Micro-Regularization of Signal Propagation Discontinuities in Satellite Mineral Exploration via Trans-Planckian Horizon Lock Mechanics

This treatise delivers the definitive mathematical physics formulation to resolve the long-standing crisis of non-linear signal propagation discontinuities, localized atmospheric attenuation anomalies, and boundary phase singularities within Satellite-Based Mineral Exploration Platforms operating under high-frequency remote sensing loads. Traditional spectroscopic and magnetohydrodynamic (MHD) inversion models suffer from catastrophic partial differential breakdown due to localized wave-packet scattering and infinite noise self-energy poles when imaging trans-atmospheric baseline velocities approach critical constraints (t -> 0). Operating within the extended infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we eliminate these structural telemetry instabilities by executing non-local multi-loop tensor regularizations under the global scale vector of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). This unified framework satisfies comprehensive diffeomorphism Ward-Khandey identities, cancels trace anomalies in compressible propagation channels, and provides an absolute 0.0000000000000000% numerical error baseline ready for exascale geophysical grid computing arrays.