Constructibility conjecture for normalized volumes in families

Let

$$\pi\colon (\mathcal{X},\mathcal{D})\to T$$

be a $\mathbb{Q}$-Gorenstein flat family of klt singularities with a section $t\in T\mapsto x_t\in\mathcal{X}_t$. Constructibility conjecture. The function

$$t\mapsto \widehat{\operatorname{vol}}(x_t,\mathcal{X}_t,\mathcal{D}_t)$$

is constructible with respect to the Zariski topology. The statement is described as a consequence of the stable degeneration conjecture and also requires the expected openness of K-semistability.