Is Cosmic Growth Universal? An Internal Consistency Criterion for Cosmic Structure

This work introduces and assesses the B3 criterion, an internal consistency test of cosmic growth designed to probe cumulative redshift-dependent drift without assuming a specific dynamical model. The method is formulated hierarchically, distinguishing between a conservative point-wise audit (B3soft) and a hard test based on explicit alternatives (B3-hard). Applying B3-soft to a baseline set of vetted fσ8 measurements and to the Sagredo(22) compilation, no evidence is found for cumulative drift in the ordered residuals. Durbin–Watson statistics, nonparametric trend tests, and leave-one-out diagnostics are all consistent with stochastic fluctuations around a redshift-independent amplitude. This paper then constructs a covariance-aware tomographic representation of the Sagredo(22) data. Generalized least-squares compression respects published correlation blocks and concentrates statistical weight at high redshift. Explicit step-like and linear-drift alternatives are penalized by information criteria, yielding a robust hard-lite statistical preference for universality, though not yet a decisive hard exclusion under aggressive pre-registered thresholds when using heterogeneous compilations. Finally, this study shows that the B3-hard criterion closes naturally at the survey level: once internally consistent tomographic products with published covariance are available, coherent hard alternatives can be excluded at the 95% level, establishing B3-hard as satisfied when sufficient high-redshift information is present. These results demonstrate that apparent inconclusiveness in heterogeneous compilations reflects limited data density rather than physical inconsistency. The B3 criterion therefore provides a transparent and model-agnostic framework to assess the internal consistency of cosmic growth measurements across redshift.