This work presents CRT V3, an effective late-time cosmological extension of the Geometric Relay Theory built as a continuation of Minazzoli’s Entangled Relativity. The central hypothesis is that late-time expansion, structure growth, and the bounded variation of fundamental constants can be treated as different observable projections of a single coarse-grained matter–geometry disequilibrium kernel. The framework introduces a delayed nonlinear controller for the mean geometric relay tension and a two-branch architecture: a strong branch associated with structure growth and late-time expansion, and a weak branch associated with the admissible drift of the fine-structure constant. This architecture leads to four falsifiable predictions: P1, a bounded present-day drift of α; P2, a structure–expansion correlation; P3, a hierarchical observable delay in which structuration precedes the expansion response; and P4, a nonlinear saturation of the strong branch. The V3 version substantially extends previous formulations by adding a quasi-static derivation map of the effective coefficients, a direct empirical test of the P3 causal ordering, a second-order correction to the relay closure, a halo-model derivation of the disequilibrium variance, a leading-order source-theory identification of the constants \ (k\), \ (m₀²\), and \ (\) from the Entangled Relativity action, and an exact canonical normalisation from the conformal transformation to the Einstein frame. In this leading-order source-theory reading, the relay constants are identified as \ (k=3/4\), \ (m₀²= (8 G/3) ₀\), \ (= (8 G/3) R\), and \ (M ₄₅₅/M ₋=1/2\). Empirically, the framework is tested through a hierarchical programme involving BOSS, eBOSS, WiggleZ, and DESI DR1 data. The pre-DESI block supports an approximately constant reduced coefficient \ (₀1\), while the DESI DR1 extension suggests a redshift-dependent signal compatible with the P3/P4 interpretation. A halo-model calculation of the nonlinear disequilibrium variance, based on virialised structures and velocity dispersion, reproduces a DESI-like slope within the exploratory dataset. This document does not claim definitive observational validation. Its status is that of a strong exploratory consistency framework and a falsifiable theoretical programme. The main contribution is to connect, within a single structured chain, Entangled Relativity, geometric relay dynamics, effective coefficient closure, nonlinear structure formation, and late-time cosmological observables. The decisive tests remain future DESI DR2 full-shape measurements, Euclid data, improved covariance treatment, full second-order ER perturbation theory, and calibration of the halo-model variance against simulations.
Olivier Lane-Larquey (Wed,) studied this question.