ψ⁸: Shadows of the Past — The Retentive Invariant of Cosmic Memory

This article introduces the Shadow-Retention Principle (SRP), a fundamental invariant of ψ⁸ Retentive Cosmology. SRP defines a non-dissipative shadow field: S(t) = ∫0 → ∞ Δψ(t − τ) · exp(−κ·τ) dτ where κ is a positive decay coefficient consistent with ψ-time across retentive regimes. The shadow field S(t) remains finite due to the presence of retentive Ξ-nodes. The framework demonstrates how structural memory persists beyond classical dynamical decay and provides testable predictions for Euclid, DESI, and weak-lensing surveys, including: • shear plateaus, • void ghost-memory, • extended topological persistence. The article outlines the Lagrangian formulation of SRP, its distinguishability from ΛCDM and modified gravity, and its applicability as a falsifiable invariant for late-time cosmology.