The iterated quantum Frobenius Ext decomposition conjecture

Let $F$ and $G$ be strict polynomial functors, let $F^{(s)_q}$ and $G^{(s)_q}$ denote their $s$-th quantum Frobenius twists, and define

$$E_s=\operatorname{Ext}_{\mathcal{P}^{}_q}^*(I^{(s)_q},I^{(s)_q}).$$

For each degree $k$, the iterated quantum Frobenius Ext decomposition conjecture. There is a graded isomorphism

$$\operatorname{Ext}^k_{\mathcal{P}^{}_q}(F^{(s)_q},G^{(s)_q})\simeq\bigoplus_{i+j=k}\operatorname{Ext}^i(F,G^j(E_s\otimes I)).$$

The paper states this as a consequence, in characteristic $p>0$, of the one-step conjecture. It would provide a uniform description of Ext-groups after arbitrary quantum Frobenius twists, beyond the cases computed in the paper.