Autoduality conjecture for the ring stack ${}^{s}W$

Let $Q$ be the quotient of the Witt vector ring stack $W$ by its formal subgroup $\hat W$, let $T_F(Q)$ denote the associated Tate module, and let ${}^{s}W$ be the extension of $W$ by $T_F(Q)$ appearing above. For $R\in\operatorname{p-Nilp}$, write

$${}^{s}W_R:={}^{s}W\times\operatorname{Spec} R$$

and let $\alpha_R\in\operatorname{Ext}({}^{s}W_R,\mathbb{Z}_p(1)_R)$ be the base change of the extension class $\alpha\in\operatorname{Ext}({}^{s}W,\mathbb{Z}_p(1))$. Let

$$f_R:{}^{s}W(R)\to\operatorname{Ext}({}^{s}W_R,\mathbb{Z}_p(1)_R)$$

be the unique $W(R)$-linear map satisfying $f_R(1)=\alpha_R$. Autoduality conjecture. The map $f_R$ is an isomorphism.

This conjecture asserts that the ring stack ${}^{s}W$ is autodual under the relevant Ext pairing, uniformly after base change to every $p$-nilpotent ring. The supplied text does not state whether the conjecture is known or open.