Hierarchical Drainage Dynamics on 4-Manifold Topology: Vortex Spiral Geometry, Stability via Mass Loss, and Universal Phase Recirculation

Standard ΛCDM cosmology and General Relativity face a structural impasse regarding singularities, the information paradox, heat death driven by cosmic-scale entropy growth, dark matter halos postulated for galactic rotation curves, and the early-matured disk galaxies observed by the James Webb Space Telescope (JWST) in the early universe. In this study, it is demonstrated that the universe is not an isolated, expanding 3-dimensional box, but rather a dynamic, closed-circuit thermodynamic fluid system undergoing continuous phase transitions on a non-orientable 4-dimensional Klein manifold. Galactic morphologies are modeled as a hierarchical hydraulic drainage network formed by the supermassive collector at the center and hundreds of millions of stellar-mass black holes across the disk. The connection of capillary throats aligned along the arms to the central main throat in the sub-manifold directly generates logarithmic spiral arms in 3-dimensional space and the sterilized voids between these arms (vortex geometry). It is analytically derived that collapse thresholds are a dynamic function of the local potential gradient, that a rapid decompression-merger cycle operates at the center, and that the siphon suction created behind the mass transiting the throat causes the mass of the central black hole to appear larger than its geometric horizon. The 13-billion-year stability of galaxies is explained by mass not accumulating internally, but being drained to the cosmic boundary plateau in the 4th dimension (dM/dt < 0). This drainage confirms an eternal recirculation ∮︁ mechanism ( dS = 0) where galaxies deplete and are replaced by new galaxies born from fresh hydrogen filtering from the boundary.