Kontsevich–Soibelman wall-crossing conjecture for quivers with potential

Let $Q$ be a finite quiver, let $W$ be a polynomial potential on $Q$, and let $\operatorname{\mathsf{nil}}(\mathcal P(Q,W))$ be the category of finite-dimensional right modules over the Jacobian algebra. For $k=\mathbb{C}$, let

$$Z:K_0(\operatorname{\mathsf{nil}}(\mathcal P(Q,W)))\to\mathbb{C}$$

be a discrete stability function. Kontsevich–Soibelman wall-crossing conjecture. The product

$$\mathbb{E}_{Q,W,Z}=\prod_{M\text{ stable}}^\curvearrowright\mathbb{E}(y^{\underline{\dim}\,M})$$

with factors ordered by decreasing phase is independent of the choice of $Z$. This is a quantum dilogarithm identity associated with a quiver with potential. The statement is presented as still conjectural in the source; it asserts stability-independence of the ordered product of quantum dilogarithms.