Geophysical Eigen-Manifolds: Coupled Laplacian Dynamics of the Earth's Stationary Phase Grid

We demonstrate that the long-noted spatial coincidence of the South Atlantic Anomaly (SAA), the dominant M₂ amphidromic node, and GRACE-derived mass deficit constitutes a geophysical eigen-manifold () governed by a coupled spherical Laplacian. Normalized gradient covariances (₈₉) quantify the interaction strengths between magnetic, tidal, and gravitational fields. Secular westward drift of the SAA (0. 30 0. 05^\, yr^-1) induces lagged reconfiguration in the anchored fields (₆ₑ₀ₕ 8\, yr, ₓ₈₃₄ 24\, yr). Lag-corrected second derivatives (jerk) align with r = 0. 87. A control analysis at the Mid-Atlantic Ridge confirms the mechanism operates globally at reduced amplitude. These dynamics redefine the historical ``planetary grid'' as the stationary-phase interference fringe of a dissipative rotating sphere and predict a 6. 5--8. 0^ westward re-anchoring of the South Atlantic M₂ node by 2040, with testable consequences for Patagonian Shelf hydrodynamics and migratory species.