Absolute convergence of the real xi logarithmic derivative

The Jensen zero-count bound gives $O(T\log T)$ zeros up to ordinate $T$. Since their real parts lie in $(0,1)$, a fixed-point real logarithmic derivative summand is $O(|\Im \rho {|}^{-2})$. Dyadic ordinate bands then contribute $O(j{2}^{-j})$. This proves absolute convergence of the real sum, while the unpaired complex sum of reciprocals need not converge absolutely.