  Building on the work of Nozaki, Sato and Taniguchi, we develop an
instanton-theoretic invariant aimed at studying strong corks and equivariant
bounding. Our construction utilizes the Chern-Simons filtration and is
qualitatively different from previous Floer-theoretic methods used to address
these questions. As an application, we give an example of a cork whose boundary
involution does not extend over any 4-manifold $X$ with $H_1(X, \mathbb{Z}_2) =
0$ and $b_2(X) \leq 1 $, and a strong cork which survives stabilization by
either of $n\smash{\mathbb{CP}^2}$ or $n\smash{\overline{\mathbb{CP}}}^2$. We
also prove that every nontrivial linear combination of $1/n$-surgeries on the
strongly invertible knot $\smash{\overline{9}_{46}}$ constitutes a strong cork.
Although Yang-Mills theory has been used to study corks via the Donaldson
invariant, this is the first instance where the critical values of the
Chern-Simons functional have been utilized to produce such examples. Finally,
we discuss the geography question for nonorientable surfaces in the case of
extremal normal Euler number.
