Global Selection of Collective Kinetic Organization

Global Selection of Collective Kinetic OrganizationNonautonomous kinetic response, attractor uniqueness, and stationary population limits Paper V of Kinetic Organization and Biological Function This paper establishes global dynamical selection of a unique maintained nonequilibrium organization in a nonlinear kinetic–chemical–electrical system of interacting mechanochemical transporters. The model retains periodic mechanical position, unbounded momentum, four conformational phases, shared finite ionic and chemical resources, and an inventory-derived membrane capacitor. Building on the stationary classification, local kinetic stability, and compact-attractor construction of Paper IV, the analysis proves that the complete maintained collective dynamics possess a singleton global attractor, (\mathcal A={X_*}), attracting every covered bounded positive finite-second-moment preparation class in the prescribed weighted kinetic-density/resource topology. The proof combines an exact bulk–kinetic-shape decomposition, a uniform fifteen-pair positive comparison for collective resource dynamics, and nonautonomous hypocoercive estimates for the full infinite-dimensional kinetic evolution. Constrained primal–dual response identities and finite-to-infinite numerical enclosures yield a strict four-current small-gain inequality, with a rational positive-vector witness below (17/20). Stoichiometric reconstruction and Markov contraction then identify the complete stationary kinetic law. The selected organization sustains strictly positive material circulation, chemical regeneration, mechanical fluctuations, and energetic turnover while its collective inventories and electrical charge remain stationary. The stationary empirical-state laws of the interacting finite populations converge to the corresponding collective point mass, with convergence of selected current, charge, and energetic observables. Population-size and long-time limits agree for the stated bounded continuous state observables, while uninterrupted charge-band survival exhibits distinct iterated limits. The paper concludes a five-part investigation motivated by the historical relationship between 氣機 (qìjī, organized movement) and 氣化 (qìhuà, material and functional transformation). Across the series, this relationship is developed into a mathematically specified physical system, from individual mechanochemical transport and functional observation through reciprocal resource coupling, interacting populations, maintained stationary organization, and global dynamical selection. The resulting theory provides a rigorous synthetic realization of sustained kinetic organization and a foundation for investigating more general forms of maintained physical and biological function.