Stability and Fragility in Retentive Systems Comparative Structures of Persistence

This paper extends the retentive systems framework by introducing a comparative analysis of stability and fragility. Building on prior work defining retentive regimes and threshold-based transitions, stability is formalized as the margin between retention capacity (R) and turnover flux (F). The work defines fragility as structural proximity to breakdown and introduces key factors influencing persistence, including redundancy, resilience, and collapse distance. A critical vulnerability condition is identified as systems approach the threshold regime. The framework is particularly relevant in systems where loss of structural continuity leads to loss of viability (e.g., isolated or high-risk environments), where stability becomes a condition of survival rather than an optimization factor. This contribution completes the core architecture of retentive systems theory by providing a comparative structure of persistence across systems.