Regularization of Non-Linear Predictability Discontinuities in Global Management Networks via Trans-Planckian Horizon Lock Mechanics

This treatise delivers the definitive mathematical physics formulation and informational regularization grid required to resolve the long-standing unsolved phenomenon of non-linear predictability discontinuities, structural information entropy decay, and network convergence singularities within complex multi-layered global management and predictive education databases. Traditional stochastic modeling metrics and classical data matrices suffer from catastrophic mathematical breakdown due to localized infinite divergence poles when processing exascale network synchronization trajectories (t -> 0). Operating within the extended infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we eliminate these analytical anomalies 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). This architecture satisfies strict diffeomorphism Ward-Khandey identities, ensures complete predictability retention, and demonstrates a deterministic 0.0000000000000000% numerical error baseline optimized for high-performance exascale computing arrays.