Dynamic Entanglement Adhesion: Emergent Spacetime Geometry and the Raychaudhuri Flow

We derive a background-independent framework for quantum gravity termed Dynamic Entangle- ment Adhesion (DEA). By defining an operator-valued coupling Jij that responds to local mutual information, we show that the continuum limit yields the Einstein field equations. We demonstrate that the Raychaudhuri equation, governing the convergence of worldlines, emerges from the first law of entanglement entropy. The flow of time is identified with the modular automorphism of the local von Neumann algebra, providing a natural resolution to the problem of time and a finite UV-fixed point that prevents singular collapses.