The fractional-decomposition hitting-time conjecture for random hypergraph processes

Let $K_k^n$ be the complete $k$-uniform hypergraph on $n$ vertices, and expose its edges one by one in a uniformly random order to obtain the random hypergraph process. A facet is a $(k-1)$-subset of vertices; it is uncovered until it belongs to an exposed edge. A fractional $K_k$-decomposition assigns weights in $[0,1]$ to the exposed $k$-edges so that every facet has total incident weight $1$. Fractional-decomposition hitting-time conjecture. As $n\to\infty$ with $k$ fixed, asymptotically almost surely the hitting time for the disappearance of uncovered facets equals the hitting time for the appearance of a fractional $K_k$-decomposition. This would show that uncovered facets are the only hitting-time obstruction to fractional decompositions, paralleling the known fractional-matching phenomenon; it remains open for these decompositions.