Unified Dark Sector Map: Retarded Metric Response of the Einstein-Gap

This document is a clean integrated package of the Effective Map branch of the Geometric Relay Programme, built upon Olivier Minazzoli’s Entangled Relativity framework. The construction is based on the conformal Einstein-gap Q_{\mu\nu} = G_{\mu\nu}(g) - G_{\mu\nu}(\kappa g), and on its gauge-fixed retarded metric response \delta g^{relay} = (E^{-1}_{ret} \circ K_{mem}) Q. The package gathers and preserves the mathematical layout of the companion notes concerning: 1. the Einstein-gap retarded metric response; 2. the trace-closure identity and the distinction between \Sigma_{QS} and \Sigma_{ER}; 3. the observational mapping of \Sigma_{ER} through the E_G statistic; 4. the effective cold-density budget; 5. the relay-coherence web leading to \Omega_\Lambda \simeq 0.69; 6. the late-time transparency limit; 7. the unified dark-sector synthesis. The controlled branch is the dark-matter-like sector: a cold retarded metric response with effective background budget \Omega^{eff}_{relay} = \Omega_m - \Omega_b, perturbative closure w_{eff} \simeq 0, clustering response \mu \simeq 1.0565, protected strict quasi-static lensing parameter \Sigma_{QS}=1, and ER-projected internal diagnostic \Sigma_{ER}=1/\mu \simeq 0.9465. The main observational target is therefore not a direct suppression of weak lensing at fixed matter contrast, but a suppression of the lensing-to-clustering statistic E_G by approximately E_G^{GRP}/E_G^{GR} \simeq 1/\mu \simeq 0.947. The dark-energy-like sector is treated more cautiously. The present package identifies a relay-coherence web in which five independent channels converge toward \Omega_m \simeq 0.30–0.33, and therefore \Omega_\Lambda \simeq 0.67–0.70 by flatness, with a preferred central value near \Omega_\Lambda \simeq 0.69. This is not claimed as a first-principles action-only derivation of \Omega_\Lambda. It is a cross-scale coherence argument linking the ER-derived relay structure to independently observed quantities. The current status is therefore: - the dark-matter-like branch is perturbatively controlled; - the dark-energy-like fraction is constrained by a relay-coherence web; - the interpretation of dark energy as an asymptotic transparency residual remains dynamically open; - the full covariant bitensor response, stability proof, and weak-field galactic bridge remain to be completed. This version replaces the previous short master synthesis by a clean integrated package preserving the original source-note typography, equations, and conceptual figures.