Integrality conjecture for the previously defined $\mathfrak{sl}(N)$-link homology

Let $N\geq 4$ and consider the $\mathfrak{sl}(N)$-link homology defined in the preceding sections over the rational theory, with its relations and homomorphisms suggested to admit integral definitions. A homology theory is integral when it is defined over $\mathbb{Z}$. Integrality conjecture. The $\mathfrak{sl}(N)$-link homology defined in the previous sections is integral. The claim is motivated by the fact that the defining relations and the relevant homomorphisms can be defined over $\mathbb{Z}$; the source gives no resolution.