Orbifold–Nichols algebra representation-category equivalence problem

Let $\mathfrak{g}$ be a Lie algebra, let $ell=4$, and let $\theta$ be a diagram automorphism. Consider an orbifold model of the logarithmic conformal field theory for $(\mathfrak{g},ell)$ under $\theta$, and a factorizable Hopf algebra associated with the authors' non-diagonal Nichols algebra associated with $(\mathfrak{g},\theta)$. Orbifold–Nichols equivalence problem. Are their representation categories equivalent? This is posed as an open question, with no answer supplied.