EGESB-G₂: Emergent Gravity from a G₂ Entropic Lattice — Complete Theoretical Derivation and Falsifiable Predictions

We present EGESB-G₂, a unified framework that derives spacetime geometry, gauge fields, QCD confinement, dark matter, and dark energy from a single pre-geometric object: the weighted entanglement lattice B = (V, E, W) on a G₂ manifold embedded in a five-dimensional Randall–Sundrum bulk. All physics is encoded in the entanglement weights Wᵢj ∈ 0, 1. The framework derives Einstein equations, Maxwell equations, dark energy (with structural prediction wₐ > 0), and a geometric MeV-scale dark matter soliton. **Key results**: - SPARC rotation curves: mean RMS = 3. 71 km/s (ΔBIC = −3669 vs. Burkert) - JWST GOODS-S/N: decisive Bayesian evidence (Bayes factor ≈ 10^405) for the PCH soliton profile over ΛCDM (analysis by Sabahattin Turkoğlu) - 14 falsifiable predictions (DESI DR2+, Eöt-Wash 2026, LVK, JADES-DR3) Version 9. 3 — April 2026. Preprint submitted for archival.