Fomin–Zelevinsky's denominator conjecture for cluster algebras

Let $\mathcal{A}$ be a cluster algebra with trivial coefficients, and fix a cluster $\mathbf{x}=(x_1,\dots,x_n)$. For every cluster monomial $z$, write its Laurent expansion uniquely as

$$z=\frac{f(x_1,\dots,x_n)}{x_1^{d_1}\cdots x_n^{d_n}},$$

where $d_1,\dots,d_n\in\mathbb{Z}$ and $f(x_1,\dots,x_n)\in\mathbb{Z}[x_1,\dots,x_n]$ is not divisible by any $x_i$. The vector $d_{\mathbf{x}}(z)=(d_1,\dots,d_n)$ is called the denominator vector of $z$ with respect to $\mathbf{x}$. Fomin–Zelevinsky's denominator conjecture. Different cluster monomials have different denominator vectors with respect to any given cluster. This conjecture concerns the combinatorial parametrization of cluster monomials by denominator vectors. In the paper's stated context it is disproved: Jiarui Fei found a counterexample.