Termination-time conjecture for random greedy independent sets in hypergraphs

Consider the random greedy independent set algorithm on a sufficiently nice hypergraph, meaning one that is almost uniform, almost regular, and not too sparse. Let $Q$ denote the number of open elements after step $i$, and let $i$ be the number of elements already chosen. Termination-time conjecture. The algorithm terminates with high probability at an asymptotic step $i$ satisfying $Q\approx i$. For the sum-free process, this predicts termination when $2np\approx n^{1/2}t$, namely at

$$i=\left(\sqrt{\frac{2}{3}}+o(1)\right)n^{1/2}\log^{1/2}n.$$

This conjecture proposes a general heuristic for locating the end of random greedy independent-set processes by comparing the number of open elements with the number already selected. The paper establishes a lower bound for the sum-free process but does not establish this predicted termination time in full, so the conjecture remains open.