Marques–Neves multiplicity one conjecture for min-max minimal hypersurfaces

Let $M^{n+1}$ be a closed manifold with a generic Riemannian metric, where $3\le n+1\le 7$. Consider closed minimal hypersurfaces obtained by min-max methods, and call a component two-sided unstable when it is two-sided and unstable for the area functional. Multiplicity one conjecture. Every two-sided unstable component of such a minimal hypersurface must have multiplicity one. This conjecture would make the Morse-index bound for the support of a min-max minimal hypersurface more informative about the original hypersurface and its unstable part. It is attributed to Marques and Neves; the supplied source does not state whether it has been resolved.