Weak-star density of Killing-vector derivations in local observables

Let $(M,g)$ be the spacetime under consideration and let $\mathcal{O}\in\mathcal{K}(M,g)$. Write $\mathrm{QuantLie}$ for the set

$$\{\delta_Z\colon Z\text{ is a Killing vector field}\}.$$

Let $\mathcal{M}^{\infty}(\mathcal{O},\mathrm{QuantLie})$ denote the corresponding smooth local observables generated using these derivations, and let $\mathcal{M}(\mathcal{O})$ be the local observable algebra. Weak-star density conjecture. $\mathcal{M}^{\infty}(\mathcal{O},\mathrm{QuantLie})$ is weak* dense in $\mathcal{M}(\mathcal{O})$.

This asserts that observables associated with Killing-vector-field derivations are sufficient to approximate every local observable in the weak-star topology. The supplied text does not state whether this claim has been proved or remains open.