The Buchsbaum equality conjecture for symmetric and exterior iterated Betti numbers

Let $\Gamma$ be a Buchsbaum simplicial complex, and let $b_{i,j}(\Gamma)$ and $b^e_{i,j}(\Gamma)$ denote its symmetric and exterior iterated Betti numbers. Let $\Delta(\Gamma)$ and $\Delta^e(\Gamma)$ be its symmetric and exterior algebraic shifts, with Stanley–Reisner ideals $I_{\Delta(\Gamma)}$ and $I_{\Delta^e(\Gamma)}$. Buchsbaum equality conjecture. If $\Gamma$ is a Buchsbaum complex, then

$$b_{i,j}(\Gamma)=b^e_{i,j}(\Gamma),$$

and hence

$$\beta_{i,j}(I_{\Delta(\Gamma)})=\beta_{i,j}(I_{\Delta^e(\Gamma)}).$$

The source presents this as an additional conjecture for Buchsbaum complexes; it does not state whether it has been resolved.