The p-curvature and Frobenius-constant quantization correspondence

Let $M_{eq,reg}$ be the $D$-module of twisted traces, let $\mathcal{A}_0^2$ be the degree-$2$ part of the relevant quantization algebra, and let $s$ be the Artin--Schreier map defining $p$-curvature. For $a\in\mathcal{A}_0^2$, write $\bar a$ for its corresponding function in the universal deformation. Trace-side p-curvature conjecture. The $p$-curvature endomorphism given by $s(a)$ is identified with the action of the Frobenius-constant quantization operator $\Lambda(\bar a)$. This is presented as a reduction of the mod-$p$ quantum Hikita conjecture when the quantization algebra is generated in degree $2$; the source does not state a resolution status.