Weaken the arrival-order assumptions for ARHM replenishment

Characterize which arrival-order assumptions weaker than a uniformly random permutation suffice for the ARHM replenishment algorithm to obtain the same space separation.

Background

The ARHM upper bound relies on uniformly random interleaving: each build interval must provide an accurate quantum state, while only a small number of requests may arrive before the next interval completes. The lower bound shows that a long suffix of fresh requests without further updates forces substantial retained space.

The paper leaves unresolved whether a weaker distributional or structural assumption on the arrival order would still guarantee successful replenishment and the associated separation.