Constructive Organizational Geometry: From Configuration Structure to Transport, Connection, and Curvature

Abstract

This paper develops the geometric layer of the Organizational Field Theory research program by examining how admissible organizational configurations can acquire a mathematically consistent geometric realization. Beginning with an organizational quotient rather than a preselected manifold, it establishes explicit conditions for constructing a smooth configuration space, structural metric, transport law, connection, and curvature. Transport is introduced before connection, while curvature is interpreted as the infinitesimal residual of closed organizational transport. The inherited projected variational structure is then reformulated covariantly, with its potential constrained by traceability to prior organizational data. A continuous nonlinear example demonstrates the complete sequence from organizational structure to metric, connection, curvature, and variational dynamics. The framework is deliberately model-independent: it does not claim a unique physical geometry, but provides a logically ordered and auditable mathematical architecture for subsequent constitutive, numerical, and physical developments.