  We present a family of four-dimensional Lorentzian manifolds whose invariant
classification requires the seventh covariant derivative of the curvature
tensor. The spacetimes in questions are null radiation, type N solutions on an
anti-de Sitter background. The large order of the bound is due to the fact that
these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2
but non-homogeneous. This means that tetrad components of $R, \nabla R,
\nabla^{(2)}R$ are constant, and that essential coordinates first appear as
components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one
additional invariant each, and $\nabla^{(7)}R$ is needed for invariant
classification. Thus, our class proves that the bound of 7 on the order of the
covariant derivative, first established by Karlhede, is sharp. Our finding
corrects an outstanding assertion that invariant classification of
four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.
