Derivation of the Strong Coupling, Proton-to-Electron Mass Ratio, and Quark Mass Spectrum via $(2,3)$ Trefoil Vortex Topology in a Compressible Superfluid

The Standard Model of particle physics requires eight unconstrained empirical parameters to specify the strong and quark-mass sectors: the strong CP phase ($\bar{\theta}_{\text{QCD}}$), the strong coupling constant ($\alpha_s(M_Z)$), and six quark masses ($m_u, m_d, m_s, m_c, m_b, m_t$), while relying on numerical lattice approximations to estimate the proton-to-electron mass ratio ($m_p/m_e$). This paper presents a self-contained, parameter-free analytical derivation of all nine quantities by modeling baryons as $(p, q) = (2, 3)$ trefoil torus knot vortices within a three-dimensional ($D = 3$) compressible Two-Fluid Bose-Einstein Condensate (BEC) at the Cosmic Microwave Background baseline ($T_{\text{CMB}} = 2.72548 \pm 0.00057\text{ K}$). At the Total Internal Reflection ($\Gamma = 1$) saturation horizon, exact achiral icosahedral inversion symmetry ($|I_h| = 120$), Sturm-Liouville self-adjointness, and the absence of transverse baroclinic radiation ($\nabla\rho \times \nabla P = \mathbf{0}$) mandate $\bar{\theta}_{\text{QCD}} \equiv 0$. Coupling the primary Kolmogorov-Arnold-Moser (KAM) Spindle Torus winding ($W_\phi = \phi^{-2}$) to the Mohr-partitioned net minor-tube winding ($W_{\text{net}} = [2\phi]^{-1}$) across $D = 3$ spatial axes of the Asymptotic Suction Boundary Layer (ASBL) derives $\alpha_s(M_Z) = [2\phi^3(1 + \frac{1}{3}\delta^*/r)]^{-1} = 0.11790$ ($-0.11\sigma$ from PDG 2024; $0.00\sigma$ from PDG 2022). Integrating the $p \cdot q = 6$ trefoil crossing determinant across the five-dimensional standing-wave phase volume ($\int_{[0,\pi]^5}(p\cdot q)\,d\Omega_5 = 6\pi^5$) and the $\frac{3}{4}$ spherical energy-to-enthalpy ratio yields $m_p/m_e = 6\pi^5[1 + \frac{3}{4}(\delta^*/r)/\alpha^{-1}] = 1836.152678$ ($+2.2\text{ ppb}$ from CODATA 2022). Finally, evaluating the $n \in \{0, 1, 2\}$ harmonic shell hierarchy and Ffowcs Williams-Hawkings (FW-H) core cavitation across the $p = 2$ (up-type) and $q = 3$ (down-type) trefoil branches derives $m_u = 2.160\text{ MeV}/c^2$ ($0.00\sigma$), $m_d = 4.670\text{ MeV}/c^2$ ($-0.43\sigma$ from PDG 2024; $0.00\sigma$ from PDG 2022), $m_s = 93.20\text{ MeV}/c^2$ ($-0.37\sigma$), $m_c = 1.2723\text{ GeV}/c^2$ ($-0.15\sigma$), $m_b = 4.180\text{ GeV}/c^2$ ($-0.43\sigma$ from PDG 2024; $0.00\sigma$ from PDG 2022), and $m_t = 172.62\text{ GeV}/c^2$ ($+0.17\sigma$).