Fractional and exact hypergraph clique-decomposition threshold conjecture

For integers $r>k\ge 2$, let $\delta_{K_r^k}$ be the minimum-degree threshold for exact $K_r^k$-decompositions, and let $\delta_{K_r^k}^*$ be the corresponding fractional decomposition threshold.

Threshold equality conjecture. For all $r>k\ge 2$,

$$\delta_{K_r^k}=\delta_{K_r^k}^*.$$

This conjecture generalizes the equality known for graph cliques. Establishing it would show that the fractional relaxation has the same asymptotic minimum-degree threshold as the exact hypergraph decomposition problem.