Organizational Phase Space and Geometric Taxonomy of Dynamical Trajectory Ensembles

This restricted-access preprint establishes the Organizational Phase Space (OPS), a three-dimensional geometric framework for describing the collective behavior of dynamical trajectory ensembles. The work introduces a reproducible taxonomy of collective regimes, an explicit admissibility functional for comparing organized and disorganized states, and a set of validation studies spanning physical and biological systems. The manuscript demonstrates that diverse dynamical ensembles—ranging from synchronized oscillators to stochastic processes and real biological measurements—occupy distinct, interpretable regions of OPS. Transitions between regimes appear as geometric trajectories, enabling a unified view of constructive and destructive collective dynamics. The framework is model-agnostic and relies only on observable trajectory data. This preprint accompanies a submission to Physical Review E and is deposited on Zenodo to establish verifiable priority of discovery. Access is restricted until journal publication. The author retains all rights to the published version in accordance with lAPS policies. Additional context: OPS provides a unified geometric language for analyzing collective organization across disciplines, offering a bridge between physical models and biological ensemble behavior. The terminology, conceptual structures, and framework introduced here are original contributions intended for long-term development and future extensions. This deposit serves as the authoritative priority record for all associated concepts, definitions, and naming conventions.