What question did this study set out to answer?

To explore the concept of ψ-Future Shadows as pre-geometric entities that stabilize properties before the emergence of spacetime.

February 11, 2026Open Access

ψ-Future Shadows: A Retentive Topology Before Time

Key Points

To explore the concept of ψ-Future Shadows as pre-geometric entities that stabilize properties before the emergence of spacetime.
Formulated axioms to define ψ-Future Shadows
Derived the relation to the Retentive Lagrangian
Illustrated mathematical concepts visually
Identified Ψᶠ as a minimal retentive substrate
Demonstrated its relevance for late-time plateaus
Showcased implications for horizon-scale persistence and structure formation

Abstract

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.

ψ-Future Shadows: A Retentive Topology Before Time

Key Points

Abstract

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