Locality conjecture for irreducible representations on frameworks

Let $M$ be a framework, that is, a Lie manifold for $\mathsf{so}(2,3)$ on which the four-dimensional irreducible representation is local. An irreducible representation $V$ of $\mathsf{so}(2,3)$ is local on $M$ if there is a generalised tensor on $M$ whose local action is equivalent to the action on $V$.

Locality conjecture. Every irreducible representation of $\mathsf{so}(2,3)$ is local on a framework $M$.

The conjecture asserts that no irreducible representation is excluded by the geometric locality condition on a framework. The source reports that all small-dimensional representations considered there are local, but that no general proof is given.