Title: First-Principles Derivation of Φ₀(ρ,T) from a Warped Extra Dimension with Thermal Cutoff Author: Ali Alhwarat Jordan Date: 2026-05-28 Version: 1.0 License: Creative Commons Attribution 4.0 International (CC-BY-4.0) Abstract: We present a first

This record documents the first-principles prediction of the metric potential Φ₀(ρ,T) from a 5D Randall-Sundrum brane-world with bulk scalar. Key result: Φ₀ = 1.21 × tanh[(ρ - 1.02×10^{-23})/2.05×10^{-23}] × exp(-k_B T / 0.044 eV) The model contains zero free parameters. All scales derive from the 5D action or the mode number N = 24.22255336. Predictions: 1. Cosmic voids exhibit Φ₀ = -0.091 ± 0.022, verified on SDSS DR7 catalog of 892 voids.2. Solar System and neutron stars recover GR due to thermal suppression. Falsifiable by CSST 2026. If confirmed, this constitutes the first direct evidence for a warped extra dimension. Full derivation and 21-system dataset provided in accompanying files. More details coming soon [email protected]