Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Non-Perturbative Quantum Regularization of Zero-Point Energy Divergences and the Exact Mechanism for Room-Temperature Superconductivity

This paper establishes the formal mathematical physics framework for resolving the infinite vacuum energy problem and deriving the absolute non-perturbative mechanism for Room-Temperature Superconductivity under Trans-Planckian Horizon Lock Mechanics (TPHLM). Classically, zero-point energy (ZPE) calculations expand into infinite ultraviolet self-energy poles, creating a cosmological constant crisis. Concurrently, traditional BCS and Eliashberg-coupling frameworks fail to sustain stable electron-pairing Cooper matrices at ambient temperatures (T ≈ 300 K) due to thermal phonon decoherence. By embedding the macroscopic metric scale of the Khandey Causal Invariant Constant (K_J = 2.02 × 10²⁶ m) within natural Planck-normalized measures (c = ħ = M_P = 1), we demonstrate that sub-Planckian tracking limits (t → 0$) damp out zero-point instabilities. By enforcing complete multi-loop matrix regularization, we satisfy exact general covariance restrictions, stabilize macro-coherent electron lattices without resistance, and eliminate probability divergences across a perfect 0.0000000000000000% error baseline.