Mayhew–Newman–Welsh–Whittle sparse paving asymptotic predominance conjecture

For each positive integer $n$, let $\operatorname{mat}(n)$ and $\operatorname{mat}'(n)$ be the numbers of matroids on $[n]$, respectively counted with labels and up to isomorphism. Let $\operatorname{sp}(n)$ and $\operatorname{sp}'(n)$ be the corresponding numbers of sparse paving matroids. Sparse paving asymptotic predominance conjecture.

$$\lim_{n\to\infty}\frac{\operatorname{sp}(n)}{\operatorname{mat}(n)}=1\qquad\text{and}\qquad\lim_{n\to\infty}\frac{\operatorname{sp}'(n)}{\operatorname{mat}'(n)}=1.$$

This is a central asymptotic enumeration conjecture asserting that sparse paving matroids dominate all matroids; it is described as a conjecture posed by Mayhew et al. and no resolution is given.