Pushforward formula for the structure sheaf of a derived blow-up

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ and let $pr_f:\mathbb{B}l_{Z/X}\to X$ be the relevant morphism. Let $\mathfrak{W}_{1-r,1-r}^{f}$ and $\mathfrak{w}_{(r-1,r-1),(0,r-1)}^{f}$ denote the objects and morphism defined in the paper. Pushforward conjecture. One has

$$pr_{f!}\mathcal{O}_{\mathbb{B}l_{Z/X}}\cong \mathfrak{W}_{1-r,1-r}^{f}.$$

When $r\leq 0$, the canonical map

$$pr_{f!}\mathcal{O}_{\mathbb{B}l_{Z/X}}\to \mathcal{O}_{X}$$

is represented by $\mathfrak{w}_{(r-1,r-1),(0,r-1)}^{f}$. This is proposed as a consequence of combining the determinant-dualizing-complex and discrepancy conjectures; the supplied text gives no resolution.