Structural Diagnostics of Gravitational Closure

This work provides the structural diagnostic component of the Ananke (Gravitational Closure) programme. Starting from the unique covariant action fixed by the Ananke Theorem, it derives the necessary and forbidden observational consequences of gravitational closure under symmetry reduction. No new field equations, phenomenological models, or data fitting are introduced. Instead, the paper classifies which features must occur, which cannot occur, and which apparent departures may arise solely through symmetry breaking rather than failure of closure. The analysis covers all admissible symmetry-reduced regimes identified by the Ananke classification: isolated vacuum configurations, stationary axisymmetric extended systems, and homogeneous cosmology. This manuscript is released as a preprint to establish intellectual priority and invite scrutiny. Gravitational closure is thereby rendered a rigid and falsifiable structural hypothesis: observation of any forbidden feature within an admissible symmetry class falsifies closure outright.