Let $M_\Sigma$ be an $n$-dimensional Thom-Mather stratified space of depth $1$. We denote by $\beta M$ the singular locus and $L$ associated link. In this paper we study problem when such a can endowed with wedge metric positive scalar curvature. relate to recent work on index theory spaces, giving first obstruction existence in terms $\alpha$-class $\alpha_w (M_\Sigma)\in KO_n$. order establis...