The Observer-Potential Framework: A Unified Hyperbolic Model and Its Projections Across Classical, Quantum, and Thermodynamic Phenomena

Modern theoretical physics operates under a severe structural fracture: General Relativ-ity and Quantum Mechanics remain mathematically incompatible, non-linear fluid dynam-ics and multi-body gravitational systems suffer from analytical instabilities, and the SecondLaw of Thermodynamics dictates an inescapable cosmic heat death. This paper establishesthe Observer-Potential Framework (OPF), a unified physical paradigm that replacessmooth, continuous spacetime manifolds with a dynamic, discrete hyperbolic network. Bydefining the Observer ( ˆO) as an active boundary state operator and the Potential Field(Φ) as a localized scalar-vector energy distribution across a multi-scale hyperbolic tilingspectrum ({5, 4}, {7, 8}, {54, 55} ⇌ {55, 54}, and {34, 35}), we formulate a single, unifiedmathematical engine. We then project this master model across five physical regimes to si-multaneously resolve: the Quantum Measurement Problem, Navier-Stokes Smoothness, theGeneral Three-Body Problem, Black Hole and Supernova Singularities, and the Thermody-namic Arrow of Time. Finally, we derive the explicit boundary parameters for a NegentropySystem, establishing the architectural foundation for reactionless deep-space propulsion,zero-loss planetary infrastructure, and self-sustaining human capital systems