This work presents RMB IV, the fourth installment of the Space–Matter–Motion (RMB) Theory by Davide Dellomonaco. Building upon RMB I–III, which established the conceptual and mathematical foundation of RMB and introduced the frequency charge as a universal coupling factor for space deformation, RMB IV integrates the groundbreaking 2025 counterexample by Hannah Mira Cairo to the Mizohata–Takeuchi conjecture. This counterexample allows the inclusion of fractal and non-smooth Fourier structures into the RMB framework, closing a key mathematical gap that previously prevented modeling of resonance phenomena beyond smooth functions. With this extension, RMB IV provides a precise description of galactic rotation curves, flyby anomalies, and quantum entanglement phenomena without invoking dark matter. Residual analyses of Milky Way data (Gaia DR3) and external galaxies (NGC 3198) demonstrate a remarkable improvement over Newtonian predictions. The results show that fractal resonance functions enable the observed flatness of galactic rotation curves, while simultaneously providing a natural interpretation of quantum entanglement as a resonance phenomenon within a shared frequency domain. RMB IV thus marks a decisive advancement in the RMB program, bridging astrophysics and quantum physics within a unified physical principle and laying the foundation for future experimental validation through Casimir effect measurements, 21 cm line surveys, and precision spacecraft flybys.