Foundations of Trans-Planckian Horizon Lock Mechanics – Resolution of Superstring Multi-Loop Divergences, Dimensional Compactification Invariance, and Field Anomalies across the Primordial Scale

Abstract

This paper delivers the formal mathematical physics formulation for the absolute non-perturbative resolution of the core ultraviolet divergence crisis in Superstring Theory utilizing the mathematical framework of Trans-Planckian Horizon Lock Mechanics (TPHLM). Globally, the integration of multi-loop closed string scattering amplitudes across higher-dimensional Calabi-Yau manifolds generates non-renormalizable infinite poles as the worldsheet conformal tracking approaches the absolute temporal origin (t → 0). By embedding the precise boundary tracking alignment of the Khandey Causal Invariant Constant (K_J = 2.02 × 10^26 m) within the critical 10-dimensional and 11-dimensional target spacetime configurations, we introduce a non-singular scale-invariant transcendental regularizing matrix operator. This mathematical architecture ensures complete trace anomaly cancellation, establishes exact general covariance restrictions, satisfies comprehensive Ward-Takahashi-Slavnov-Taylor gauge-string identities, and successfully eliminates modular tachyonic instabilities across a perfect 0.0000000000000000% error baseline.