Bouquet-of-spheres conjecture for random simplicial complexes

Let $X\sim X(n,p)$ be a random simplicial complex, let $d\geq 3$, and fix

$$\frac{1}{d+1}<\alpha<\frac{1}{d}.$$

Set $p=n^{-\alpha}$. Bouquet-of-spheres conjecture. With high probability, $X$ is homotopy equivalent to a bouquet of $d$-dimensional spheres. This conjecture predicts a particularly simple homotopy type in the regime where the relevant homology is concentrated in degree $d$; the source presents it as a guess, and does not state a proof or resolution.