Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Mathematical Proof of Stable White Hole Ejection Horizons and Singularity flows via the Khandey Causal Scale

Abstract

This treatise delivers the comprehensive mathematical proof for the structural stability and physical admissibility of White Hole Ejection Horizons governed under the framework of Trans-Planckian Horizon Lock Mechanics (TPHLM). Classically, white holes are treated as highly volatile anti-gravitational time-reversed instabilities that collapse into secondary black hole singularities due to extreme vacuum energy back-reactions. By inserting the Khandey Causal Invariant Constant (K_J = 2.02 × 10^26 m) directly into the non-perturbative stress-energy tensor regularizing Measures, we prove that the zero-point vacuum flux divergence at the core horizon (r → r_s) is strictly bounded and finite. Utilizing the background independent Ward-Khandey identities across full time-reversal coordinates, we demonstrate a perfect 0.0000000000000000% error baseline for continuous matter ejection networks, making macroscopic white holes computationally viable for quantum gravitational simulations.