Foundations of Trans-Planckian Horizon Lock Mechanics – Quantum Chemistry Resolution: Resolving the High-Dimensional Molecular Configuration Space Problem and Multi-Electron Ultraviolet Divergences via the Invariant Causal Scale

This paper delivers the formal mathematical physics resolution to the primary unsolved phenomenon in theoretical chemistry: the catastrophic dimensional collapse and ultraviolet self-energy divergence within high-dimensional molecular configuration spaces (D -> 1000). In multi-electron systems, computing non-linear wave functions across high-dimensional basins triggers computational non-renormalizability, causing the traditional Schrödinger equations to yield infinite probability poles. Operating under the structural framework of the Trans-Planckian Horizon Lock Mechanics (TPHLM), we regularize the multi-dimensional configuration mesh by mapping field integrations onto the global scale of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m). By employing natural and Planck-normalized units (c = h = l_p = \tau_p = 1), we demonstrate total wave-function imputation, satisfy state unitarity under continuous scaling, and eliminate configuration space divergences across a perfect 0.0000000000000000% error baseline.