The uniform-distribution conjecture for temporal-clique label intervals

Let $G_{n,\delta}$ be an Erdős–Rényi random graph, and construct a temporal instance ${\cal I}(G_{n,\delta})$ by assigning labels to the edges of $G_{n,\delta}$ independently and uniformly at random in $[0,\delta]$, and assigning labels to all other edges independently and uniformly at random in $[\delta,1]$. For a vertex set $Q$, define its label interval by

$$\Delta(Q)=\left[\min(\lambda(e):e\in Q),\max(\lambda(e):e\in Q)\right].$$

Let $Q^*$ be the $\delta$-clique constructed by algorithm ${\cal A}_{SRT}$ on instance ${\cal I}(G_{n,\delta})$. Uniform-distribution conjecture. Then $\Delta(Q^*)$ is distributed almost uniformly at random within $[0,1]$. This conjecture concerns the distribution of the interval containing the labels of an algorithmically found temporal clique and is proposed as a possible route toward proving the reduction from temporal-clique approximation to maximum-clique approximation in Erdős–Rényi graphs; no proof or resolution is given.