A Boundary Certificate ΔYM for Stationary Yang–Mills Limits

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. This work forms part of a broader research program on Boundary-Coherence Architecture, in which defect formation, invariant extraction, and stable continuation are studied across multiple limit problems. Within that program, the present note isolates the Yang–Mills boundary certificate. It is presented as the Yang–Mills companion to ΔZ, where boundary invariants are developed in the setting of limiting mixed Hodge structures. Related records include: Boundary-Coherence Architecture: Defect, Invariant Extraction, and Stable Continuation in Limit Problems (DOI: 10.5281/zenodo.20588237) A Family of Author-Constructed Curvature Invariants for Limiting Mixed Hodge Structures (DOI: 10.5281/zenodo.17746195) Addendum: Two-Parameter Base-Change Invariance and Polysector Independence for I16 (ΔZ) (DOI: 10.5281/zenodo.18344613)