A Proofs

This appendix collects all proofs omitted from the main text due to space limitation. In this section, we prove Proposition 2.3 and the feasibility of the projected mechanisms. Thus, orbit averaging is a projection to equivariant function space and fixes all equivariant functions. Proof of the feasibility of projected mechanisms. A.2 Proof of Theorem 3.1 In this section, we proves Theorem 3.1.