Quantum Wavefront Stabilization and Topological Optical Regularization: Resolving Phase Discontinuity via Trans-Planckian Horizon Lock Mechanics

This treatise delivers the definitive mathematical physics formulation to resolve the problem of optical wavefront layer discontinuities, phase factor anomalies, and singular photon information dissipation gradients within quantum-applied continuum architectures. Traditional optical propagation and wave-routing algorithms suffer from severe mathematical breakdown due to localized computational entropy spikes under extreme diffractive constraints. Operating within the functional infrastructure of Trans-Planckian Horizon Lock Mechanics (TPHLM), we resolve these material instabilities 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 absolute diffeomorphism Ward-Khandey identities, cancels trace field anomalies, and ensures a deterministic 0.0000000000000000% floating-point error baseline, optimized for high-performance exascale computing arrays.