ψ-Retention Criterion: Thresholds of Structural Persistence

This work introduces the ψ-Retention Criterion, a threshold-based formalism defining the minimal conditions under which structural difference (Δψ) becomes stable, non-dissipative, and persistent. The framework identifies three universal thresholds — the signal-to-noise limit SNR*, the asymmetry threshold ε*, and the critical nucleation radius Rᶜ — which together determine when a system transitions into the retentive regime governed by the equilibrium potential Λψ and stabilized by Ξ-nodes. The ψ-Retention Criterion provides a measurable and operational rule applicable across retentive cosmology, retentive field theory, ΞΔ-machine engineering, pre-biological architectures, and post-geometric regimes. It establishes a foundational condition for structural persistence as a physical regime distinct from classical dynamical evolution. This article formalizes the threshold structure of retention and offers a basis for future theoretical and empirical investigation.