Reflection-vector conjecture for exceptional objects and collections

Let $X$ be the variety under consideration, let $D^b(X)$ be its bounded derived category, and let $\Psi_q$ assign to an object of $D^b(X)$ its quantum-cohomological vector. Assume that the quantum cohomology of $X$ has reflection vectors, denoted by $\mathcal{R}$, with pairing $(x|y)$ and monodromy group $W$. An object of $D^b(X)$ is exceptional if

$$\operatorname{Ext}^k(\mathcal{E},\mathcal{E})=\begin{cases}\mathbb{C}&\text{if }k=0,\\0&\text{otherwise},\end{cases}$$

and a sequence of exceptional objects is a full exceptional collection if it generates $D^b(X)$ under isomorphisms, shifts, and cones.

Reflection-vector conjecture. (a) If the quantum cohomology of $X$ is convergent and semisimple, then $\Psi_q(\mathcal{E})$ is a reflection vector for every exceptional object $\mathcal{E}\in D^b(X)$. (b) If $(\mathcal{E}_1,\dots,\mathcal{E}_N)$ is a full exceptional collection in $D^b(X)$, then the reflection vectors $\alpha_i:=\Psi_q(\mathcal{E}_i)$ $(1\leq i\leq N)$ generate the set $\mathcal{R}$ of all reflection vectors in the following sense: the reflections $x\mapsto x-(x|\alpha_i)\alpha_i$ $(1\leq i\leq N)$ generate the monodromy group $W$ of quantum cohomology, and for every $\alpha\in\mathcal{R}$ there exists $w\in W$ such that $w(\alpha)\in\{\alpha_1,\dots,\alpha_N\}$.

This relates convergence and semisimplicity of quantum cohomology to exceptional objects and full exceptional collections in the derived category. The supplied text does not state whether the conjecture has been proved or remains open.