Gravity as the Condition of Realized Continuity

This work develops a force-free conceptual and mathematical framework for gravitation, interpreting gravitational motion not as the result of interaction, but as the structural condition that enables continuity of physical realization in the absence of local forces. Starting from the observation that bodies in free fall experience no force while nevertheless following well-defined trajectories, the paper proposes that gravitation operates as a global admissibility principle governing which continuations of motion remain physically realizable when no local agency determines evolution. An axiomatic formulation is introduced in which physical systems are represented by system-dependent sets of admissible velocity continuations. Motion emerges through iterative elimination of non-admissible directions rather than through dynamical forcing. Using tools from convex geometry and projection theory, the framework demonstrates how distinct gravitational regimes arise from differences in system structure alone. Within this formulation, free fall, orbital motion, and galactic rotation correspond to different geometries of admissibility associated with terrestrial, planetary, and galactic systems, respectively. A single selection principle governs all regimes, while qualitative differences emerge from system-dependent structural constraints. The work does not modify general relativity or introduce additional fields, forces, or dark matter components. Instead, it provides a structural interpretation underlying gravitational motion, offering a unifying conceptual foundation for gravitational phenomena across scales.