Birational categorical Torelli conjecture for Gushel–Mukai varieties

Let $X_1$ and $X_2$ be Gushel–Mukai varieties of the same dimension, and let $\mathcal{K}\!u(X_i)$ denote their Kuznetsov components. Birational categorical Torelli conjecture. If there is an equivalence

$$\mathcal{K}\!u(X_1)\simeq\mathcal{K}\!u(X_2),$$

then $X_1$ and $X_2$ are birational. This conjecture asks whether the Kuznetsov component determines the birational class within a fixed-dimensional Gushel–Mukai family. The source notes that the analogous implication is expected in this setting, while an inverse implication should not hold in general; the conjecture remains open.