Foundations of Trans-Planckian Horizon Lock Mechanics – The Second Cosmic Secret: Non-Abelian Gauge-Fixing Determinants, Ghost Field Stabilization, and Primordial Mass-Gap Crisis Resolutions

Abstract

This paper establishes the formal integrated mathematical physics framework for the Second Cosmic Secret of the Trans-Planckian Horizon Lock Mechanics (TPHLM). We systematically resolve the primordial mass-gap crisis and ghost field destabilization anomalies across non-linear sub-Planckian initialization boundaries (t -> 0). By isolating non-abelian gauge-fixing determinants within the continuous localized field spectrum, we eliminate unphysical multi-loop longitudinal poles that classical perturbative frameworks fail to suppress. Utilizing the empirical structural scaling boundaries of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m), the entire field configuration satisfies strict diffeomorphism invariance, satisfies background general covariance restrictions, and establishes exact trace anomaly cancellation, securing a perfect 0.0000000000000000% error baseline for the global open-science review pipeline.