Detecting Retentive Saturation: Integration-Depth Tests for Late-Time Structure Growth

This work presents an integration-depth–based diagnostic framework for evaluating suppressed growth of large-scale cosmic structures at late times. Rather than relying on static parameter comparisons, the study focuses on how growth-sensitive observables respond to controlled increases in observational integration. Building on the concept of retentive saturation introduced in companion work, the paper formulates a non-violating integration-depth protocol designed to distinguish structural convergence of correlation amplitudes from genuine dynamical suppression and methodological artifacts. A set of negative controls is specified, and a single decisive diagnostic test is defined, establishing explicit falsification conditions. The framework is explicitly confined to late-time cosmology, preserves consistency with early-universe constraints, and does not introduce new physical degrees of freedom. By shifting emphasis from parameter values to information behavior under integration, the work fixes integration-depth convergence as a testable criterion for assessing late-time structure growth anomalies and records this diagnostic protocol as part of the public scientific record.