Completing shellings with $d-2$ extra vertices

Simon's conjecture (1994) asserts that any pure $d$-dimensional shellable complex on $n$ vertices can be extended to the $d$-skeleton of the simplex on $n$ vertices, one facet at a time, while maintaining shellability. Bolognini and Sentinelli (2026) recently disproved it for every $d \geq 3$. We sh