Emergent Gravity from Informational Geometry and Informational Density

We propose a theoretical framework in which gravitational dynamics and spacetime geometry emerge from the informational structure of physical systems. The central notions are \textbf{informational density} $\rho_I$, which quantifies the local concentration of distinguishable informational states, and \textbf{informational geometry}, which encodes the relational organization of these states. We construct an effective informational stress-energy tensor and derive modified gravitational equations that recover General Relativity in the weak informational regime. In regimes of high informational density or strong gradients, the framework predicts systematic deviations from classical gravity. Black holes are reinterpreted as surfaces of informational saturation, while inertial mass emerges as a consequence of informational inertia. The theory offers a unified informational perspective on gravity, black hole thermodynamics, and cosmology, and yields falsifiable predictions that can be tested with precision gravitational and cosmological observations.