This note defines a boundary certificate (ΔYM) for stationary Yang–Mills limits in the standard weak compactness regime. Given a bounded-energy sequence of stationary Yang–Mills connections, the weak-limit curvature-energy measure decomposes into a smooth part and a defect measure on the concentration set. The certificate ΔYM records whether that defect measure vanishes. The purpose of this release is certificate-level and technical: to isolate the boundary where smooth Yang–Mills continuation is no longer closed under weak limits once curvature concentration occurs. This note states the boundary and the binary test, without pursuing full bubbling classification in this release. Posted as a companion boundary certificate to the author’s earlier ΔZ note, with the Yang–Mills setting presented independently in standard geometric language.
Joseph C. Wehmeyer (Mon,) studied this question.