Scholz's conjecture on distinguished dihedral cubic fields

Let $L$ be a non-Galois totally real cubic field with Galois closure $N$, and let $K$ be the real quadratic subfield of $N$. Write $f=f(N/K)$ for the conductor, let $U_N$ be the unit group of $N$, and let $U_0=\langle U_K,U_L,U_{L^{\prime}},U_{L^{\prime\prime}}\rangle$ be the subgroup generated by the units of the proper subfields. Let $\varrho_3(K)$ denote the $3$-class rank of $K$, and let capitulation mean that the relevant ideal classes of $K$ become principal in $N$.

Scholz's conjecture. There should exist such fields $L$ for which either $f=1$, $\varrho_3(K)=2$, the complete $3$-elementary class group of $K$ capitulates in $N$, and $U_N=U_0$, or $f>1$ and $U_N=U_0$.

The conjecture predicts the existence of distinguished cases in which the unit group of the normal closure is generated by units from its proper subfields, both in the unramified setting and for ramified ring class fields in Scholz's terminology.