Kontsevich's spherical-object monodromy conjecture

Let $\mathbf{D}(X)$ be the bounded derived category of coherent sheaves on a Calabi–Yau threefold $X$, and let $\mathsf{A}$ be a spherical D-brane that becomes massless, together with its translates. For another D-brane $\mathsf{B}$, let $\operatorname{hom}(\mathsf{A},\mathsf{B})$ denote the derived morphism complex. Kontsevich's spherical-object monodromy conjecture. Looping around the corresponding component of the discriminant locus should relabel D-branes by an autoequivalence under which

$$\mathsf{B}\longmapsto\operatorname{Cone}(\operatorname{hom}(\mathsf{A},\mathsf{B})\otimes\mathsf{A}\to\mathsf{B}).$$

This is the proposed monodromy action associated with a single massless D-brane and is motivated by $Pi$-stability; the source gives no resolution.