The Energy Information Gradient: General Relativity's Weak-Field Signatures and the Radial Acceleration Relation from a Discrete Information-Exchanging Substrate

Open gap: weak-field general relativity and the galactic radial acceleration relation are usually explained by different mechanisms, with little shared microphysics and few pre-registered falsifiers. This paper tests whether both can arise from a discrete lattice of information-exchanging units whose temporal “tick” and spatial “pitch” shift reciprocally. Persistent structure imposes a maintenance cost on the substrate; gravity is read as the response to gradients in that cost. From reciprocal tick/pitch change, the framework derives three tested weak-field results with zero adjustable parameters: PPN γ = 1 and β = 1, and an active gravitational source of the form ρ + 3p (hypothesis-ceiling results). At galactic scales the same substrate yields a parameter-free RAR form; convergence with Cadoni & Tuveri is noted without claiming priority. Because the floor is tied to the cosmological horizon, a0 is predicted to drift with redshift as H(z)/H0 — registered as a falsifier before data comparison. The first intermediate-redshift test is reported in full, with the derivation chain, ruled-out mechanisms, and falsifying observations listed explicitly. Version note: v1.1 (July 2026) incorporates the result that the specific microphysical mechanism tested for the acceleration floor does not produce a crossover at the coupling strength where matter formation occurs. Framework note (last): Energy Information Gradient (EiG) / tick–pitch substrate line.