Organizational Phase Space and Geometric Taxonomy of Dynamical Trajectory Ensembles: Extended Validation and Biological Applications (Version 2.0)

This restricted-access preprint presents Version 2.0 of the Organizational Phase Space (OPS) framework, a geometric approach for characterizing collective behavior in dynamical trajectory ensembles. The work introduces a unified organizational representation of collective states and develops a reproducible geometric taxonomy capable of distinguishing multiple classes of dynamical organization across diverse systems. The framework is designed to operate directly on observable trajectory data and does not depend on system-specific governing equations, making it applicable to a broad range of physical, biological, and engineered systems. Version 2.0 substantially extends the original study through additional validation analyses, expanded theoretical interpretation, independent robustness assessments, and new proof-of-concept applications involving biological and physiological datasets. The manuscript also explores connections between organizational geometry, synchronization phenomena, collective stability, and transition dynamics. The results suggest that collective regimes occupy distinct and reproducible regions of organizational state space, providing an interpretable geometric language for describing the emergence, maintenance, and degradation of collective organization. This record is deposited on Zenodo to establish a verifiable and citable archival version of the work prior to journal publication. The file is maintained as a restricted-access research preprint while the manuscript undergoes evaluation for publication. Access may be granted to editors and reviewers for the purposes of scientific assessment. The associated concepts, terminology, framework structure, organizational observables, taxonomic classifications, and interpretive methodology presented in this work constitute original contributions of the author and are intended for scholarly evaluation and future development. Author: Josef Piskač ORCID: 0009-0004-1434-0724