Positive-characteristic freeness conjecture for Weyl-algebra bimodules

Let $R$ be a finitely generated smooth commutative algebra over $\mathbb Z$, let $g\in\operatorname{Aut}(P_{n,R})$, and for each sufficiently large prime $p$ let $M_{g,p}$ be a bimodule over $A_{n,R/pR}$ corresponding to the Morita autoequivalence induced by the Frobenius transform of $g$. Positive-characteristic freeness conjecture. For all sufficiently large $p$, the bimodule $M_{g,p}$ is a free rank-one left $A_{n,R/pR}$-module.

This is stated as an equivalent reformulation of the main Weyl–Poisson automorphism conjecture. The paper notes a lack of clear evidence and points to characteristic-zero projective Weyl-algebra modules that are rank one without being free; no resolution is supplied.