General correlations to $b \to s\mu^+\mu^-$ anomalies from a rank condition

It is assumed that the New Physics addressing neutral-current $B$-meson anomalies couples to a single direction in quark flavor space, i.e., that the Wilson coefficient matrix of the relevant semi-leptonic operators be of rank one. By correlating the observed anomalies to other flavor and high-$_{pT}$ observables, we constrain the possible flavor directions involved in our assumption.