Critical Wisdom Principle: Phase-Bounded Emergence of Hierarchical Complexity in Deterministic Feedback Systems

We study a minimal deterministic timing-loop system with bounded memory and feedback to test whether hierarchical structure can emerge from temporal coherence alone. Using a model with no injected randomness, we measure inter-iteration gap distributions and long-range dependence under three memory regimes: windowed averaging, exponentially weighted memory (EMA), and scale-aware log-EMA. Results identify a boundary condition—the Critical Wisdom Principle—according to which coherence and adaptability can be sustained without hierarchy, which requires additional representational dimensions.