Kuznetsov's Fano threefold correspondence conjecture

Let $\mathcal{MF}^i_d$ denote the moduli space of smooth Fano threefolds of index $i$ and degree $d$. For a smooth Fano threefold $Y_d$ of index $2$ and degree $d$, and a smooth Fano threefold $X_{4d+2}$ of index $1$ and degree $4d+2$, write $\mathcal{K}u(Y_d)$ and $\mathcal{K}u(X_{4d+2})$ for their non-trivial admissible subcategories.

Kuznetsov's conjecture. There is a correspondence

$$\mathcal{Z}_d\subset\mathcal{MF}^2_d\times\mathcal{MF}^{1}_{4d+2},$$

such that for any pair $(Y_d,X_{4d+2})\in\mathcal{Z}_d$, there is an equivalence of categories

$$\mathcal{K}u(Y_d)\simeq\mathcal{K}u(X_{4d+2}).$$

This conjecture proposes a relationship between the non-trivial admissible subcategories of two families of smooth Fano threefolds. The source states that it was disproved rather than proved.