The EZ-transformation monodromy autoequivalence conjecture

Let $X$ be a Calabi–Yau threefold containing a subspace $E$, let $i:E\hookrightarrow X$ be the inclusion, and let $q:E\to Z$ be the contraction associated with an EZ-transformation. Let $i^!$ be the right adjoint of $i_*$ on derived categories, characterized by

$$\operatorname{Hom}_X(i_*\mathsf{E},\mathsf{F})\cong\operatorname{Hom}_E(\mathsf{E},i^!\mathsf{F}).$$

EZ-transformation monodromy autoequivalence conjecture. The monodromy around the discriminant in the wall associated with a phase transition given by an EZ-transformation should act on $\mathbf{D}(X)$ by the autoequivalence

$$\mathsf{B}\longmapsto\operatorname{Cone}(i_*q^*q_*i^!\mathsf{B}\to\mathsf{B}).$$

This is the proposed autoequivalence induced by the massless objects from the preceding conjecture; the source gives no resolution.