A First Internal CLASS Implementation of the GRP Tracked Memory Branch: A Late-Soft mu-Sigma Test

This companion note presents a first internal CLASS implementation of the effective mu-Sigma projection of the tracked-memory branch of the Geometric Relay Programme (GRP). The implementation is based on the perturbative closure developed in the companion v9 paper on memory-mediated cold closure. The GRP relay response is projected into an effective dynamical-lensing split, encoded by two time-dependent functions mu (a) and Sigma (a). This is not yet a full relay-field Boltzmann implementation, but a controlled perturbation-level insertion of the GRP late-soft branch into CLASS. The patch is applied internally at the perturbation/source level rather than as a post-processing rescaling. A matched Lambda-CDM control run is used for comparison. The resulting CLASS outputs include CMB spectra, lensed spectra, matter power spectra P (k, z), sigma8, and ratio diagnostics. The first numerical results show a mild and stable deviation from Lambda-CDM. The sigma8 shift is approximately +0. 30 percent. The robust matter-power deviation remains below the percent level over the central k-range, with Delta P/P around 0. 6 percent at the lowest tested redshift and rapidly decreasing at higher redshift. The CMB spectra show no apparent spectral instability. Large-scale edge-grid excursions near k = 10^-5 Mpc^-1 are identified and treated separately as numerical or large-scale stability diagnostics. This record includes the paper, the LaTeX source, the reproducibility script, and the Colab notebook used to perform the CLASS and comparison workflow. The document should be read as a numerical companion to the GRP memory-closure v9 paper, not as a final full-field implementation of the relay dynamics. Epistemic status: A- numerical milestone for the effective GRP mu-Sigma CLASS projection; full relay-field Boltzmann implementation, MCMC inference, BAO, S8, f sigma8, and multi-observable constraints remain open.