Topological Localization and Emergent Cosmological Inversion in Warped AdS₅

Version 2.0 This work presents a unified mathematical framework for warped five-dimensional (AdS₅) spacetime based on a single geometric stability principle governing localized brane configurations. The framework proposes that physically admissible branes satisfy a vanishing pullback of the five-dimensional Ricci tensor, leading to a finite localized brane ensemble selected through topological consistency rather than arbitrary assumptions. From this construction, the model derives a discrete pressure hierarchy, thermodynamic energy exchange between neighboring branes, and an emergent cosmological inversion that produces an effective evolution of the dark-energy equation of state without introducing adjustable free parameters. The theory remains compatible with General Relativity within its tested domain and is intended as a higher-dimensional mathematical extension rather than a replacement. Several quantitative observational predictions are presented, including comparison with DESI DR2 cosmological measurements and additional falsifiable predictions for future observations.