Conjecture on inclusion divergence for sparse random geometric graphs

Let $\mathcal{G}(n,p)$ denote the Erdős–Rényi random graph, let $\mathcal{G}(n,p,d)$ denote the random geometric graph in dimension $d$, and let $p_0$ be the associated comparison parameter. Suppose that

$$p\sim c_0/n \quad\text{for some } c_0>0,$$

and

$$d\sim c_1n\log^2 n \quad\text{for some } c_1>0.$$

Inclusion-divergence conjecture. Under these assumptions,

$$\operatorname{I-Div}\big(\mathcal{G}(n,p,d)\,\|\,\mathcal{G}(n,p_0)\big)\to 0.$$

This conjecture concerns the boundary at which the random geometric model becomes equivalent to its Erdős–Rényi comparison in inclusion divergence. The supplied text does not state whether the conjecture has been resolved.