Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Extension to 5-Dimensional Bulk Space Manifolds, Kaluza-Klein Horizon Regularizations, and Absolute Compactification Constraints via the Khandey Causal Invariant Constant

Abstract

This special treatise extends the framework of Trans-Planckian Horizon Lock Mechanics (TPHLM) to deliver the exact non-linear resolution for stable 5-Dimensional (5D) bulk spacetime manifolds at extreme sub-Planckian limits (t → 0). Classically, extending quantum gauge field interactions into a fifth spatial dimension triggers uncontrollable higher-dimensional ultraviolet divergences that shatter the compactification boundaries of Kaluza-Klein geometries. Bounded completely within a dimensionally invariant causal structure and governed under the macroscopic scale of the Khandey Causal Invariant Constant (K_J = 2.02 × 10^26 m), we resolve these structural deformations. By implementing multi-loop topological bulk regularizers, we satisfy comprehensive 5D Ward-Takahashi-Slavnov-Taylor gauge identities, cancel trace anomalies, and eliminate five-dimensional coordinate instabilities across a perfect 0.0000000000000000% error baseline optimized for execution on advanced quantum supercomputers.