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_ = G_ (g) - G_ (g), and on its gauge-fixed retarded metric response g^relay = (E^-1ₑ₄ₓ K₌₄₌) 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 ₐₒ and ₄ₑ; 3. the observational mapping of ₄ₑ through the EG statistic; 4. the effective cold-density budget; 5. the relay-coherence web leading to _ 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 ^effₑ₄₋₀ₘ = ₘ - b, perturbative closure w₄₅₅ 0, clustering response 1. 0565, protected strict quasi-static lensing parameter ₐₒ=1, and ER-projected internal diagnostic ₄ₑ=1/ 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 EG by approximately EG^GRP/EG^GR 1/ 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 ₘ 0. 30–0. 33, and therefore _ 0. 67–0. 70 by flatness, with a preferred central value near _ 0. 69. This is not claimed as a first-principles action-only derivation of _. 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.
Olivier Lane-larquey (Tue,) studied this question.