Weak-star separability conjecture for Lipschitz functions

Let $M$ be a metric space, let $\operatorname{dens} M$ denote its density, and let $\operatorname{Lip}_0(M)$ be the Banach space of Lipschitz functions on $M$ vanishing at the distinguished base point, equipped with the weak-star topology $w^*$ induced by its canonical predual. Weak-star separability conjecture. If

$$\operatorname{dens} M\leq 2^\omega,$$

then $(\operatorname{Lip}_0(M),w^*)$ is separable. The conjecture concerns weak-star separability of Lipschitz-function spaces over possibly nonseparable metric spaces. It is proved in the paper for several classes, including Banach spaces with a projectional skeleton, Banach spaces with a weak-star separable dual unit ball, and locally separable complete metric spaces; the general case remains open.