Rationality conjecture for affine osp(1|2) super VOAs

Let $k$ be a positive integer. The affine algebra $L_k({\mathfrak{sl}}_2)$ is expected to be a sub-VOA of $L_k({\mathfrak{osp}}(1|2))$. Affine osp(1|2) rationality conjecture. The coset satisfies

$$\operatorname{Com}\left(L_k({\mathfrak{sl}}_2),L_k({\mathfrak{osp}}(1|2))\right)\cong\operatorname{Vir}(k+2,2k+3),$$

and, in particular, $L_k({\mathfrak{osp}}(1|2))$ is a rational super VOA. This proposes an explicit Virasoro coset description together with rationality for every positive integer level; the supplied text gives no resolution status.