Artin prime-pair error-term conjecture

Let $E_{d,g}(x)$ be the error contribution defined by

$$E_{d,g}(x):=\sum_{\substack{k,l\text{ odd}\square\textnormal{-free}\\(k,l)\neq(1,1)}}S_{k,l}(x;d,g),$$

where $S_{k,l}(x;d,g)$ is the sum defined in the source, and let $[d,g]$ be Artin admissible. Artin prime-pair error-term conjecture.

$$E_{d,g}(x)=o\left(\frac{x}{(\log x)^2}\right).$$

The conjecture asserts that the non-main contribution in the decomposition of the Artin prime-pair count is of lower order than the expected prime-pair scale. No resolution status is supplied in the text.