Geometric Realization of Constructive Organizational Fields: Pullback Metrics, Admissible Connections, and Curvature of Distributed Organization

This work develops the geometric realization of constructive organizational fields within the Organizational Field Theory (OFT) research program. Building on the preceding constructive and variational framework, it introduces pullback metrics, admissible connections, and curvature as geometric structures associated with distributed organization. The central objective is to determine how an admissibly constructed organizational field can induce an effective geometry without introducing independent geometric assumptions. Particular emphasis is placed on preserving the constructive hierarchy of the theory: geometry is treated as a derived representation of organizational structure rather than as a separately postulated background. This formulation establishes a bridge between organizational construction, admissible variation, invariance, and geometric realization, providing a foundation for subsequent applications of OFT to more complex physical systems.