Theorems of Retentive Stability A Formal Architecture of Self-Maintaining Difference

This paper presents a complete theorem-based framework for retentive stability in complex systems. Building on previously established operational thresholds of retentive nucleation, it formulates twenty-one core results characterizing the existence, persistence, invariance, topology, and epistemic consequences of self-maintaining difference. Retention is treated not as equilibrium, stored memory, or sustained dynamics, but as an architectural regime in which structured difference persists autonomously after the withdrawal of active driving processes. The framework introduces retentive nodes (Ξ) as minimal units of autonomous coherence and establishes necessary and sufficient conditions for their emergence and stability. The results define a closed, domain-independent architecture applicable across physical, informational, and abstract systems, without presupposing specific material substrates or disciplinary models. This work provides a formal foundation for subsequent extensions involving Lagrangian formulations, topological analysis, and retentive field theories.