Giordano's generic cohomology conjecture for twisted polynomial superfunctors

Let $\mathcal{P}$ be the category of strict polynomial functors and let $\mathbfcal{P}$ be its super analogue. For $r\geq 0$, write $F_0^{(r)}$ and $G_0^{(r)}$ for Frobenius twists, and set

$$\boldsymbol{E_{r}}:=\operatorname{Ext}^*_{\mathbfcal{P}}(\textbf{I}_0^{(r)},\textbf{I}_0^{(r)}).$$

Generic cohomology conjecture. For all $F,G\in\mathcal{P}$, there is a graded isomorphism, natural in $F$ and $G$,

$$\operatorname{Ext}^*_{\mathbfcal{P}}(F_0^{(r)},G_0^{(r)})\simeq\operatorname{Ext}^*_{\mathcal{P}}(F,G_{\boldsymbol{E_{r}}}).$$

This is a conjectural extension of the known formula when one of the functors is additive, and relates cohomology of twisted polynomial superfunctors to untwisted generic cohomology. The source presents the displayed isomorphism as a particular case of a broader conjecture; no resolution is supplied here.