Recognizing oriented knots from finite quotients with one marked element

For an oriented tame knot $K$, let $G_K$ be its group, with positive meridian $μ_K$ and preferred longitude $λ_K$. We prove that the profinite completion $\widehat{G_K}$, marked by the conjugacy class of $μ_Kλ_K$, determines $K$ up to oriented equivalence. In fact, every isomorphism preserving this