Uniqueness conjecture for weakly reversible deficiency-zero realizations

A reaction network is a directed network of complexes whose mass-action kinetics induces a kinetic differential equation; it is weakly reversible when every reaction lies in a strongly connected component, and its deficiency is the standard quantity $\delta$. Uniqueness conjecture. Any weakly reversible reaction network of deficiency zero has a unique realization. The source notes that a proof has been proposed, but does not establish that the conjecture is resolved.