Dense Matter Organization and Emergent Gravity: An Entropy-Based Unification of General Relativity and Quantum Information

This work presents the development of an emergent gravity model based on quantum entropy density gradients ($\rho_{\rm QM}$), aimed at explaining galaxy rotation curves without invoking dark matter. In this Phase 8 paper, we introduce the theoretical framework, derive the effective gravitational acceleration from entropy considerations, and demonstrate preliminary fits to publicly available rotation curve data. Bayesian likelihood methods are applied to evaluate model performance, and the top 10 outlier galaxies are identified for further analysis. This phase lays the groundwork for Phase 9, where all 175 galaxies are analyzed, and a fully interactive browser-based visualization is provided.