Rational contractibility conjecture for dual complexes of rational hypersurface singularities

Let $D$ be the exceptional divisor of a resolution of an isolated rational hypersurface singularity of dimension at least $3$, and let $\Delta=\Delta(D)$ be its dual complex. Rational contractibility conjecture. The rationalization of $\Delta$ is contractible. Stepanov's theorem gives simple connectedness of $\Delta$ in this setting, while the preceding cohomological conjecture would provide the corresponding vanishing of complex cohomology; the integral cohomology is not determined by these statements, so the conjecture concerns contractibility after rationalization.