Constrained SO(3,3) Spacetime: Part VII. Euclidean Path Integrals and the Asymptotic Recovery of Lorentz Covariance

Abstract

Previous works established a geometric framework wherein transverse-time quantum tunneling is suppressed across mass and velocity scales via macroscopic Phase-Anchors. This paper formalizes that suppression mechanism within a rigorous path-integral framework. By applying a temporal Wick rotation to the primary Meta-Time axis, we derive the exact WKB tunneling probability amplitude through the saddle-point approximation of instanton trajectories. We demonstrate that the massive kinematic penalty imposed by the topological constraint field's vacuum expectation value (v>1/2) allows for the functional integration out of heavy transverse-time modes. This strict decoupling proves the asymptotic recovery of 4D local Poincaré symmetry at low energies, fully reconciling the 3+1+2 constrained multi-time geometry with observable Special Relativity.