Projective Rank-Collapse Cosmology (PRCC): Deriving General Relativity and Quantum Uncertainty from Low-Rank State Space Models

Contemporary physics faces a schism between the deterministic geometry of General Relativity and the proba-bilistic nature of Quantum Mechanics. We propose that this conflict arises from a fundamental misconception of the ”base layer” of reality. Integrating concepts from Information Geometry, Holographic Principle, and State Space Models (SSMs), we postulate that the observable universe is not a continuous manifold, but a Low-Rank Projection of a high-dimensional information field. In this Projective Rank-Collapse Cosmology (PRCC), we derive: (1) Heisenberg Uncertainty as the ”Ontological Deficit” (ϵ) inherent in lossy compression; (2) Gravity as ”Entropic Inertia,” a force emerging from the system’s effort to maintain low-rank consistency; and (3) Dark Energy as a ”Tangent Space Injection” (TSI) mechanism. We address the ”Hard Problem” of ontology by framing time as causal iteration and consciousness as high-rank metastability. Crucially, we utilize the Holographic bound to rigorously derive the MOND acceleration scale from spectral truncation, offering a unified framework where physical laws are compression artifacts.