Topological Irreversibility and Phase Divergence in Helical Conjugate Wave Systems

In standard continuous wave mechanics, periodic systems admit closed-loop recurrenceswhere phase states re-intersect their origin. However, within the Binary Vacuum Paradox(BVP) framework, the Universe emerges from a symmetry-breaking bifurcation between acoupled Vacuum Phase (ΨB) and a Vacuum Conjugate Phase (ΨC) evolving along a chiralhelical manifold. This paper demonstrates analytically that due to the orthogonality betweenexponential radial expansion and invariant axial pitch, the conjugate wave system exhibitstopological unreachability of the initial symmetry-breaking point. We derive the phase-driftequations, establish the mismatch parameter evolution, and demonstrate how this geometricisolation generates natural scale hierarchies without arbitrary fine-tuning