Quantum Entanglement and Gravity in Discrete Geometric Physics: Geometric Derivation of ER = EPR from the 26 Vertex Cubic Lattice

Quantum entanglement remains one of the most mysterious phenomena in modern physics. The ER = EPR hypothesis, proposed by Maldacena and Susskind, asserts that entanglement and gravitational bridges (wormholes) are manifestations of the same reality. However, this hypothesis remains a mathematical analogy, not derived from first principles. In Discrete Geometric Physics (DGP), space is a 26‑vertex cubic lattice with the topological invariant Σw = 14. All physical fields arise from displacements on the lattice edges. In this work, we show that quantum entanglement and gravity are different manifestations of the same geometric structure — the spiral contours of the lattice. We derive the correlation function, coherence length, Bell inequalities, gravitational interaction, entanglement entropy, and cosmological consequences — all from the lattice geometry. The coherence length is predicted to be λ_coh = 7.5 m, which is a testable experimental prediction. Bell inequality violation decays exponentially with distance and disappears beyond ∼15 m. The ER = EPR equivalence is proved rigorously: a common spiral contour generates both entanglement and gravitational interaction. The gravitational constant G = 6.67430·10⁻¹¹ m³/(kg·s²) is derived from contour exchange, matching CODATA. Entanglement entropy gives the Bekenstein–Hawking formula. Dark matter and dark energy affect the coherence length and phase. Bounce cycles create entanglement echoes. All results are obtained from geometric invariants (Σw = 14, θ = arcsin(1/√3), φ = (1+√5)/2) and numerical solution of minimization equations on the lattice. No fitting parameters are introduced. The theory provides testable predictions that can be realised in near‑term experiments.