This paper introduces the Rotor Curvature Field ψ(x,t), the fundamental field variable describing the geometric state of the vacuum in the Rotor Dynamics Framework. The field is defined as a complex scalar quantity whose magnitude represents the local intensity of circulating curvature and whose phase represents the orientation of curvature circulation. Observable quantities such as curvature intensity and curvature energy density arise directly from the field magnitude. A hierarchy of spatial derivative operators governs the evolution of the field, producing distinct dynamical regimes corresponding to curvature relaxation, transport, wave propagation, particle stability, and collective coherence. Localized bounded solutions of the field correspond to rotor structures interpreted as elementary particles, while small perturbations propagate as curvature waves associated with electromagnetic radiation. Collective synchronization of the field across many rotor domains produces macroscopic coherent states, and large-scale curvature distributions modify the effective geometry of the vacuum manifold. The definition of the Rotor Curvature Field establishes a single mathematical object underlying the equations used throughout the rotor program and provides the foundation for future work deriving the Rotor Field Equation from an action principle.
S. Cobb (Wed,) studied this question.