Unistructurality of cluster algebras

We prove that any skew-symmetrizable cluster algebra is unistructural, which is a conjecture by Assem, Schiffler, and Shramchenko. As a corollary, we obtain that a cluster automorphism of a cluster algebra $\mathcal A(\mathcal S)$ is just an automorphism of the ambient field $\mathcal F$ which restricts to a permutation of cluster variables of $\mathcal A(S)$.

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