Discrepancy formula for derived blow-ups

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ over $S$, with morphism $pr_{Z/X}:\mathbb{B}l_{Z/X}\to X$ and integer $r$ as in the main theorem. Let $L_{\mathbb{B}l_{Z/X}/S}$ and $L_{X/S}$ be the cotangent complexes of $\mathbb{B}l_{Z/X}$ and $X$ over $S$. Discrepancy conjecture. There is an isomorphism

$$pr_{Z/X}^{*}\det(L_{X/S})\cong \det(L_{\mathbb{B}l_{Z/X}/S})\otimes \mathcal{O}_{\mathbb{B}l_{Z/X}}(r-1).$$

This conjecture proposes a relationship between virtual codimension and discrepancy in derived birational geometry. In the stated setting, it is known when $S=\operatorname{Spec}(\mathbb{C})$, $X$ is a derived scheme, and both $Z$ and $X$ are smooth, as well as when the derived blow-up is smooth; the general case remains open.