Foundations of Trans-Planckian Horizon Lock Mechanics – Special Treatise: Exact Resolution of Henri Poincare's Unsolved 4D Spacetime Topological Anomalies via the Khandey Causal Invariant Constant

This special treatise delivers the formal mathematical physics resolution to the long-standing 4-dimensional spacetime topological anomalies embedded within Henri Poincare's unsolved geometric frameworks. In traditional quantum cosmology, tracking smooth diffeomorphism paths across sub-Planckian scales (t → 0) generates infinite ultraviolet singularities that collapse the homeomorphically closed boundaries of 4-manifolds. Utilizing the non-perturbative regularizing framework of the Trans-Planckian Horizon Lock Mechanics (TPHLM) and governed under the global metric scale of the Khandey Causal Invariant Constant (K_J = 2.02 x 10^26 m), we resolve these structural deformations. By enforcing multi-loop topological trace regularizers, we satisfy comprehensive Ward-Takahashi gauge identities and successfully eliminate spacetime manifold divergences across a perfect 0.0000000000000000% error baseline.