Mayer's refinement of Scholz's conjecture for ramified cubic extensions

Let $L$ be a non-Galois totally real cubic field with ramified Galois closure $N$, conductor $f>1$ over a real quadratic field $K$, and type $\alpha$, with $U_N=U_0$. Let $T_{K,N}:\operatorname{Cl}_3(K)\to\operatorname{Cl}_3(N)$ be the transfer homomorphism, defined by $\mathfrak{a}\cdot\mathcal{P}_K\mapsto(\mathfrak{a}\mathcal{O}_N)\cdot\mathcal{P}_N$, and let $s$ count the prime divisors of $f$ that split in $K$. Mayer's conjecture. Such fields should exist in each of the following situations: type $\alpha_1$ with $\dim_{\mathbb{F}_3}(\ker(T_{K,N}))=2$, $\varrho_3(K)=2$, and $s=0$; type $\alpha_2$ with $\dim_{\mathbb{F}_3}(\ker(T_{K,N}))=1$, $\varrho_3(K)=1$, and $s=1$; or type $\alpha_3$ with $\dim_{\mathbb{F}_3}(\ker(T_{K,N}))=0$, $\varrho_3(K)=0$, and $s=2$. This refines Scholz's existence conjecture by specifying three ramified configurations of the unit and capitulation data; the supplied text gives no resolution status.