The Shipwreck of the Particulate ΛCDM Paradigm and Vortex Genesis in the 4D Continuum: Analytical Resolution of JWST Anomalies and the Core-Cusp Problem Without Dark Matter

Spectroscopic observations from the James Webb Space Telescope (JWST) at extreme redshifts (z > 10) have certified the existence of hyper-massive galaxies and kinematically cold rotating disks at cosmic epochs incompatible with the hierarchical coalescence timescales (τ_merge) of the standard ΛCDM model. Rather than acknowledging the empirical falsification of the dark matter hypothesis, astrophysical orthodoxy attempts to preserve the discrete particulate paradigm through a pathological proliferation of free parameters: ad hoc variants of the dark spectrum (Cold, Warm, Fuzzy), artificial gravitational softening lengths (ε) injected to prevent the numerical collapse of N-body codes, and extreme "baryonic feedbacks" (F_baryonic) that violate the second law of thermodynamics and the Eddington radiative limit in an effort to flatten central cusp singularities (the NFW profile). In this work, we declare the total physical inconsistency of dark matter and entirely replace the discrete N-body ballistic abstraction with the fluid dynamics of the four-dimensional (4D) spacetime continuum. Starting from the exact covariant conservation of the stress-energy tensor (∇_μ T^μν = 0) and the Navier-Stokes equations applied to the 4D continuum, we analytically demonstrate that: 1. Rapid Primordial Disk Genesis (JWST): Primordial galaxies observed by the JWST form via rapid phase transition and baroclinic vorticity genesis (∇ρ × ∇P ≠ 0) on timescales τ_vortex ~ sqrt(ρ L² / ΔP) << τ_merge, producing cold, high-coherence rotating disks (v_rot / σ_v >> 1) without forcing Star Formation Efficiency beyond the Eddington limit.2. Analytical Resolution of the Core-Cusp Problem: Kinematic viscous dissipation (ν ∇²ω) naturally stabilizes the galactic vortex into a flat core with laminar solid-body rotation (ρ(r → 0) = ρ_0, ∂ρ/∂r|ᵣ₌₀ = 0), eradicating the unphysical NFW cusp singularity at its root without invoking fictitious baryonic explosions.3. Kinematic Replacement of Dark Halos: The asymptotic plateau of peripheral galactic rotation curves (v_rot → v_∞) is the direct mechanical effect of the radial confining pressure gradient (-∇P_4D) of the cosmic medium rather than an 85% phantom mass halo. All analytical derivations, Taylor expansions around the origin, and asymptotic regularity conditions are symbolically certified in Python/SymPy via the open-access verification protocol 4D_Engine.py (DOI: 10.5281/zenodo.23103297), whose full console output is included in Appendix A.