Quantum consistency conjecture for the quantum exceptional category

Let $R$ be a ring and let $\mathsf{QExc}_{R,v,w}$ be the quantum exceptional diagram category, with $\mathbb Q(v,w)$-valued closed-diagram evaluations defined by the stated relations. Quantum consistency conjecture. If every polynomial in $\mathbf P=\{v,w,\Psi_1,\Psi_2,\Psi_3,\Psi_6,[\lambda],[1-\lambda]\}$ is invertible, then the map sending $r\in R$ to $r$ times the empty diagram embeds $R$ into $\mathsf{QExc}_{R,v,w}$. Consequently, any two applications of the relations to a closed diagram that return a rational function in $v,w$ produce the same rational function. This is the quantum counterpart of classical consistency and asserts confluence of closed-diagram reductions.