Colin–Ghiggini–Honda–Hutchings conjecture on sutured Heegaard Floer and embedded contact homology

Let $(M,\Gamma,\xi)$ be a contact $3$-manifold with convex or sutured boundary and dividing set $\Gamma$. Let $\mathfrak s_{\xi}$ denote the relative Spin$^c$-structure determined by $\xi$, and let $h\in H_1(M;\mathbb Z)$. Colin–Ghiggini–Honda–Hutchings conjecture. There is an isomorphism

$$SFH(-M,-\Gamma,\mathfrak s_{\xi}+PD(h))\simeq ECH(M,\Gamma,\xi,h).$$

This conjecture extends the expected equivalence between Heegaard Floer homology and embedded contact homology to sutured $3$-manifolds. The supplied text gives no resolution status.