Aouchiche–Hansen Randić index diameter bound

Let $G$ be a graph, with Randić index $\operatorname{R}(G)$, diameter $\operatorname{d}(G)$, and order $\#V(G)$. Aouchiche–Hansen's conjectured bound.

$$\operatorname{R}(G)\geq \operatorname{d}(G)+\sqrt{2}-\frac{\#V(G)+1}{2}.$$

This is a proposed lower bound relating the Randić index to graph diameter. The supplied source does not state whether the bound has been resolved.