Phase 6: Microscopic Origin of the Entropic Action — Holographic Vacuum Information and Emergent Gravity

This upload presents Phase 6 of an emergent gravity framework developed across prior phases, focusing on the microscopic origin of the entropic action responsible for modified gravitational dynamics in the weak-field regime. Earlier phases established that a conserved entropy functional, when varied with respect to the gravitational acceleration field, reproduces observed galactic phenomenology without invoking particle dark matter. The remaining open question addressed here is the physical origin of the logarithmic entropy term used in the action. Phase 6 provides a minimal holographic interpretation. Vacuum degrees of freedom are treated as coarse-grained information rather than energy. Weak gravitational acceleration truncates local entanglement wedges associated with holographic screens, reducing the number of accessible vacuum microstates. Because entropy is defined as the logarithm of the number of accessible microstates, this truncation naturally yields a logarithmic entropy functional. A universal acceleration scale emerges from saturation of holographic information flow and is not introduced as a free parameter. The construction avoids the quantum vacuum energy divergence problem because vacuum information does not gravitate directly; only entropy gradients sourced by baryonic matter enter the field equations. The derivation is explicitly limited to weak-field conditions and scalar entropic response. Failure regimes are clearly stated, including cluster cores, neutron stars, and black hole horizons, where nonlinear holographic effects are expected to dominate. This phase completes the conceptual foundation of the theory while preserving falsifiability and prepares the framework for further stress-testing and observational confrontation.