Kontsevich–Soibelman integral identity conjecture for regular functions

Let $(x,y,z)$ be the standard coordinates of the vector space $k^d=k^{d_1}\times k^{d_2}\times k^{d_3}$. Let $f\in k[x,y,z]$ satisfy $f(0,0,0)=0$ and

$$f(\lambda x,\lambda^{-1}y,z)=f(x,y,z)$$

for every $\lambda\in\mathbb G_{m,k}$. Let $\tilde f$ be the restriction of $f$ to $\mathbb A_k^{d_3}$, and let $i:\mathbb A_k^{d_1}\hookrightarrow f^{-1}(0)$ be the inclusion. Kontsevich–Soibelman's integral identity conjecture. The identity

$$\int_{\mathbb A_k^{d_1}}i^*\mathscr{S}_f=\mathbb L^{d_1}\mathscr{S}_{\tilde f,0}$$

holds in $\mathscr M_k^{\hat\mu}$. This identity is a building block of Kontsevich–Soibelman's theory of motivic Donaldson–Thomas invariants for noncommutative Calabi–Yau threefolds, and its proof establishes the full regular-function version of the conjecture.