Injective strong Chow subring conjecture for good moduli spaces

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map from a properly stable smooth Artin stack, and let $A^*_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}$ denote its strong relative Chow ring. Injective strong Chow subring conjecture. Assuming the strong Chow pushforward conjecture and the strong Chow ring conjecture, there exists a subring

$$A^*_{inj}(\mathcal {X}/{\mathbf X})_\mathbb{Q}\subseteq A^*_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}$$

that contains the subalgebra generated by $A^1_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}$ and on which $\pi_{st,*}$ is injective. If ${\mathbf X}$ has only quotient singularities, then $\pi_{st,*}$ is bijective on all of $A^*_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}$. This conditional statement strengthens the expected relationship between strong cycles on the stack and cycles on its good moduli space.