ψ-Future Shadows: A Retentive Topology Before Time

This work introduces ψ-Future Shadows (Ψᶠ) — pre-geometric residues of difference that arise before time, metric, or spacetime extension. Within ψ-Retention Cosmology, Ψᶠ functions as the minimal retentive substrate capable of stabilizing Δψ in the absence of geometry. The article formalizes Ψᶠ through axioms, derives its relation to the Retentive Lagrangian, and demonstrates its relevance for late-time plateaus, horizon-scale persistence, and pre-geometric structure formation. The submission includes two hand-drawn research-based illustrations (Figure 1 and Figure 2), representing the mathematical Future Shadow condition in visual, pre-temporal form.