Quantitative stratification of stationary connections

Let $A$ be a connection of a principal bundle $P$ over a Riemannian manifold $M$, such that its curvature $F_A\in L_{\text{loc}}^2(M)$ satisfies the stationarity equation. It is a consequence of the stationarity that $θ_A(x,r)=e^{cr^2}r^{4-n}\int_{B_r(x)}|F_A|^2$ is monotonically increasing in $r$, for some $c$ depending only on the local geometry of $M$. We are interested in the singular set defined by $S(A)=\{x: \lim_{r\to 0}θ_A(x,r)\neq 0\}$, and its stratification $S^k(A)=\{x: \text{no tange...