ψ-Retention Criterion & ψ-Phase Structure: A Formal Framework of Critical Thresholds and Stability Conditions in ψ-Architecture

A formal and testable framework for the ψ-Retention Criterion — the condition under which structural difference (Δψ) becomes a conserved quantity in post-dynamical systems. This work derives the critical thresholds (SNR*, ε*, Rc), defines the ψ-Phase Structure (Dynamic, Transitional, Retentive), and presents the Retentive Lagrangian governing stability, nucleation, and hysteresis. The theory offers falsifiable predictions for cosmology, materials science, and correlation-based experiments, establishing ψ-Architecture as a rigorous physical discipline.