Bernig–Fu–Solanes characterization conjecture for angular valuations

Let $M$ be a Riemannian manifold. A valuation $\mu$ is called angular when

$$\mu\cdot \mathcal{A}(M)\subset \mathcal{A}(M),$$

where $\mathcal{A}(M)$ is the space of angular curvature measures and $\cdot$ denotes the Alesker product. Bernig–Fu–Solanes' characterization conjecture. The algebra of angular valuations on $M$ equals the Lipschitz–Killing algebra:

$$\text{the algebra of angular valuations on }M=\mathcal{L}\mathcal{K}(M).$$

This conjecture asks whether the property of preserving angular curvature measures characterizes Lipschitz–Killing valuations. The source presents it as a conjecture following the proved angularity result.