Phase–Modulated Inertial Resonance (PMIR) in the Terra–Luna System: Geometry, Gating, and Temporal Robustness

This preprint introduces and applies the Phase-Modulated Inertial Residual (PMIR) diagnostic to the Earth–Moon–Sun (Terra–Luna) system. Using daily ephemeris data spanning modern and deep-time windows, we construct a coupling-state residual from the Moon–Sun phase difference, extract a curvature-based event observable, and project events onto an outer-state torus defined by lunar latitude and Earth–Moon distance. We demonstrate statistically significant enrichment of high-curvature events within localized regions of the outer-state manifold that persist across multiple historical windows. A suite of deterministic robustness tests—including block-shuffle breaks, time-roll nulls, excursion pairing, persistence gating, and enrichment mapping—shows that the observed structure is not explained by simple temporal coincidence, secular drift, or random phase mixing. The results support a geometrically constrained, resonance-like coupling between Terra–Luna orbital geometry and the PMIR curvature observable, with implications for lunar–terrestrial dynamics, long-term orbital coherence, and the physical interpretation of curvature-based diagnostics in coupled celestial systems. All figures, tables, and methods are fully reproducible from the included data products.