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

This deposit contains a master synthesis and companion notes for the Effective Map branch of the Geometric Relay Programme. The central construction reformulates the dark-matter-like sector as a gauge-fixed retarded metric response to the conformal Einstein-gap \[ Q_{\mu\nu} = G_{\mu\nu}(g) - G_{\mu\nu}(\kappa g), \] where \(g_{\mu\nu}\) is the physical metric and \(\kappa g_{\mu\nu}\) is the conformal relay metric. The master document summarizes the current status of the programme: the dark-matter-like sector is described as a cold retarded metric response with background budget \[ \Omega_{\rm relay}^{eff} = \Omega_m-\Omega_b, \] clustering response \[ \mu\simeq1.0565, \] and protected strict quasi-static lensing response \[ \Sigma_{QS}=1. \] The ER-projected internal diagnostic \[ \Sigma_{ER}=1/\mu\simeq0.9465 \] is clarified as a v10.1 potential-closure diagnostic, not as the strict QS PPF weak-lensing parameter. Its observational role is identified through the lensing-to-clustering ratio and the \(E_G\) statistic, with the predicted signature \[ E_G^{GRP}/E_G^{GR}\simeq0.947. \] The package also includes an exploratory extension to the dark-energy-like sector, where late-time acceleration is interpreted as a transparency limit of the same effective map. In this regime, the active cold relay response freezes and a residual curvature behaves as a cosmological-constant-like term. The mechanism is identified, but the quantitative derivation of \(\Omega_\Lambda\) from the map remains open. The deposit should be read as a structured working package: the master document gives the global synthesis, while the companion notes provide the technical derivations, diagnostic clarifications, and observational mapping.