Baker–Jin conjecture on the scarcity of finite hyperfield quotients

Let $\mathcal{H}_n$ be the set of isomorphism classes of hyperfields of order $n$, and let $\mathcal{Q}_n \subseteq \mathcal{H}_n$ be the subset of those which are isomorphic to a quotient of some field.

Baker–Jin conjecture.

$$\lim_{n \to \infty} \frac{\#\mathcal{Q}_n}{\#\mathcal{H}_n} = 0.$$

This conjecture asserts that almost all finite hyperfields are not quotients of fields, extending the quotient constructions and necessary criteria discussed in the surrounding work. Its resolution is not established in the supplied text.