The article introduces the Δψ-floor as a minimal, falsifiable invariant governing late-time structural retention in the ψ⁸ framework. It formalizes the asymptotic stabilization of structural difference, linking the Δψ-floor to the formation of non-zero retentive nodes Ξ. The work derives the equilibrium solution from the retentive Lagrangian and demonstrates how this invariant manifests in Euclid weak-lensing residuals, DESI clustering data, and topological persistence diagrams. The Δψ-floor provides a clear observational discriminator from ΛCDM and modified gravity models by predicting persistent correlation-time plateaus and void ghosting in the redshift range 0.2 < z < 0.5. The framework is designed as a test-ready structure for NASA ADAP/ATP, NSF Foundational Physics, and ERC Consolidator evaluation. This article strengthens ψ⁸ as a structurally parsimonious alternative for late-time cosmology.