Geometric Unification of Gravity and Quantum Mechanics via 5D Bulk-Brane Entanglement: Mathematical Foundations and Falsifiable Cosmological Signatures

**Falsifiable Prediction:** Δt ≈ 1.1 × 10⁻²⁴ µs × [E/GeV] × [D/Gpc] Submitted to NASA Fermi Team on July 4, 2026 for GRBs with z>1, E>10GeV. This work establishes the mathematical and physical consistency of the 5D Bulk-Brane Entanglement framework as a candidate theory for the unification of gravity and quantum mechanics. We demonstrate dynamical stabilization of the extra dimension without ad-hoc fields, derive the recovery of General Relativity and Newtonian gravity, and provide a geometric origin for the cosmological constant and dark energy with w = -1. Critically, the model yields three distinct, falsifiable astrophysical signatures: modified gravitational wave propagation testable by LISA, large-angle CMB suppression consistent with Planck anomalies, and enhanced early galaxy formation explaining JWST observations. This framework bridges quantum entanglement and spacetime geometry, offering a new paradigm for fundamental physics.