The Bounded Coherence Operator (BCO): A Computable Stability Metric for Symbolic-Recursive Simulation

This work introduces the Bounded Coherence Operator (BCO) as a practical bridge between symbolic-recursive theory and executable simulation. BCO defines coherence as a measurable system variable, models observers as transformation operators, and evaluates whether a system maintains viable persistence under uncertainty, perturbation, and nonlinear drift. Rather than attempting total prediction or complete formal closure, BCO treats incompleteness, non-computability, and chaotic sensitivity as structural limits that complex systems must operate within. The framework provides threshold-based criteria for collapse, transition, and stable persistence, making it suitable for simulation, diagnostics, and comparative stability analysis. Two toy implementations are included: a neutral nonlinear logistic-map system and an applied economic-governance simulation. These examples show how bounded coherence can distinguish stable regimes from collapse-prone or chaotic regimes, supporting BCO as a testable operational metric for complex adaptive systems, symbolic-recursive frameworks, AI governance models, and resilience-oriented simulation architectures.