The operational-to-primarily-strong Chow isomorphism conjecture

Let $\mathcal{X}$ be a smooth connected properly stable Artin stack with good moduli space $\pi\colon\mathcal{X}\to X$. Let $A^*_{\operatorname{op}}(X)_\mathbb Q$ be the operational Chow ring of $X$, let $A^*_{\operatorname{tst}}(\mathcal{X}/X)_\mathbb Q$ be the relative topologically strong Chow group, and let $A^*_{\operatorname{pst}}(\mathcal{X}/X)_\mathbb Q$ be generated by primarily strong integral substacks, meaning topologically strong integral substacks whose inverse images under $\pi$ have no embedded components. The injection

$$\pi^*\colon A^*_{\operatorname{op}}(X)_\mathbb Q\to A^*_{\operatorname{tst}}(\mathcal{X}/X)_\mathbb Q$$

induces an isomorphism Operational-to-primarily-strong Chow isomorphism conjecture.

$$A^*_{\operatorname{op}}(X)_\mathbb Q\simeq A^*_{\operatorname{pst}}(\mathcal{X}/X)_\mathbb Q.$$

The conjecture proposes an intrinsic description of the image of operational Chow classes under pullback, refining the fact that the pullback is injective but need not surject onto all topologically strong classes. Its status is not resolved in the supplied text.