Phase-Coupled Orbital Dynamics (PCOD): A Bounded Predictive Refinement Framework for Asteroid Safety Modeling (Including Proof Set Appendix A)

Long-arc orbital prediction of near-Earth objects (NEOs) is constrained by nonlinear sensitivity to small perturbations. Ensemble covariance growth introduces uncertainty in impact corridor projections over decadal timescales. This document proposes a bounded, testable refinement framework termed Phase-Coupled Orbital Dynamics (PCOD). The framework introduces a dimensionless heliophysical phase index Φ(t) as a strictly bounded perturbative parameter within classical orbital propagation. The objective is to determine whether inclusion of this term measurably reduces ensemble uncertainty growth without modifying gravitational mechanics.