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

Causal Memory Gravity VII presents the main observational test of the fixed-background linear CMG closure using DESI DR1 compressed growth and full-shape clustering data. The compressed six-tracer ShapeFit analysis gives a growth amplitude of 0. 9962 ± 0. 0437, only 0. 086 standard deviations from the GR prediction. The corresponding difference in chi-square is negligible, so this free-amplitude null test provides no preference for CMG over LambdaCDM. The paper also computes the DESI survey response to scale-dependent CMG growth. This maps the measured growth amplitude onto a degeneracy curve in the closure parameters etacl and betaIR, rather than selecting a unique parameter point or directly constraining the action coupling etaₐct. An independent multi-start full-shape analysis, with nuisance parameters refitted at every CMG point, gives compatible one-sided 95 percent limits of approximately 0. 015 to 0. 032 on etacl in the DESI-sensitive large-betaᵣatio regime. At betaᵣatio = 30, the physical interval remains unconstrained. The result is clear: where DESI DR1 is sensitive, the tested fixed-background linear CMG closure is compatible with the data only close to general relativity, but it is not statistically preferred over LambdaCDM. The paper also includes a separate interface test connecting an action-derived CMG cosmological background to the DESI DR2 BAO likelihood at fixed standard cosmological parameters. This test is not a profiled parameter constraint or an evidence measure and is not combined with the DR1 limits. A matched CMG background-and-perturbation Boltzmann treatment, a joint cosmological likelihood, and nonlinear screening calibration remain open. For the full CMG corpus, theory map, and related materials, visit: https: //cmg. beogradpc. com/