GRP-CLASS: an .ini-controlled CLASS prototype for a late-activated geometric relay field

This updated version documents the GRP-CLASS v2.1 Q00-QS addendum to the terminal CLASS implementation of a Geometric Relay Programme (GRP) relay field. The original GRP-CLASS prototype inserted the relay variables chi, pi = dchi/du, and M directly into the CLASS perturbation vector, with activation controlled through .ini parameters. The relay can be disabled to recover the LambdaCDM reference, or enabled to generate controlled late-time signatures in the Newtonian-gauge potentials and in external growth/lensing diagnostics. The main change in v2.1 is the replacement of the previous phenomenological Poisson-relaxation channel, phi'_GRP = phi'_CLASS + epsilon_P T(a) H C_Q chi, by a quasi-static Q00 channel derived from the perturbative GRP closure: delta Q^0_0 |_QS = +(k^2/a^2) chi. Operationally, the v2.1 implementation applies the effective Newtonian-gauge correction Psi -> Psi + epsilon_slip T(a) chi - 1/2 epsilon_Q00 T(a) chi. For the benchmark configuration, grp_relay = yes grp_eps_slip = 1e-2 grp_eps_poisson = 0 grp_eps_q00 = 1e-2 grp_a_star = 0.6 grp_n_power = 4 grp_C_Q = 1.0 the net tested correction is Psi_GRP = Psi_GR + 5e-3 T(a) chi. The v2.1 implementation compiles, runs, and preserves the controlled late-time diagnostic pattern previously found in the terminal GRP-CLASS prototype. At z = 0, over the conservative range 10^-4 <= k <= 1 Mpc^-1, the corrected external diagnostics give approximately: mu_eff - 1 ≈ -0.00623, Sigma_eff - 1 ≈ -0.00034, E_G proxy - 1 ≈ +0.00593. At z = 1, the signal is attenuated: mu_eff - 1 ≈ -0.00329, Sigma_eff - 1 ≈ -0.00112, E_G proxy - 1 ≈ +0.00217. At z = 10, the signal is essentially switched off, with median deviations of order 10^-6. This version therefore improves the theoretical status of the prototype: the earlier Poisson-relaxation placeholder is replaced by a derived quasi-static Q00 channel while preserving numerical stability and the late-time growth/lensing split. This release remains a technical prototype, not a final physical closure of the GRP/ER perturbation equations. The Q00-QS channel is quasi-static and effective. A complete non-QS Q^0_0 derivation, gauge-consistency checks, native CLASS outputs for chi, pi and M, and full C_l / lensing-spectrum tests remain future work. The archive includes Markdown and LaTeX versions of the v2.1 addendum, together with the GRP-CLASS v2.1 Q00-QS outputs bundle containing patched source files, .ini configurations, diagnostic CSV files, plots, and validation summaries. The technical note is released under CC-BY-4.0. The patched CLASS-related files are provided for reproducibility and should be used consistently with the original CLASS license.