The Geometric Relay as an Effective Dark-Matter Response: Background Equivalence, Memory Filtering, and Open Perturbative Tests

This document presents a revised and more cautious synthesis of the Geometric Relay Programme interpretation of dark-matter phenomenology. The central idea is not that dark matter is simply “solved”, nor that the relay is already proven to be dynamically identical to a cold dark matter fluid. Rather, the paper argues that several background-level and effective linear observables usually attributed to CDM may be reinterpreted as consequences of a geometric relay response. The discussion is built on the Entangled Relativity action Lₘ²/R and on the scalar relay structure developed in the GRP. The relay is interpreted as an effective geometric response between matter and curvature. In this framework, the apparent non-baryonic contribution Omegacdm can be read as an effective relay tension rather than as an independently postulated dark substance. The paper reviews three main ingredients: 1. the effective CMB decoupling of the relay sector in the radiation-dominated regime; 2. the identification of a background relay density scale related to the galactic acceleration scale a0; 3. the role of memory filtering, which may allow the relay response to behave as a non-oscillating, CDM-like effective component in the reduced linear regime. This v2 explicitly incorporates the lessons of later GRP developments, especially the memory-closure v9 paper and the first CLASS mu-Sigma implementation. These later results refine the original claim: the relay should not be interpreted as exactly equivalent to a CDM fluid. Instead, it may reproduce part of the effective dark-matter phenomenology while predicting a mild dynamical-lensing split, encoded by mu (a) and Sigma (a). The document therefore presents the geometric relay as an effective dark-matter response, not as a completed replacement of all dark-matter dynamics. The full relay-field Boltzmann implementation, cluster lensing, Bullet-like systems, non-linear structure formation, MCMC inference, BAO, S8 and f sigma8 constraints remain open tests. Epistemic status: programmatic B/B+ synthesis. The background and effective-density connections are structurally motivated and quantitatively suggestive, but the full perturbative and non-linear equivalence to CDM remains to be demonstrated.