Solomon's annihilation conjecture for class groups

Let $F$ be an abelian number field in which the prime $p$ is unramified, let ${\mathcal O}$ be the topological closure in ${\mathbb C}_p$ of the image of its ring of integers under a fixed embedding, and let $\operatorname{sol}_F$ be Solomon's element defined from the $p$-adic logarithms of a unit of $F$.

Solomon's conjecture. The element $\operatorname{sol}_F$ annihilates

$$Cl_F\otimes {\mathcal O}.$$

This is presented as a real analogue of the Stickelberger theorem, seeking an explicit group-ring annihilator for the class group. The supplied text gives no resolution status.