Zaidenberg's finiteness conjecture for Eisenbud–Neumann diagrams

Let $\bar E\subseteq\mathbb{P}^2$ be a rational cuspidal curve, and let $(X,D)\to(\mathbb{P}^2,\bar E)$ be the minimal log resolution of singularities. Zaidenberg's finiteness conjecture. The set of possible Eisenbud–Neumann diagrams of $D$ is finite. This conjecture predicts a finite combinatorial classification of the resolution data of rational cuspidal curves; the source states that it proves an effective version, so the conjecture is solved.