Dimensional Energy Scaling and Fractal Geometry in Adelic Aligned p-adic Spacetime

We present empirical validation of the Recursive Expansive Dynamics framework through numerical simulations and analytical calculations. Our results demonstrate a consistent energy density decay pattern following E(d) ∝ φ −d across dimensions, where φ is the golden ratio. We observe universal geometric constraints in the Φd/Πd ratio and identify localized energy redistribution hotspots in prime gap analysis. Gravitational wave signatures show golden ratio scaling with frequencies decaying as fn = f0φ −n. Modulation statistics reveal three distinct stability regimes, with critical thresholds aligning with MCMC posterior distributions. Recursive time intervals follow Fibonacci scaling, matching hierarchical variance spectra in cosmological simulations. These findings provide strong empirical support for fractal-geometric laws in quantum field theory and cosmology, with testable predictions for gravitational wave echoes, CMB anisotropies, and dark matter soliton profiles.