Ext-group decomposition conjecture for quantum Frobenius twists

Let $\mathbb{K}$ be a field, let $q\in\mathbb{K}^{\times}$ be a non-zero scalar, and let $F$ and $G$ be strict polynomial functors. Write $F^{(1)_q}$ and $G^{(1)_q}$ for their quantum Frobenius twists, and let $G^j_E$ be the strict polynomial functor constructed from $G$ in the explicit way specified by the source. Ext-group decomposition conjecture. There is a graded isomorphism

$$\operatorname{Ext}^k_{\mathcal{P}^{}_q}(F^{(1)_q},G^{(1)_q})\simeq\bigoplus_{i+j=k}\operatorname{Ext}^i_{\mathcal{P}^{}_1}(F,G^j_E).$$

This conjecture predicts that Ext-groups between quantum Frobenius twists can be computed from Ext-groups in the classical category together with the functors $G^j_E$. It is presented as a conjecture motivating the construction of quantum Troesch complexes; the supplied text gives no evidence that it has been resolved.