Artin prime-pair asymptotic conjecture

Fix an even integer $d$ and an integer $g\in\mathbb{Z}\setminus\{-1\}$ satisfying the hypotheses in the source, and let $[d,g]$ be the Artin-admissibility condition. Let $\pi_d(x)$ be the set of prime pairs $(p,p+d)$ with both entries at most $x$, and let $\pi_{d,g}(x)$ be the subset for which both primes are Artin primes for the root $g$. Artin prime-pair asymptotic conjecture. If $[d,g]$ is Artin admissible, then

$$\lim_{x\to\infty}\frac{\pi_{d,g}(x)}{\pi_d(x)}=4\frac{C_{d,\widetilde g}A_{d,g}}{|\varphi_d(\widetilde g)|},$$

where $|\varphi_d(\widetilde g)|$, $C_{d,\widetilde g}$, and $A_{d,g}$ are the quantities defined in the cited formulas and theorem of the source. The paper presents this as its main conjecture, predicting the limiting proportion of Artin prime pairs among prime pairs; the supplied text gives no resolution evidence.