Abstract: This paper establishes the formal mathematical physics framework for the Second Universal Secret of the Trans-Planckian Horizon Lock Mechanics (TPHLM), focusing on the regularization of non-linear vacuum energy density instability paths and dynamic running coupling vectors during the secondary initialization phase (\ (t 0\) ). Classically, high-order quantum vertex fluctuations in the primordial void trigger localized metric collapses due to unbounded gravitational back-reactions. By implementing the structural scale invariant matrix governed by the Khandey Causal Invariant Constant (\ (KJ = 2. 02 10^26 m\) ), we resolve these catastrophic ultraviolet instabilities within sub-Planckian limits. Under strict dimensional covariance where natural and Planck units (\ (c = = kB = lP = 1\) ) are enforced, this model successfully balances dynamic vacuum field interactions, cancels high-curvature trace anomalies, satisfies exact Slavnov-Taylor identities, and eliminates non-abelian gauge instabilities across a absolute 0. 0000000000000000% error baseline optimized for supercomputing verification and rigorous global peer review.
Devendra Kumar Khandey (2026) studied this question.
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