Cieliebak–Eliashberg's Stein-to-Weinstein weak homotopy equivalence conjecture

Let $\mathfrak{Stein}$ and $\mathfrak{Weinstein}$ denote the spaces of Stein and Weinstein structures, respectively, and let

$$\mathfrak W:\mathfrak{Stein}\to\mathfrak{Weinstein}$$

be the map sending a Stein structure to its associated Weinstein structure. Cieliebak–Eliashberg's conjecture. The map

$$\mathfrak W:\mathfrak{Stein}\to\mathfrak{Weinstein}$$

is a weak homotopy equivalence. This would extend the known isomorphism on $\pi_0$ and surjection on $\pi_1$ to all homotopy groups, identifying the homotopy types of the spaces of Stein and Weinstein structures. The supplied text does not state whether the conjecture has been resolved.