Unified Theory of GQI- Gravity: Informational Entropy Scaling and the Resolution of the Dark Sector Crisis.

This compendium presents the formal derivation and empirical validation of the Geometric Quantum Information Gravity (GQI-) framework. Moving beyond the CDM paradigm, this work derives the scalar gravitational degrees of freedom from the scaling limit of Araki-Uhlmann relative entropy and Tomita-Takesaki modular flow. Key Technical Highlights: Formalism: Derivation of the Modified Einstein Equations (MEE) including a non-linear Cubic Galileon sector for Vainshtein screening. Empirical Validation: Full statistical analysis of the SPARC database (n=175), demonstrating a 73. 5% reduction in residuals compared to standard NFW dark matter profiles. Universal Scaling: First-principles derivation of the MOND acceleration scale a₀ from cosmological horizon entanglement. Note on Peer Review: The following derivations and numerical results are submitted to the scientific community for authoritative technical scrutiny. This work is intended for researchers possessing the requisite analytical proficiency in Information Geometry and Gravitational Formalism to rigorously vet the non-linear coupling and stability of the field. Mail Me