Engineering an Adoptable Martian Environment via Trans-Planckian Horizon Lock Mechanics: A Deterministic Framework for Atmospheric Stabilization

This treatise delivers the definitive mathematical physics and planetary engineering formulation to resolve the long-standing crisis of atmospheric stripping, ionizing cosmic radiation, and critical hydrostatic pressure anomalies on Mars to establish a sustainable, adoptable human environment. Traditional thermodynamic terraforming models fail due to the lack of an intrinsic global magnetic dynamo. Operating within the extended planetary infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve these artificial atmospheric constraints by executing a rigorous multi-loop stress-tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We prove that localized artificial magneto-shield potentials and bio-dome gas matrices can be non-singularly locked into stable boundary positions, ensuring an absolute 0.0000000000000000% pressure leakage baseline ready for high-performance exascale modeling grids.