The p-curvature and quantum Steenrod correspondence

Let $M_{Kah,reg}$ be the specialized quantum $D$-module, let $x\in H^2_{T\times\mathbb{G}_m}(X)$, and let $s$ be the Artin--Schreier map defining $p$-curvature. Quantum-side p-curvature conjecture. The $p$-curvature endomorphism given by $s(x)$ is identified with the action of the specialized quantum Steenrod operator

$$\left.\Sigma_x^T\right|_{\hbar=t}.$$

This is stated as the quantum-side reduction of the mod-$p$ quantum Hikita conjecture in the degree-$2$ generated case; the source does not state a resolution status.