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 ${\mu }_K$ and preferred longitude ${\lambda }_K$. We prove that the profinite completion $\widehat{G_K}$, marked by the conjugacy class of ${\mu }_K{\lambda }_K$, determines $K$ up to oriented equivalence. In fact, every isomorphism preserving this mark preserves the meridian and longitude with the same conjugator. The proof combines Xu’s genuineness theorem with profinite JSJ theory and simultaneous boundary realization, and applies to satellite and composite knots. Consequently, Eisermann’s colouring polynomials over all finite groups determine oriented knots.