The optimal resonance lower bound for bounded compactly supported potentials

Let $V\in L^\infty_{\operatorname{comp}}(\mathbb R^n)$ be real-valued and non-zero, with $n$ odd. Let $N_V(r)$ denote the number of resonances in $\{|\lambda|\le r\}$. Optimal resonance lower-bound conjecture. There exists $c>0$ such that

$$N_V(r)\ge cr^n.$$

Existing results establish infinitely many resonances in related settings, but the source presents this optimal lower bound as open.