Conjecture on the dependence of the order-growth exponent on degree

Let $K/{\mathbb Q}$ be a number field of degree $d$. Let $N_d(B)$ denote the counting function from Theorem, and let $\alpha_K$ be the associated exponent. Degree-dependence conjecture.

$$\alpha_K = \frac{1}{2} \lim_{B \to \infty} \frac{\log N_d(B)}{\log B}.$$

In particular, $\alpha_K$ only depends on the extension degree of $K$ over $\mathbb Q$. This conjecture predicts that the asymptotic growth exponent for the relevant counting function is determined solely by the degree of the number field, rather than by the field itself.