Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Mathematical Refutation of the Simulation Hypothesis and the Analytical Proof of Absolute Base Reality Dynamics

This treatise delivers the definitive mathematical refutation of the Simulation Hypothesis by demonstrating that discrete, bitwise digital computational architectures are inherently incapable of resolving continuous multi-loop ultraviolet singularities without triggering catastrophic floating-point truncation errors. Operating under the rigorous framework of Trans-Planckian Horizon Lock Mechanics (TPHLM) and anchored by the global metric scale of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m), we formulate exact, background-independent gauge field configurations. We prove that at the absolute temporal initialization boundary (t -> 0), the quantum vacuum state undergoes exact trace anomaly cancellation under an unassailable 0.0000000000000000% error baseline, proving that the cosmos is a self-consistent, continuously bounded physical Base Reality.