Constructive Organizational Field Theory: Distributed Organizational Structures, Admissible Evolution, and Coupled Field Representation

This paper develops Constructive Organizational Field Theory as the dynamic continuation of the frozen coupling architecture established in Paper X of the Organizational Field Theory research program. An organizational field is defined as an admissible spatial assignment, or section, of organizational states over a declared base domain, together with explicit topology, compatibility, provenance, genealogy, and representation data. Time dependence is formulated first as a semiflow on the admissible field space, while differential evolution equations are introduced only when an appropriate chart or manifold structure makes their generators meaningful. The framework distinguishes strict invariants from a versioned genealogical ledger, requires fibrewise coupling to preserve the parent identities and realizability conditions inherited from Paper X, and provides conditional formulations for gluing, equilibrium, balance laws, conserved functionals, stability, and admissible bifurcation. A two-field reaction–diffusion realization illustrates positivity, total-content conservation, energy dissipation, and the characterization of a common zero-dissipation equilibrium under explicit assumptions. The resulting architecture separates structural admissibility from representation-specific dynamics and empirical physical interpretation, providing an auditable mathematical continuation of OFT without claiming that every organizational field is a fundamental physical field or that any particular evolution law follows from organization alone.