The algebraic and symmetric shifting Betti-number conjecture

Let $\Delta$ be a simplicial complex over a field $K$ of characteristic zero. Let $I_{\Delta^s}$ and $I_{\Delta^e}$ denote the Stanley–Reisner ideals of the symmetric and exterior shifts of $\Delta$, respectively, and let $\beta_{i,j}$ denote graded Betti numbers.

Algebraic and symmetric shifting conjecture. For all $i,j$,

$$\beta_{i,j}(I_{\Delta^s})\leq \beta_{i,j}(I_{\Delta^e}).$$

This conjecture compares the graded Betti numbers arising from symmetric and exterior algebraic shifting; the supplied source does not indicate whether it has been resolved.