The qAGH knot invariance conjecture

Let $\Bbbk$ be a field, and let $q$ be a parameter. The homology theory ${\mathit{qAGH}}$ is constructed from the quantum annular foam complex associated with a knot closure.

qAGH knot invariance conjecture. If $\Bbbk$ is a field of characteristic $0$, then ${\mathit{qAGH}}$ is a knot invariant for any $q$.

This conjecture asserts that the quantum theory is invariant under changing the braid representative of a knot, extending the stated characteristic-zero invariance of the specialization ${\mathit{AGH}}$. The supplied text gives no resolution, so its status remains open.