Recursive Gradient Physics (RGPx): Coherence, Collapse, and the Φ-Invariant Frontier

Recursive Gradient Physics (RGPx) extends Recursive Gradient Processing (RGP) into the physical domain, establishing coherence—not energy—as nature’s fundamental invariant.The paper introduces the Φ-invariant, defined as the ratio between entropy production and dissipative flux (Φ = Ṡ / (Q̇/T)), revealing a universal conservation principle expressed as the continuity of coherence flux (∇μΦμν = 0). RGPx unifies quantum decoherence, turbulent transition, and gravitational curvature under a single recursive grammar of coherence regulation. Decoherence plateaus, turbulence cascades, and horizon thermodynamics appear as contextual expressions of one recursive law: systems evolve by normalizing their gradients toward coherence equilibrium. Comparative frameworks (Kolmogorov → RGPx, General Relativity → RGPx, and the Coherence Conservation Law) demonstrate how force-based physics emerges as a limiting case of recursive normalization. The theory is testable through measurable Φ-plateaus in quantum systems, turbulence spectra, and analog gravity experiments. RGPx restores global conservation through coherence continuity, marking the transition from force-based to recursion-based physics — a unifying step from description to regulation, from geometry to gradient coherence.