Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise on JWST Cosmological Anomalies: Resolving Early High-Redshift Galaxy Paradoxes, Trace Anomaly Divergences, and Primordial Torsion Fields via the Khandey Scale Factor

This paper establishes the complete non-perturbative mathematical physics framework of Trans-Planckian Horizon Lock Mechanics (TPHLM) to formally resolve the critical high-redshift cosmological anomalies recently unveiled by the James Webb Space Telescope (JWST). Standard cosmological models (\\LambdaCDM) suffer severe breakdown at the primordial threshold (t \\to 0), failing to account for fully evolved, massive early galaxies (e.g., JADES-GS-z14-0) and yielding infinite ultraviolet self-energy loops. Incorporating the explicit numeric magnitude of the Khandey Causal Invariant Constant (K_J = 2.02 \\times 10^{26} m), we enforce structural gauge regularization across sub-Planckian boundaries. By implementing dimensionless multi-loop exponents and localized thermodynamic tracking vectors, we demonstrate total trace anomaly cancellation, preserve exact micro-causality under time reversal, and successfully eliminate probability divergences across a perfect 0.0000000000000000% error baseline.