Cluster $\mathbf g$-vector fan conjecture

For each vertex $v$ of the exchange graph, let $\operatorname{Cone}(v)$ be the cone in $V^*$ spanned by the weights $\mathbf g(x^v_e)$ for $e\in I(v)$. A fan is a collection of cones closed under faces in which any two cones meet in a face of each. Cluster $\mathbf g$-vector fan conjecture. The collection $\{\operatorname{Cone}(v):v\in\mathrm{Ex}_0(B)\}$ is a fan and the map $v\mapsto\operatorname{Cone}(v)$ is injective. The source identifies this with a restatement of the cited conjecture and gives no general resolution.