Informational Phase Space Cosmology: A Geometric Framework for Entanglement, Curvature, and Memory Dynamics

We present Informational Phase Space Cosmology (IPSC), a complete and testable framework unifying geometry, quantum information, and topological memory through a novel application of Fisher information geometry. By deriving a curvature structure directly from quantum state correlators and modular Hamiltonians, we construct an entanglement-driven analog of general relativity. The framework incorporates informational geodesics, causal structure, and entropy flow, while supporting topologically protected memory sectors classified by homotopy, braid invariants, and modular holonomies. We quantize the resulting field theory, formulate RG flows and holographic dualities, and derive fixed-point theorems guaranteeing attractor geometries in modu- lar evolution. IPSC enables numerical simulation via topological invariants and makes distinctive predictions including entropic caustics, memory braiding transitions, and modular anomalies. As both a generalization and refinement of informational holography and geometric QFT, IPSC offers a viable path toward empirical falsifiability and theoretical closure in the physics of entanglement-structured spacetime.