The generic abundance conjecture for resonances of negatively curved cusp manifolds

Let $M$ be a cusp manifold, let $d$ be the dimension of its cusp cross-section as used in the paper, and let $\mathcal{G}(M)$ be the space of $C^\infty$ metrics $g$ for which $(M,g)$ is a cusp manifold with negative sectional curvature. For $\delta$ as in the surrounding resonance estimates, consider the vertical strip

$$d/2>\Re s>d-\delta.$$

Generic resonance abundance conjecture. For an open and dense set of $g\in\mathcal{G}(M)$, there is an infinite number of resonances outside any such strip. The conjecture asserts that the existence of resonances beyond the strip is more stable than their absence; the paper presents this as a proposed generic phenomenon rather than a proved result.