Coates–Sinnott conjecture on higher Stickelberger annihilators

Let $F/K$ be an abelian CM extension of a totally real number field $K$, let ${\bf f}$ be the conductor of $F/K$, and let $\Theta_n({\bf b},{\bf f})$ be the higher Stickelberger element, where ${\bf b}$ is an integral ideal of $K$ coprime to ${\bf f}$ and $w_{n+1}(F)={\rm card}\,H^0(F,\mathbb Q/\mathbb Z(n+1))$. Coates–Sinnott conjecture. For all $n\geq 1$ and all ${\bf b}$ coprime to $w_{n+1}(F)$, $\Theta_n({\bf b},{\bf f})$ annihilates $K_{2n}({\mathcal O}_F)$. This is a higher analogue of Brumer's conjecture; the source records the claim but gives no resolution status.