Causal Memory Gravity VII: DESI Compressed Benchmark and Full-Shape Nuisance-Profile Constraint

Causal Memory Gravity VII presents an observational test of the fixed-background, no-slip linear CMG closure using DESI DR1 ShapeFit and full-shape galaxy-clustering data. The revised six-tracer analysis uses native ShapeFit amplitude coordinates and covariances extracted directly from identified public DESI likelihood files. It gives a common template amplitude of 1.01211 ± 0.04367, approximately 0.277 standard deviations from the fiducial GR value. This result is reported in its native ShapeFit convention. The earlier illustrative growth vector and cross-bin covariance are preserved as historical material because their public-data provenance could not be established. The paper reconstructs the survey response to scale-dependent CMG growth, with consistent geometric rescaling in the spectrum and BAO template. Historical reference and archived results are reconciled explicitly, and a single reproducible numerical record supplies the current compressed constraints. The response connects the observations to the closure parameters eta_cl and beta_IR, yielding scale-dependent limits rather than a unique parameter pair. The complementary multi-start full-shape calculation profiles nuisance parameters at each CMG point. Its retained pointwise one-sided 95 percent limits on eta_cl range from approximately 0.015 to 0.032 at beta_ratio = 1000, 3000, and 10000. At beta_ratio = 30, the physical interval remains unconstrained. These bounds use the conventional profile threshold and show no statistically significant improvement over general relativity. Direct-template validation now covers seven nonzero parameter points across all six tracers, including the three quoted full-shape boundaries and their half-amplitude points. All sampled points pass the declared approximation criteria, with a maximum relative residual of approximately 2.46 percent in the growth and shape coordinates. This supports the local compression at the tested points without asserting uniform accuracy over the entire parameter plane. The constraints apply to the operational closure at fixed background geometry and initial normalization, using standard-gravity nonlinear templates. Interpreting them as limits on the action coupling eta_act requires a matched action-derived calculation. A separate DESI DR2 BAO background-interface test is also documented. A unified background-and-perturbation cosmological likelihood and nonlinear screening calibration remain open. CMG papers, the theory map, and supporting materials are available at cmg.beogradpc.com.