Möbius cancellation conjecture for ramified primes

Let $G$ be a nontrivial finite group and let $\mathcal E^C(G;X)$ be the family of totally real tamely ramified $G$-extensions $K/\mathbb Q$ specified by the prescribed inertia classes, with radical discriminant $D_K<X$. The Möbius function of $D_K$ is $\mu(D_K)=(-1)^{|\operatorname{ram}(K)|}$.

Möbius cancellation conjecture. As $X\to\infty$,

$$\sum_{K\in\mathcal E^C(G;X)}(-1)^{|\operatorname{ram}(K)|}=o\bigl(|\mathcal E^C(G;X)|\bigr).$$

Equivalently, the number of ramified primes is predicted to be even approximately as often as it is odd. The source presents this as an additional conjectural asymptotic motivated by random-prime and Galois-distribution heuristics.