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 (θ₁₂CKM, θ₂₃CKM, θ₁₃CKM, or |Vᵤₛ|, |Vcb|, |Vub|) and one CP-violating phase (δCPCKM). This paper presents a self-contained, parameter-free derivation of all four quantities, alongside the Jarlskog invariant (JCKM) and the complete 3 × 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 (TCMB = 2.72548 ± 0.00057 K). Whereas un-knotted neutrino waves couple freely across the Kolmogorov-Arnold-Moser (KAM) Spindle Torus (W_φ = φ⁻²) to produce large PMNS mixing angles, quark harmonic shells are confined inside the Γ = 1 spherical horizon (δ^*ₜₒₜₐₗ/r = 7/3δ^*/r, dual exclusion width Δexcl = 14/3δ^*/r ≈ 0.01607) of the Asymptotic Suction Boundary Layer (ASBL). Projecting the net Spindle Torus winding (Wₙₑₜ = [2φ]⁻¹) across the 3/4 spherical energy-to-enthalpy ratio and $p = 2$ exterior poloidal exclusion sheaths (sinθ₁₂CKM = 3/[8φ(1 + 2Δexcl)] = 0.22455), while evaluating internal cavity mass-eigenstate diagonalization via the n = 0 ↔ 1 trefoil lobe inertia ratio (√md/mₛ[1 + 3/2δ^*/r] = 0.22500), derives the Cabibbo angle within 0.00σ--0.31σ of observation and mechanically resolves the experimental Cabibbo Angle Anomaly between semileptonic kaon decay (|Vᵤₛ|) and unitarity-constrained global fits (λ). Coupling the central spindle overlap (W_φ² = φ⁻⁴) across the spherical-to-exclusion boundary ratio (δ^*ₛₚₕ/Δexcl = 2/7) yields sinθ₂₃CKM = |Vcb| = 2/7φ⁻⁴(1 + δ^*/r) = 0.041829 (+0.01σ), while evanescent radial boundary-layer transmission dressed by the Mohr-partitioned 1 ↔ 3 spindle overlap (1/2φ⁻⁴) yields sinθ₁₃CKM = |Vub| = (δ^*/r)(1 + 1/2φ⁻⁴) = 0.003694 (+0.03σ). Finally, partitioning the 2π poloidal circulation across the $p = 2$ trefoil strands (π W_φ) compressed by the meridian spindle overlap (1 + 1/3φ⁻⁴) derives δCPCKM = πφ⁻²/(1 + 1/3φ⁻⁴) = 1.14433 rad (65.565^∘, -0.01σ to -0.10σ from PDG 2024; +0.01σ from PDG 2022) and JCKM = 3.08 × 10⁻⁵ (-0.23σ from PDG 2024; 0.00σ from PDG 2022).