Conjecture on conformal-gravity observables and the inclusion of Einstein observables

Let $d4d4_g$ and $d4d4$ denote the linearized conformal-gravity and general-relativity theories, respectively, and let $d4d0\mathrm{bs}^{\mathrm{cl}}(-,d4d4)$ denote their classical observables on $d4d0d0c$. Conformal-gravity observables conjecture. The observables $\mathrm{Obs}^{\mathrm{cl}}(-,d4d4)$ of linearized conformal gravity define a time-orderable and Cauchy constant prefactorization algebra on $\mathbf{Loc}$. Moreover, there is an inclusion

$$\mathrm{Obs}^{\mathrm{cl}}(-,d4d4) \hookrightarrow \mathrm{Obs}^{\mathrm{cl}}(-,d4d4)$$

of the observables of linearized general relativity into those of linearized conformal gravity. This is expected to follow if the underlying cochain complex for conformal gravity is Green hyperbolic; that Green hyperbolicity remains an outstanding question.