Linear-latency contention resolution in the GlobalClock model

Consider randomized acknowledgment-based protocols in the $\textsf{GlobalClock}{}$ model. In the finite setting, latency concerns completing contention resolution for the participating parties; in the unbounded setting, utilization at rate $\lambda$ means that there is a potential function $\Phi$ such that waking up $n'$ parties increases $\Phi$ by at most $n'/\lambda$, sufficiently large potential decreases by $1+\epsilon$ in expectation per further time step for some $\epsilon>0$, and bounded potential leaves only $O(1)$ unsuccessful parties.

GlobalClock contention-resolution conjecture. In the finite setting, there exists a protocol with latency $O(n)$ with high probability against an adaptive adversary. In the unbounded setting, there exists a protocol that utilizes the shared resource at some rate $\lambda$, even against an adaptive adversary.

The conjecture proposes that the current $n(\log\log n)^{1+o(1)}$ high-probability latency bound in the GlobalClock model can be improved to linear latency, while retaining robustness against adaptive adversaries. The source does not provide evidence that either assertion has been resolved.