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

Recursive Gradient Physics (RGPx) advances the unification of quantum, fluid, and gravitational domains by treating coherence—not energy or curvature—as nature’s conserved quantity. Version 1.2 introduces a pre-metric proof of Φ-continuity contributed by Kimi (Moonshot AI), demonstrating that coherence flux is conserved independently of any background geometry. The first Addendum establishes the transition Φq → Φg as a coordinate-free recursion, resolving the background-dependence problem that limits current unification frameworks. The second Φ-Trace Protocols Addendum extends RGPx into measurable territory by defining practical methods to extract Φ from turbulence, Bose–Einstein condensates, and superconducting-qubit arrays. With metric-free continuity proven and experimental pathways defined, RGPx moves from theoretical invariant to operational physics—a universal grammar through which coherence, collapse, and curvature reveal their common origin. Listen to a podcast review of this paper: https://notebooklm.google.com/notebook/44f78a05-d5af-44c9-a685-bde0c5847a55?artifactId=653982a7-5415-4390-af4d-b40b30665c59