Indecomposability criterion for Calabi–Yau admissible subcategories

Let $\mathsf{Y}$ be a projective smooth variety, let $\mathcal{B}$ be an admissible $\mathsf{m}$-Calabi–Yau subcategory of $\mathsf{D}^{\mathsf{b}}(\mathsf{Y})$, and assume $\mathsf{m}\geq 0$.

Indecomposability criterion. The category $\mathcal{B}$ is indecomposable if and only if

$$\mathsf{HH}^{0}(\mathcal{B})\cong \mathsf{k}.$$

The criterion relates categorical connectedness to degree-zero Hochschild homology for Calabi–Yau admissible subcategories. In the supplied text it is stated as a conjecture, and no resolution is given.