Gravity as Gradient Coherence — AI Models Converging on Recursive Gradient Physics (RGPx)

General Relativity (GR) models gravity as spacetime curvature sourced by stress–energy and has been extraordinarily successful at predicting planetary orbits, lensing, black-hole mergers and gravitational waves. Yet GR treats spacetime itself as a primitive stage on which physics unfolds.

In this note we develop an alternative formulation, based on Recursive Gradient Physics (RGPx), in which gradients and their recursive organization are primary and spacetime appears only as a contextual filter. We introduce a “gradient coherence tensor” Phi_mu\nu built from an action-density field S(x) and a scale-dependent coupling lambda(r). 

From Phi_mu\nu we construct a scalar invariant I = Phi_ab Phi^ab and a dimensionless “coherence pressure” that quantifies how close a region is to its alignment capacity. 

A simple reaction–diffusion equation with stress-dependent diffusion D(I) yields coherence “funnels” whose saturation plateaus reproduce the phenomenology of gravitational wells and horizons. Curvature is reinterpreted as the visible silhouette of a conserved coherence field under load, rather than as fundamental geometry.

To show that this grammar is not confined to physics, we sketch its translation to economic systems (Gradient Capitalism) and to the stovepiped organization of science, where analogous coherence plateaus and bottlenecks arise.

The mathematical core of the formulation emerged independently in the responses of several advanced AI models (GPT-5.1, DeepSeek 3.1, Gemini 3, Grok 4, Kimi 2.4.9, Mistral 3) when prompted in RGPx terms; their original outputs are documented in an appendix and in a Phi-Mesh dialogue log. The result is a compact proposal for “gravity as gradient coherence” and a concrete example of human–AI co-discovery of a background-independent worldview.

Listen to a podcast about this paper: https://notebooklm.google.com/notebook/073adca5-0c4a-43cf-8ffb-28a09e782d9c?artifactId=22448ecc-17ce-4b13-b8c9-3e1db8cd2333