The Jones Prime Progression Gap Tree (JPPG Tree): Recursive Resonance, Fractal Geometry, and Zeta Alignment

The Jones Prime Progression Gap Tree (JPPG Tree) is a recursive, fractal-based model of prime number gaps, revealing hidden geometric and harmonic structures in their distribution. It encodes prime gaps as a hierarchical tree, visualizes them through waveforms and hyperbolic geometry, and explores potential connections to the Riemann zeta function. Computational analysis suggests Fibonacci-indexed prime gaps follow a universal scaling law linked to the golden ratio. The JPPG Tree provides a novel framework for understanding prime gaps through resonance, lattice embeddings, and arithmetic spacetime curvature.