Cross-Scale Coordination Landscapes Reveal Emergent Admissibility and Boundary-Constrained Dynamics

We present a data-driven framework in which neural dynamics are understood as trajectories constrained by the geometry of an empirically reconstructed state space. By mapping neural activity into a low-dimensional coordination space, we derive an effective landscape and a reduced dynamical coordinate governing system evolution. Analysis of drift, diffusion, and occupancy reveals that neural trajectories are confined within a restricted region of state space, rather than undergoing repeated barrier-crossing transitions. This motivates the introduction of an admissibility operator Φq, which formalizes the boundary separating accessible from inaccessible states. The results suggest that neural dynamics are fundamentally shaped by boundary constraints, providing a geometric perspective on the organization of neural activity and its possible role in constraining realizable states.