Transitions in complex systems are commonly studied through dynamical evolution, prediction, or external forcing. However, a fundamental question remains insufficiently addressed: whether all regions of the state space are equally capable of supporting transitions. This work introduces a geometric framework in which dynamical transitions are constrained by structural admissibility conditions defined over the state space. Rather than focusing on when transitions occur, the framework identifies where they are possible. The central element is the admissibility functional Phi, a data-driven measure of structural coherence across system components, constructed from inter-layer correlations mediated by a mismatch operator between external forcing and internal system state. Phi does not act as a predictive indicator, but as a structural operator that partitions the state space into regions of differing dynamical accessibility. Empirical analysis and controlled numerical experiments demonstrate that transition probability is not uniformly distributed, but is significantly elevated within high-Phi regions. This effect disappears under temporal shuffling and noise substitution, confirming that it reflects an underlying structural property rather than a statistical or dynamical artifact. Cross-system validation shows that the framework applies to systems exhibiting collective structural organization, including empirical Earth–Sun data and nonlinear oscillator networks, while failing in low-dimensional deterministic chaos. This establishes a clear domain of validity and demonstrates that Phi is a selective structural measure rather than a universal complexity indicator. These results support the existence of a state-space selection mechanism in which only structurally admissible regions permit dynamical transitions. In this interpretation, system behavior is governed not only by dynamical evolution, but also by geometric constraints that define the domain of accessible states. Transitions are not universally accessible in state space, but are restricted to structurally admissible regions defined by coherence.
Josef Piskač (Sun,) studied this question.