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 cosmological singularity and the non-supersymmetric vacuum energy divergence. 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 stochastic dynamics, and the counter-phase elastic response of the projected electric Weyl tensor, we demonstrate the realization of a stable non-singular quantum bounce, the suppression of UV radiative instability, and the dynamical selection of the observed cosmological constant Λ₄ ~ 10⁻¹²² M_Pl².