Dubrovin's Stokes matrix conjecture for quantum connections

Let $X$ be a Fano manifold, let $\mathcal{H}_X=H^\bullet(X)\otimes\mathcal{O}_{\mathbb{C}_z}$, and let

$$\nabla={d}-\left(\frac{1}{z}(c_1(X)*_0)-\mu\right)\frac{dz}{z}$$

be its quantum connection at quantum parameter $\tau=0$. Assume that the quantum cohomology ring of $X$ is semisimple, and write $\chi(E,F):=\sum_k(-1)^k\dim \operatorname{Hom}(E,F[k])$ for $E,F\in D^b(X)$. Dubrovin's Stokes matrix conjecture. There exists a full exceptional collection $E_1,\dots,E_m$ of $D^b(X)$ such that the Stokes matrix of $(\mathcal{H}_X,\nabla)$ at $z=0$ equals

$$(\chi(E_i,E_j))_{i,j}.$$

This refines the relationship between semisimple quantum cohomology, exceptional collections, and the quantum connection; it is established in many cases but remains open in general.