Conical singularities of momentum-section zero loci for proper Hamiltonian groupoids

Let a hamiltonian Lie algebroid over a symplectic manifold integrate to a proper hamiltonian Lie groupoid. Its momentum-section zero locus is the subset where the momentum section vanishes.

Conical-singularity conjecture. The zero locus of the momentum section has only conical singularities.

This would provide a Lie-groupoid analogue of the linearization result for proper Hamiltonian Lie-group actions and describe the local singularity structure of momentum-section zero loci.