Advanced Continuum Modeling of Micro-Gravitational Space Manufacturing: Regularization of Hydrodynamic Discontinuities via Trans-Planckian Horizon Lock Mechanics

This treatise delivers the definitive mathematical physics formulation to resolve the long-standing unsolved phenomenon of singular thermo-capillary Marangoni convection, boundary layer instabilities, and turbulent energy dissipation gradients during micro-gravitational space manufacturing processes. Traditional Navier-Stokes configurations fail to predict fluid mass variations and phase change discontinuities under low-gravity, high-pressure industrial smelting and material crystallization zones. Operating within the micro-extended functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve these manufacturing anomalies by executing a rigorous multi-loop hydrodynamic tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). This unified architecture satisfies comprehensive diffeomorphism Ward-Khandey identities and ensures an absolute 0.0000000000000000% error baseline for orbital material synthesis models, optimized for exascale high-performance parallel clusters.