Operational Thresholds of Retentive Nucleation Minimal Criteria for the Emergence of Self-Maintaining Difference

This work establishes a minimal operational framework for identifying the emergence of retentive structures in complex systems. Retention is defined not as sustained dynamics, equilibrium, or stored memory, but as the capacity of structured difference to persist once active driving processes diminish. The paper introduces three empirically grounded threshold parameters—signal-to-noise ratio (SNR*), asymmetry threshold (ε*), and critical nucleation scale (Rₙ)—that jointly determine whether a fluctuation transitions into a self-maintaining retentive node (Ξ). These thresholds define a phase structure separating dissipative regimes, transitional regimes, and regimes of autonomous coherence. The framework is domain-independent and does not presuppose specific physical, biological, or informational substrates. It provides an operational basis for detecting persistence without invasive measurement, supporting a non-violation observational approach. This work functions as a foundational reference within the ψ-Architecture (Psi-Architectura) research series and establishes the threshold-based groundwork for subsequent formal theorems of retentive stability.