Separation between Sink-or-Clash and Sink-USO in deterministic query complexity

Ascertain whether the deterministic query complexity t(n) of Sink-or-Clash is strictly larger than the deterministic query complexity q(n) of Sink-USO for some dimension n, by establishing tighter upper bounds for q(n) or lower bounds for t(n) that yield a provable separation.

Background

The paper shows that for dimensions up to 4, the deterministic query complexities of Sink-or-Clash and Sink-USO coincide, even though Sink-or-Clash appears to be harder in general because it must either find a sink or identify a clash.

Despite this intuition, the authors were unable to derive bounds that demonstrate a strict hardness separation between the two problems, leaving the question of separation open.