Kontsevich–Soibelman motivic integral identity conjecture

Let $k$ be the coefficient field, let $d_1,d_2,d_3$ be nonnegative integers, and write $x=(x_1,\ldots,x_{d_1})$, $y=(y_1,\ldots,y_{d_2})$, and $z=(z_1,\ldots,z_{d_3})$. For a tuple $x$ and a new variable $t$, write $tx=(tx_1,\ldots,tx_{d_1})$. Let $f \in k[[x,y,z]]$ satisfy $f(0,0,0)=0$ and

$$f(tx,y,z)=f(x,ty,z)$$

in $k[[x,y,z,t]]$. Then $f$ is a series in $k\{x\}[[y,z]]$. Writing $\tilde f(z)=f(0,0,z)\in k[[z]]$, the Kontsevich–Soibelman conjecture asserts that

$$\int_{\mathbb A^{d_1}_k}\mathscr S_f=\mathbb L^{d_1}\mathscr S_{\tilde f,0}$$

holds in $\mathscr M_k^{\hat\mu}$. This identity is a building block in Kontsevich–Soibelman's theory of motivic Donaldson–Thomas invariants for noncommutative Calabi–Yau threefolds and would imply their existence directly; its resolution status is not specified in the supplied text.