Born's rule conjecture for spacetime observables

Let $(\mathcal{M}, g)$ be a classical globally hyperbolic spacetime. Let $B$ be a compact simply connected subset of a Cauchy surface $\mathcal{N}$. Suppose that

$$\mathcal{U}=D(B)$$

is the domain of dependence of $B$.

Born's rule conjecture. The result of Proposition 3.1 of Finster (2013) should apply to pull back the spacetime observable of $\mathcal{U}$ to an observable on $B$.

This conjecture would relate the spacetime-region observable to an observable on a spatial hypersurface in the continuum limit, extending the analogy with Born's rule from spatial hypersurfaces to general spacetime regions. The supplied context does not state whether this conjecture has been proved or disproved.