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 ($\sin^2\theta_W$), the $W^\pm$ and $Z^0$ gauge boson masses ($M_W, M_Z$, or equivalently the Fermi scale $v_{\text{EW}} = (\sqrt{2}G_F)^{-1/2}$), and the Higgs boson mass ($M_H$). We present a self-contained, parameter-free derivation of all four quantities---alongside both the $\overline{\text{MS}}$ 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 ($T_{\text{CMB}} = 2.72548 \pm 0.00057\text{ K}$). Partitioning the net Kolmogorov-Arnold-Moser (KAM) Spindle Torus winding fraction ($W_{\text{net}} = W_\phi - \frac{1}{2}W_\phi^2 = [2\phi]^{-1}$) across the three-dimensional spherical radiation-pressure enthalpy ratio ($h_E/\rho_E = 4/3$) and the Stokes compressible dilation factor ($\frac{2}{3}\delta^*/r$) of the Asymptotic Suction Boundary Layer (ASBL) derives the $\overline{\text{MS}}$ weak mixing angle $\sin^2\hat{\theta}_W(M_Z) = 3/[8\phi(1 + \frac{2}{3}\delta^*/r)] = 0.23123$ ($+0.55\sigma$ from PDG 2024). Across the Total Internal Reflection ($\Gamma = 1$) horizon interface, Mohr's Circle principal stress equalization ($\beta = \pi/4$) fixes the on-shell boson mass ratio to $\cos\theta_W^{\text{OS}} = M_W/M_Z = \frac{1}{2}(1 + \phi^{-2} + \alpha^{-1}/N_{\text{cym}}) = 0.881311$ ($\sin^2\theta_W^{\text{OS}} = 0.22329$, $+0.34\sigma$). When energy injected into a vortex core exceeds the three-generation Chirikov shell limit ($n_{\max} = 2$), the boundary layer undergoes hydrodynamic cavitation governed by the Ffowcs Williams-Hawkings (FW-H) aeroacoustic equation. Driving the fundamental spherical overtone ($\Lambda_1 m_e = [1 + \frac{3}{2}\alpha^{-1}]m_e$) to dipole and monopole cavitation over a closed $2\pi$ circulation loop against the inviscid Spindle Torus baseline ($\Theta_\phi = 360\phi^{-2}$) predicts $M_Z = 2\pi\Theta_\phi\Lambda_1 m_e = 91.1926 \pm 0.0191\text{ GeV}/c^2$ ($+0.26\sigma$), $M_W = M_Z\cos\theta_W^{\text{OS}} = 80.3692\text{ GeV}/c^2$ ($0.00\sigma$), a spin-$0$ monopole thickness resonance of $M_H = M_Z(1 + \alpha^{-1}/360)/[1 + \frac{3}{2}(\delta^*/r)] = 125.252\text{ GeV}/c^2$ ($+0.47\sigma$ from PDG 2024; $+0.01\sigma$ from PDG 2022), and a cavitation scale of $v_{\text{EW}} = 246.29\text{ GeV}$ ($+268\text{ ppm}$).