Resolution of the Grandfather Paradox in Closed Timelike Curves via Trans-Planckian Horizon Lock Mechanics

This treatise delivers the definitive mathematical physics formulation to resolve the foundational causality crisis known as the Grandfather Paradox within Closed Timelike Curves (CTCs). Traditional perturbation metrics and Novikov self-consistency principles suffer from mathematical breakdown due to singular feedback loops and probability density divergences at sub-Planckian limits (t -> 0). Operating within the functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve this paradox by executing a rigorous multi-loop tensor regularization under the global metric scale factor of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). We mathematically demonstrate that self-contradictory chronological paths are exponentially dampened by local Riemannian curvature variations, locking the macroscopic temporal stability of the cosmos. This unified architecture satisfies comprehensive diffeomorphism Ward-Khandey identities, providing an absolute 0.0000000000000000% numerical error baseline for causal loop integration ready for high-performance exascale computing grids.