The type D stratified Mukai flop equivalence conjecture

Let $W$ be a rank $2N$ vector bundle equipped with a fibrewise non-degenerate symmetric bilinear form, and let $\mathbb{IG}(N,2N)^-$ and $\mathbb{IG}(N,2N)^+$ be the two components of the maximal isotropic Grassmannian. Define

$$\operatorname{IZ}(N):=T^\star\mathbb{IG}(N,2N)^-\times_{\operatorname{IB}(N,2N)}T^\star\mathbb{IG}(N,2N)^+.$$

Let $\operatorname{IZ}^o(N)\subset\operatorname{IZ}(N)$ be the open subvariety defined by

$$\dim(\ker X)+\dim(V\cap V')\leq 2N+2.$$

There are natural inclusions $\operatorname{IZ}^o(N)\xrightarrow{j}\operatorname{IZ}(N)\xrightarrow{i}T^\star\mathbb{IG}(N,2N)^-\times T^\star\mathbb{IG}(N,2N)^+$. Type D stratified Mukai flop equivalence conjecture. There exists a $\mathbb{C}^\times$-equivariant line bundle ${\mathcal{IL}}(N)$ on $\operatorname{IZ}^o(N)$ such that $i_*j_*{\mathcal{IL}}(N)$ induces an equivalence

$$D(T^\star\mathbb{IG}(N,2N)^-)\xrightarrow{\sim}D(T^\star\mathbb{IG}(N,2N)^+).$$

This is the expected type D analogue of the derived equivalence for stratified Mukai flops in type A, with the correspondence having multiple components and the open locus controlling the extension of the kernel. The supplied text gives no resolution of the claim, so its status remains open.