Relational Gravity: Microphysically Allowed Forms of the Informational Deviation δIcoh A Technical Companion to “Coherence from Atoms to Cosmos”

NOTE: This work is conceptual and exploratory. It outlines early motivations and heuristic ideas, and should not be taken as identical to the phenomenological models currently under development — including both the structural Δw approach and the scalar-field formulation used in technical perturbation and MCMC analyses. It is intended as background context rather than a formal physical model. This technical companion refines the results of “Relational Gravity: Coherence from Atoms to Cosmos” by deriving the microphysically allowed forms of the informational deviation δIcoh. In Relational Gravity (RG), spacetime curvature is proportional to coherent information density, G = κ Icoh, with κ fixed by nuclear microphysics. Small departures δIcoh from the nuclear-determined background generate a universal late-time correction δw ≈ +0.07, a zero-parameter prediction previously shown to be consistent with DESI DR2 BAO-only measurements (Hummel 2025). This document provides the formal derivation of the master equation governing informational perturbations and characterizes the four dynamical regimes compatible with microphysics: wave-like, diffusive, solitonic, and stochastic. These produce a narrow, falsifiable family of deviations in δIcoh(a), linking nuclear physics directly to late-time cosmology. The report is a technical companion to “Coherence from Atoms to Cosmos,” extending the physical intuition of the conceptual paper with mathematical structure and testable predictions.