Spiral Harmonic Geometry: A Universal Encoding Framework for Multiscale Containment and Resolution

This paper introduces a rigorous mathematical framework for spiral harmonic geometry as a unifying structure underlying multiscale physical and computational systems. We define and derive a fractal-encoded coordinate transformation θ(k) = α log(k)/k that governs recursive containment and orthogonality within high-dimensional systems. This geometry provides a falsifiable mechanism for energy stabilization, computational resonance control, and topological isolation across differential equation spaces. Applications include Navier-Stokes regularity, Yang-Mills gap stability, NP-complete problem encoding, and connections to the Riemann Hypothesis via prime distribution symmetry.