Forward-closure conjecture for linkage-class-one weakly reversible systems

Let a weakly reversible chemical reaction network have linkage class one, meaning that its underlying graph has only one strongly connected component. Consider a trajectory that reaches a positive stable point, and let its convex hull be the convex hull of the points on that trajectory. Forward-closure conjecture. The convex hull of the trajectory reaching a positive stable point is forward closed. The conjecture concerns the geometric structure of attainable regions for weakly reversible chemical reaction networks; the supplied text does not state whether it has been resolved.