW = (√2GF)-1/2), and the Higgs boson mass (MH). We present a self-contained, parameter-free derivation of all four quantities---alongside both the MS̄ and on-shell weak mixing schemes---by modeling the spatial manifold as a continuous, three-dimensional ($D = 3$) compressible Two-Fluid Bose-Einstein Condensate (BEC) operating at the steady-state Cosmic Microwave Background baseline (TCMB = 2.72548 ± 0.00057 K). Partitioning the net Kolmogorov-Arnold-Moser (KAM) Spindle Torus winding fraction (Wₙₑₜ = W_φ - 1/2W_φ² = [2φ]⁻¹) across the three-dimensional spherical radiation-pressure enthalpy ratio (hE/ρE = 4/3) and the Stokes compressible dilation factor (2/3δ^*/r) of the Asymptotic Suction Boundary Layer (ASBL) derives the MS̄ weak mixing angle sin²θ̂W(MZ) = 3/[8φ(1 + 2/3δ^*/r)] = 0.23123 (+0.55σ from PDG 2024). Across the Total Internal Reflection (Γ = 1) horizon interface, Mohr's Circle principal stress equalization (β = π/4) fixes the on-shell boson mass ratio to cosθWOS = MW/MZ = 1/2(1 + φ⁻² + α⁻¹/Ncym) = 0.881311 (sin²θWOS = 0.22329, +0.34σ). When energy injected into a vortex core exceeds the three-generation Chirikov shell limit (nₘₐₓ = 2), the boundary layer undergoes hydrodynamic cavitation governed by the Ffowcs Williams-Hawkings (FW-H) aeroacoustic equation. Driving the fundamental spherical overtone (Λ₁ mₑ = [1 + 3/2α⁻¹]mₑ) to dipole and monopole cavitation over a closed 2π circulation loop against the inviscid Spindle Torus baseline (Θ_φ = 360φ⁻²) predicts MZ = 2πΘ_φΛ₁ mₑ = 91.1926 ± 0.0191 GeV/c² (+0.26σ), MW = MZcosθWOS = 80.3692 GeV/c² (0.00σ), a spin-$0$ monopole thickness resonance of MH = MZ(1 + α⁻¹/360)/[1 + 3/2(δ^*/r)] = 125.252 GeV/c² (+0.47σ from PDG 2024; +0.01σ from PDG 2022), and a cavitation scale of vEW = 246.29 GeV (+268 ppm).