The asymptotic suspension conjecture for 2-level polytopes

Let $\ell(d)$ and $s(d)$ respectively denote the numbers of combinatorially distinct $2$-level polytopes and $2$-level suspensions in dimension $d$. Suspension conjecture for 2-level polytopes. We have

$$\ell(d)=\Theta(s(d)).$$

Experiments show that suspensions constitute a growing majority of the $2$-level polytopes in dimensions at most $7$, but the asserted asymptotic comparison remains open and is described in the source as the riskiest of the three conjectures.