The p-curvature formula for equivariant quantum Steenrod operators

Let $X^!$ be a $T^!$-equivariant conical symplectic resolution over $\mathbb{C}$, let $x\in H^2_{T^!}(X^!;\mathbb{F}_p)$, and let $t$ be the loop-rotation equivariant parameter of degree $2$. Define

$$\nabla_x^{T^!}=t\partial_x+x\star_{T^!}.$$

p-curvature conjecture. The equivariant quantum Steenrod operator satisfies

$$\Sigma_x^{T^!}=\left(\nabla_x^{T^!}\right)^p-t^{p-1}\nabla_x^{T^!}.$$

Here $\star_{T^!}$ is equivariant quantum multiplication. The paper states that this conjecture was established for Springer resolutions and verified there for hypertoric varieties, so its general status beyond those cases remains open.