Moree's density formula for polynomial Artin primes

Let $f(x)\in\mathbb{Z}[x]$ produce infinitely many primes, and let $g$ be a square-free integer such that all but finitely many primes produced by $f(x)$ remain inert in $\mathbb{Q}(\sqrt{g})$. Define $\delta_g(f,x)$ as the proportion of prime values $f(n)$ up to $x$ that are Artin primes for $g$. Moree's density conjecture. The limit $\delta_g(f)=\lim_{x\rightarrow\infty}\delta_g(f,x)$ exists and is independent of $g$, and

$$\delta_g(f)=\delta(f):=\prod_{q>2\ \text{prime}}\left(1-\frac{\#\{s\pmod q\mid f(s)\equiv1\pmod q\}}{q\#\{s\pmod q\mid f(s)\not\equiv0\pmod q\}}\right).$$

This is a proposed explicit density in the inert quadratic-field case; its general validity is open.