Equivariant degree-interval conjecture for quantum K-theory products

Let $X=G/P_X$ be a cominuscule flag variety, let $u,v\in W^X$, and let $\operatorname{QK}_T(X)$ be its equivariant quantum $K$-theory. Write $d_{\max}(u,v)$ for the maximal degree associated with $u$ and $v$, and call a degree exceptional for ${\mathcal O}_{u^\vee}\star{\mathcal O}^v$ when it satisfies the exceptional-degree condition defined in the paper.

Equivariant degree-interval conjecture. The power $q^d$ occurs in

$${\mathcal O}^u\star{\mathcal O}^v\in\operatorname{QK}_T(X)$$

if and only if $0\leq d\leq d_{\max}(u,v)$ or $d=d_{\max}(u,v)+1$ is an exceptional degree of ${\mathcal O}_{u^\vee}\star{\mathcal O}^v$.

The statement extends the nonequivariant degree description to equivariant quantum $K$-theory. The supplied text presents it in a remark alongside results implying the corresponding degree theorem, but does not provide a resolution of this exact equivariant assertion.