The b5-conjecture for class group torsion

Let $K/\mathbb{Q}$ be a number field of degree $s$ with discriminant $D_K$. For an integer $\ell\geq 1$, write $h_K[\ell]$ for the order of the $\ell$-torsion subgroup of the class group of $K$. The $\varepsilon$-conjecture. For every integer $\ell\geq 1$ and every $\varepsilon>0$,

$$h_K[\ell]\ll_{s,\ell,\varepsilon}D_K^{\varepsilon}.$$

This conjecture predicts essentially negligible growth of fixed-order class group torsion relative to the discriminant. The source presents the bound as evidence-supported conjectural input for arithmetic statistics of number fields, with no resolution stated here.