Bernig–Fu–Solanes angularity conjecture for curvature measures

Let $M$ be a Riemannian manifold. The space of angular curvature measures is denoted by $\mathcal{A}(M)$, and the Lipschitz–Killing algebra by $\mathcal{L}\mathcal{K}(M)$. Here a valuation is called angular if its Alesker product with every angular curvature measure is angular. Bernig–Fu–Solanes' angularity conjecture. The space $\mathcal{A}(M)$ is invariant under the action of the Lipschitz–Killing algebra:

$$\mathcal{L}\mathcal{K}(M)\cdot \mathcal{A}(M)\subset \mathcal{A}(M).$$

This conjecture asserts that Lipschitz–Killing valuations preserve angular curvature measures under the Alesker product. The source also describes a stronger characterization conjecture: angular valuations should be exactly the Lipschitz–Killing valuations.