Kundt's conjecture on curvature alignment and degenerate Kundt spacetimes

We consider a Lorentzian spacetime $(M,g)$ of arbitrary dimension $n$. A null congruence $c$ is Kundt if it is non-twisting, geodetic, non-shearing and non-expanding. A spacetime is degenerate Kundt if it admits a Kundt null congruence with respect to which all curvature tensors, namely the Riemann tensor and its covariant derivatives, are of aligned type II or more special.

Kundt's conjecture. If all curvature tensors of $(M,g)$ are of aligned type II or more special with respect to some null congruence, then $(M,g)$ is degenerate Kundt: for each point $p\in M$, the curvature tensors are of aligned type II or more special with respect to a Kundt null congruence $c^{\prime}$ defined in a neighborhood of $p$.

The conjecture asks whether curvature alignment alone forces the existence, locally around every point, of a Kundt congruence realizing that alignment. It is attributed in the source to; its resolution is not specified in the supplied text.