Entropic Geometry: The Unitary Dynamics of Energy and Causal Information in an Emergent Spacetime

This paper proposes Entropic Geometry, a framework that reinterprets spacetime as an emergent phenomenon arising from the unitary coupling of Energy (E) and Causal Information (Entropy, S). We challenge the classical view of entropy as a secondary byproduct of disorder, postulating instead that it serves as the fundamental ”causal record” that preserves the history and stochastic outcomes of physical transitions. By defining every physical event as a functional mapping of an energy-entropy pair, we demonstrate that the accumulation of ”residual information” in high-interaction zones accounts for galactic rotation anomalies (Dark Matter) and that vacuum expansion is a systemic requirement for information capacity (Dark Energy). This framework provides a falsifiable alternative to ΛCDM, predicting energy-dependent gravitational shifts without the necessity of undetected particles.