Asymptotic enumeration conjecture for racks

A rack is a set equipped with a binary operation satisfying the rack axioms; two racks are identified when they are isomorphic. Let $n$ denote the size of the rack. Rack enumeration conjecture. There are

$$2^{(1/4+o(1))n^2}$$

racks of size $n$, up to isomorphism.

The preceding theorem gives the matching upper bound for $2$-reductive racks, while the paper cites a lower bound of $2^{n^2/4-O(n\log n)}$ for such racks. The conjecture asserts that all racks have the same leading asymptotic count, reflecting the observed predominance of $2$-reductive racks.