The critical-window product conjecture for random digraph components

Let $D(n,p)$ be the random directed graph and $G(n,p)$ the random graph, with $p=n^{-1}+\lambda n^{-4/3}$. Let $X^\lambda=n^{-2/3}|\mathcal{C}_1(G(n,p))|$ and $Y^\lambda=n^{-1/3}|\mathcal{C}_1(D(n,p))|$, and let $X_1^\lambda$ and $X_2^\lambda$ be independent copies of $X^\lambda$. Critical-window product conjecture. The distributions satisfy

$$Y^\lambda=X_1^\lambda X_2^\lambda.$$

This conjecture proposes an exact relation between the critical-window component-size distributions of random directed and undirected graphs, extending the known connection between giant strongly connected components in $D(n,p)$ and giant components in $G(n,p)$ for larger $p$.