Localization-number bound for unit disk graphs

Let $G$ be a unit disk graph, let $\zeta(G)$ denote its localization number, and let $\omega(G)$ denote its clique number. Unit-disk localization conjecture. There is a function $f$ such that every unit disk graph satisfies

$$\zeta(G)\leq f(\omega(G)).$$

This conjecture asks whether the localization number of unit disk graphs is bounded by a function of their clique number, linking a pursuit-game parameter with a standard geometric graph invariant. The source presents it as a problem for future study and gives no resolution.