Retentive Saturation versus Fata Morgana: Integration-Depth Invariance as a Diagnostic for Late-Time Cosmological Structure

This work introduces a diagnostic framework for evaluating late-time anomalies in cosmological structure growth based on integration-depth behavior rather than dynamical modification. The study formalizes integration-depth invariance as a non-violating null test and establishes explicit criteria for distinguishing genuine structural saturation from observational or methodological mirages (Fata Morgana effects). The manuscript defines a set of invariance conditions—including estimator independence, covariance robustness, achromaticity, null-control rejection, and window stability—and proves that satisfaction of these criteria uniquely admits a structural interpretation of plateau convergence. The framework is parameter-free in the dynamical sense, preserves early-universe consistency, and is explicitly falsifiable. It provides a rigorous diagnostic tool applicable across late-time cosmological surveys without reliance on model-specific assumptions.