Conjecture on geometrically maximal degenerations of simply-connected surfaces

Let $S$ be a simply-connected surface with Hodge numbers $h^{1,0}=h^{2,0}=0$. A geometrically maximal degeneration is a degeneration having the geometric maximality property used in the paper, and its dual complex is called non-collapsible when it cannot be collapsed by the relevant elementary collapses. The geometrically maximal degeneration conjecture. Every simply-connected surface with $h^{1,0}=h^{2,0}=0$ admits a geometrically maximal degeneration with non-collapsible contractible dual complex. This proposes a broad existence principle extending the example constructed in the paper; the supplied text does not state whether it has been resolved.