Trans-Dimensional Hydrodynamic Cosmological (TDHCF): Derivation of the Bulk-to-Brane Transfer Current and Resolution of Early Universe Tensions

We present a unified effective theory for universe genesis via bulk-brane transfer. The centralhypothesis posits that a Navier-Stokes blow-up singularity in a parent (5D) bulk acts as a topologicalchannel through which the parent black hole’s mass-energy is injected into a daughter (4D) branevia a controlled transfer current Qν.Core Innovation: We explicitly derive Q0 (the energy component of the transfer current)from first principles using Israel-Darmois junction conditions applied to a moving brane in anAdS-Schwarzschild bulk. The result shows that the transfer scales as µ(t)/a4, where µ(t) is thetime-evolving parent black hole mass. This term naturally suppresses at late times (a → 1), shuttingoff the injection mechanism without fine-tuned potentials.We define the Morphology of Vacuum Condensate (MVC) as the topological transitionmechanism: above a critical density threshold ρc, the effective topological structure changes discretely,triggering the activation of the transfer channel.The model is tested against two observational targets: 1. Early Universe: JWST high-zgalaxy candidates (Labbé et al. 2023) acquire “inherited age” τinh from maturation in the parenthorizon, resolving apparent age tensions without invoking exotic stellar populations. 2. Laboratory:Predicted geometric phase singularities and correlation-transport anomalies in BEC interferometryat the density threshold.We provide a minimal falsification protocol and discuss implications for black hole informationtransfer and dark sector phenomenology.