Malle's polynomial bound conjecture for number fields

For a number field $k$, write $\mathcal{D}_k$ for its discriminant. Malle's polynomial bound conjecture. There exists an absolute constant $B$ such that, for sufficiently large $x$, the number of isomorphism classes of number fields with discriminants less than $x$ is at most $x^B$. This conjecture predicts a uniform polynomial upper bound for the number of number fields of bounded discriminant; the supplied text does not state a resolution.