2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210657Given a hypersurface $M$ of null scalar curvature in the unit sphere $\mathbb{S}^n$, $n\ge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in $\Rr^{n+1}$ as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.Paper accepted to publication in Manuscripta MathematicaDifferential Geometry53C42text