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 (θ̄QCD), the strong coupling constant (αₛ(MZ)), and six quark masses (mᵤ, md, mₛ, mc, mb, mₜ), while relying on numerical lattice approximations to estimate the proton-to-electron mass ratio (mₚ/mₑ). 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 (TCMB = 2.72548 ± 0.00057 K). At the Total Internal Reflection (Γ = 1) saturation horizon, exact achiral icosahedral inversion symmetry (|Iₕ| = 120), Sturm-Liouville self-adjointness, and the absence of transverse baroclinic radiation (∇ρ × ∇ P = 0) mandate θ̄QCD ≡ 0. Coupling the primary Kolmogorov-Arnold-Moser (KAM) Spindle Torus winding (W_φ = φ⁻²) to the Mohr-partitioned net minor-tube winding (Wₙₑₜ = [2φ]⁻¹) across $D = 3$ spatial axes of the Asymptotic Suction Boundary Layer (ASBL) derives αₛ(MZ) = [2φ³(1 + 1/3δ^*/r)]⁻¹ = 0.11790 (-0.11σ from PDG 2024; 0.00σ from PDG 2022). Integrating the p · q = 6 trefoil crossing determinant across the five-dimensional standing-wave phase volume (∫[0,π]⁵(p· q)\,dΩ₅ = 6π⁵) and the 3/4 spherical energy-to-enthalpy ratio yields mₚ/mₑ = 6π⁵[1 + 3/4(δ^*/r)/α⁻¹] = 1836.152678 (+2.2 ppb from CODATA 2022). Finally, evaluating the n ∈ \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 mᵤ = 2.160 MeV/c² (0.00σ), md = 4.670 MeV/c² (-0.43σ from PDG 2024; 0.00σ from PDG 2022), mₛ = 93.20 MeV/c² (-0.37σ), mc = 1.2723 GeV/c² (-0.15σ), mb = 4.180 GeV/c² (-0.43σ from PDG 2024; 0.00σ from PDG 2022), and mₜ = 172.62 GeV/c² (+0.17σ).