Fractal Seismic Scaling Laws of the Golden Function

We introduce a novel framework for seismic scaling based on the Golden Function, integrating fractal geometry and hierarchical φ-scaling to describe earthquake occurrence. By modeling earthquake magnitudes, released seismic energy, and temporal aftershock sequences as emergent properties of a φ-based fractal hierarchy, this approach establishes a mathematically rigorous connection between observed seismicity and the golden-ratio structure of fault networks. The framework naturally reproduces classical empirical laws, including the Gutenberg-Richter magnitude-frequency relation and the Omori law for aftershock decay, while providing a predictive, scale-invariant formulation grounded in the Pellis Function. Numerical simulations of φ-scaled fault systems demonstrate accurate replication of magnitude distributions, energy dissipation patterns, and temporal clustering, highlighting an intrinsic hierarchical organization in seismic phenomena. This methodology provides a unified, quantitatively robust perspective on earthquake dynamics and offers potential for enhanced seismic hazard assessment.