Memory Topology in Human-Adjacent Systems: Structural Continuity, Legitimacy Decay, and Stability Across Long-Lived AI Architectures

This paper introduces a topology-based framework for understanding how legitimacy evolves in long-lived human-adjacent systems that maintain persistent memory and adaptive behavior. The work formalizes replayability horizons, propagation half-life, locality-sensitive legitimacy, authority degradation gradients, and structural revalidation as mechanisms for evaluating whether previously authorized actions remain structurally valid under changing continuity conditions. The framework integrates Human-Adjacent System Design (HASD), Asymmetric Interaction Governance (AIG), and the Resonant Synthesis Engine (RSE), linking memory topology to measurable indicators of coherence, continuity, and structural stability. The resulting model provides a substrate-independent governance methodology for maintaining trust, resilience, and operational integrity across persistent AI systems, distributed infrastructures, organizational systems, and other long-lived adaptive architectures.