Non-Equilibrium Holographic Brane Cosmology in AdS5: Effective Quantum-Gravitational Unification, Singularity Resolution, and Dynamical Vacuum Selection

An analytical framework of effective quantum gravity and brane cosmology is formulated that resolves the initial singularity, the non-supersymmetric vacuum energy divergence, and the loss of unitarity across cosmological horizons. The four-dimensional universe is modeled as a quasi-de Sitter 3-brane nucleated during gravitational collapse in an asymptotically AdS₅ bulk. By means of reduction to Type II₁ von Neumann factors, non-equilibrium Langevin stochastic dynamics, and the exact counter-phase elastic response of the projected electric Weyl tensor, the finite horizon entropy bound Smax ~ 10¹²² kB, the observed cosmological constant Λ₄ ~ 10⁻¹²² MPl², a stable non-singular quantum bounce, and holographic Yang-Mills color confinement with a positive mass gap are self-consistently derived.