Non-perturbative Cancellation of Stokes Singularities in Compactified Yang-Mills Theory via Magnetic Bions: A Rigorous Proof of Adiabatic Continuity and the Reality of the Vacuum Energy

AbstractThis paper establishes a rigorous proof of the reality of the vacuum energy in SU(N) Yang–Mills theory on ℝ³ × S¹. We demonstrate that the imaginary ambiguity inherent in the Borel summation of the perturbative series (Infrared Renormalons) is exactly canceled by the imaginary part of the magnetic bion amplitude, defined via the Bogomolny–Zinn–Justin (BZJ) prescription. This result confirms the absence of Stokes walls in the flow toward the infrared, validating the adiabatic continuity hypothesis utilized in the Constructive Gauge Theory Program (CGTP).