Simon's conjecture on extendable shellability of simplex skeleta

Let $\Delta_{n-1}^{(d)}$ denote the $d$-skeleton of the $(n-1)$-dimensional simplex. A pure $d$-dimensional shellable complex on $n$ vertices is extendably shellable if every shelling of a subcomplex can be extended to a shelling of the entire complex. Simon's conjecture. The complex $\Delta_{n-1}^{(d)}$ is extendably shellable. Equivalently, any pure $d$-dimensional shellable complex on $n$ vertices can be extended to $\Delta_{n-1}^{(d)}$ by attaching one facet at a time while maintaining shellability. This conjecture concerns whether shelling sequences in simplex skeleta can always be completed; the source gives no resolution status.