Geodesics as Admissible Continuation: A Structure-First Interpretation

Geodesics are commonly introduced in physics as extremal paths derived from equations of motion, variational principles, or metric structure. While mathematically precise, this framing leaves implicit the structural conditions under which geodesic motion is meaningful at all. In this note, we adopt a structure-first ordering in which constraint precedes dynamics and reinterpret geodesics as admissible continuations selected by underlying constraint geometry rather than as force-generated trajectories. We introduce the descriptive notion of geodesic cavities to explain why families of paths persist, remain recoverable under perturbation, and dominate long-term behavior without invoking attraction, equilibrium, or active stabilization. Geodesic cavities are not proposed as physical entities or mechanisms, but as a structural substrate whose observable signatures include bounded effective degrees of freedom, spectral banding, and invariance under perturbation. This interpretation preserves all regime-valid results of general relativity and classical dynamics while making explicit the structural layer they already presuppose.