The GHS conjecture on crystalline Serre weights

Let $K/{\mathbb{Q}}_l$ be a finite extension, and let $\overline{\rho}:G_K\to\operatorname{GL}_2(\overline{{\mathbb{F}}}_l)$ be a continuous representation. Let $W^{\operatorname{cris}}(\overline{\rho})$ be the set of crystalline Serre weights and let $W^{\operatorname{explicit}}(\overline{\rho})$ be the explicit Serre weight set defined in the source. GHS conjecture.

$$W^{\operatorname{cris}}(\overline{\rho})=W^{\operatorname{explicit}}(\overline{\rho}).$$

This conjecture predicts that the crystalline Serre weights are exactly the explicitly defined weights, with the latter agreeing with the Schein weights in the semisimple case. The source attributes the conjecture to GHS and does not state that it has been resolved.