This record presents the v10 clean native-LaTeX revision of the Geometric Relay Programme (GRP) technical note on the memory-mediated cold closure of geometric relay perturbations in Entangled Relativity, based on the \ (Lₘ²/R\) action. The central result is that the ER-reduced counter-curvature tensor \ Q_ = __ - g_ - 12__ - 14g_ () ² \ admits an exact conformal Einstein-gap reconstruction: \ Q_ = G_ (g) -G_ (g), =. \ This gives a geometric interpretation of the GRP counter-curvature sector: the effective dark component is read as the difference between the Einstein tensor of the physical metric and that of the normalized conformal relay metric. The v10 revision integrates this result natively into the main text, with continuous equation numbering and corrected vector-quality rendering. The revision also clarifies the ER/Maxwell/Palatini bridge: \ Q ₄₌=2LₘR, Lₘ, |F|^-2. \ It distinguishes the normalized relay metric \ h^ (Q) _=|F|^-1/2g_ \ from the raw Palatini metric \ h^ (P) _=|F|g_. \ The memory-closure construction shows how the instantaneous quasi-static relay response is transformed into an effective pressureless branch by a distributed memory kernel. The structural damping coefficient \ f=14 \ is fixed by the ER-reduced normic sector, by the cold background closure, and by the conformal Einstein-gap structure. The tracked mixed-memory branch gives a self-consistent cold fixed point \ A ₓₑ -1. 345657, B ₓₑ -0. 345657, \ leading to the reduced potential diagnostic \ 0. 9465, 1. 0565. \ New in v10 is the exact reduced Mori–Zwanzig self-energy correction: \ (s) = -2s²1+4s. \ The local Taylor expansion around \ (s=0\) is explicitly identified as non-controlled at the tracked physical mode, while the closed-form self-energy confirms that the tracked cold closure and the reduced \ (-\) split are stable within the reduced framework. A first internal CLASS-level late-soft \ (-\) implementation is reported as a numerical milestone. In the tested configuration, the patched solver runs to CMB and matter spectra, gives \ ₈^ GRP/₈^ CDM1. 003, \ and keeps the robust central-\ (k\) matter-power deviation below \ (0. 6\%\), with no immediate CMB or growth catastrophe. The accompanying reproduction scripts verify the memory-closure chain, the tracked \ (-\) diagnostic, the affine Einstein-gap identity, and the exact Mori–Zwanzig correction. Epistemic status: the conformal reconstruction \ (Q_=G_ (g) -G_ (g) \) is an exact geometric identity within the adopted normalization. The memory-mediated cold closure and tracked fixed point are established within the ER-reduced dressed-propagator framework. A full relay-field Boltzmann implementation with explicit evolution of the relay perturbation and memory variable remains open.
Olivier Lane-larquey (Tue,) studied this question.