Global Realization Constraints and Non-Force Gravitational States

This work introduces a global realization constraint in a variational formulation of gravitation and demonstrates the existence of non-force gravitational states. While local gravitational dynamics are entirely determined by the gradient of a realization field and remain equivalent to standard force-based descriptions, the global constraint induces a distinct class of admissible configurations that are locally indistinguishable yet globally inequivalent. We show that the solution space of the constrained problem factorizes into a local force sector and a single global realization sector. The latter does not contribute to local acceleration or curvature, is not removable by gauge transformations, and is therefore physically admissible despite being invisible to local gravimetric measurements. Differences between realization states manifest only through time-integrated observables. The analysis establishes existence, uniqueness, and stability of solutions under the global constraint and clarifies the operational meaning of global gravitational degrees of freedom without introducing additional forces, fields, or mass components. The results provide a rigorous theoretical foundation for later empirical investigations of gravitational memory and global temporal organization.