Derivation of the CKM Quark Mixing Matrix and CP-Violating Phase via $(2,3)$ Trefoil Vortex Topology in a Compressible Superfluid

In the Standard Model of particle physics, the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix requires four unconstrained empirical parameters: three inter-generational mixing angles ($\theta_{12}^{\text{CKM}}, \theta_{23}^{\text{CKM}}, \theta_{13}^{\text{CKM}}$, or $|V_{us}|, |V_{cb}|, |V_{ub}|$) and one CP-violating phase ($\delta_{\text{CP}}^{\text{CKM}}$). This paper presents a self-contained, parameter-free derivation of all four quantities, alongside the Jarlskog invariant ($J_{\text{CKM}}$) and the complete $3 \times 3$ CKM magnitude matrix, 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 ($T_{\text{CMB}} = 2.72548 \pm 0.00057\text{ K}$). Whereas un-knotted neutrino waves couple freely across the Kolmogorov-Arnold-Moser (KAM) Spindle Torus ($W_\phi = \phi^{-2}$) to produce large PMNS mixing angles, quark harmonic shells are confined inside the $\Gamma = 1$ spherical horizon ($\delta^*_{\text{total}}/r = \frac{7}{3}\delta^*/r$, dual exclusion width $\Delta_{\text{excl}} = \frac{14}{3}\delta^*/r \approx 0.01607$) of the Asymptotic Suction Boundary Layer (ASBL). Projecting the net Spindle Torus winding ($W_{\text{net}} = [2\phi]^{-1}$) across the $\frac{3}{4}$ spherical energy-to-enthalpy ratio and $p = 2$ exterior poloidal exclusion sheaths ($\sin\theta_{12}^{\text{CKM}} = 3/[8\phi(1 + 2\Delta_{\text{excl}})] = 0.22455$), while evaluating internal cavity mass-eigenstate diagonalization via the $n = 0 \leftrightarrow 1$ trefoil lobe inertia ratio ($\sqrt{m_d/m_s}[1 + \frac{3}{2}\delta^*/r] = 0.22500$), derives the Cabibbo angle within $0.00\sigma$--$0.31\sigma$ of observation and mechanically resolves the experimental Cabibbo Angle Anomaly between semileptonic kaon decay ($|V_{us}|$) and unitarity-constrained global fits ($\lambda$). Coupling the central spindle overlap ($W_\phi^2 = \phi^{-4}$) across the spherical-to-exclusion boundary ratio ($\delta^*_{\text{sph}}/\Delta_{\text{excl}} = 2/7$) yields $\sin\theta_{23}^{\text{CKM}} = |V_{cb}| = \frac{2}{7}\phi^{-4}(1 + \delta^*/r) = 0.041829$ ($+0.01\sigma$), while evanescent radial boundary-layer transmission dressed by the Mohr-partitioned $1 \leftrightarrow 3$ spindle overlap ($\frac{1}{2}\phi^{-4}$) yields $\sin\theta_{13}^{\text{CKM}} = |V_{ub}| = (\delta^*/r)(1 + \frac{1}{2}\phi^{-4}) = 0.003694$ ($+0.03\sigma$). Finally, partitioning the $2\pi$ poloidal circulation across the $p = 2$ trefoil strands ($\pi W_\phi$) compressed by the meridian spindle overlap ($1 + \frac{1}{3}\phi^{-4}$) derives $\delta_{\text{CP}}^{\text{CKM}} = \pi\phi^{-2}/(1 + \frac{1}{3}\phi^{-4}) = 1.14433\text{ rad}$ ($65.565^\circ$, $-0.01\sigma$ to $-0.10\sigma$ from PDG 2024; $+0.01\sigma$ from PDG 2022) and $J_{\text{CKM}} = 3.08 \times 10^{-5}$ ($-0.23\sigma$ from PDG 2024; $0.00\sigma$ from PDG 2022).