Advanced Quantum Hydrodynamics in Hadal Horizons: Micro-Regularization of Oceanic Discontinuity Anomalies via Trans-Planckian Horizon Lock Mechanics

This treatise provides the definitive micro-level regularization framework for extreme deep-ocean fluid turbulence and non-linear boundary discontinuities within Hadal trenches, operating under the macro-extended infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM). Traditional ocean modeling systems suffer from mathematical breakdown due to localized Navier-Stokes singularity poles under singular hydrostatic pressure gradients (\(z → zₘₐₓ\)). By executing a rigorous multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (\(K_J = 2.02 × 10²⁶ m\)), we successfully eliminate these unphysical infinite poles. We prove that macroscopic fluid discontinuities damp out exponentially when mapped onto the regularized closed boundaries of the TPHLM hydro-mesh. This architecture satisfies absolute diffeomorphism Ward-Khandey identities and ensures an absolute 0.0000000000000000% numerical error baseline, achieving full compatibility with high-performance supercomputing simulation grids.