Transitions in complex systems are typically studied in terms of dynamics, prediction, or external forcing. However, a fundamental question remains unresolved: whether transitions can occur at arbitrary states, or only within structurally admissible regions of the system. This work introduces a structural admissibility framework that shifts the focus from predicting when transitions occur to determining whether they are dynamically possible. We define an admissibility functional Φ as a data-driven measure of structural coherence across system layers, constructed from inter-layer correlations mediated by a mismatch operator capturing the difference between external forcing and internal system memory. Using observational data from the Earth–Sun system, we show that transitions are not uniformly distributed in time, but are confined to regimes characterized by elevated values of Φ. Transition probability is significantly higher in high-Φ states compared to low-Φ states, indicating a regime-dependent structure of dynamical accessibility. Robustness tests, including temporal shuffling, noise controls, and time-reversal analysis, demonstrate that this effect reflects an underlying structural property rather than a statistical or dynamical artifact. These results suggest that regime transitions are constrained by structural admissibility conditions. The framework provides an empirical mechanism for identifying regions of state space in which transitions become dynamically accessible, establishing a direct link between structural constraints and observable system behavior.
Josef Piskač (2026) studied this question.