Subquadratic minimal generation conjecture for random hypertree fundamental groups

Let $T_n$ be the random hypertree in the paper, let $\pi_1(T_n)$ be its fundamental group, and let $\operatorname{mg}(\pi_1(T_n))$ denote the minimal number of generators of that group.

Subquadratic generation conjecture. The normalized minimal number of generators converges to zero in probability:

$$\frac{\operatorname{mg}(\pi_1(T_n))}{n^2}\longrightarrow 0$$

in probability.

The conjecture asks for subquadratic growth of the minimal number of generators of the fundamental group of a random hypertree; the source gives no resolution.