The forcing-axiom rigidity conjecture for C*-algebra coronas

Let $A$ and $B$ be separable non-unital $\mathrm{C}^*$-algebras. Write $\mathcal Q(A)$ and $\mathcal Q(B)$ for their coronas, and call an isomorphism topologically trivial when it has a Borel lifting in the sense defined immediately before the claim.

Corona rigidity conjecture. CH implies that there are automorphisms of $\mathcal Q(A)$ that are not topologically trivial. Forcing Axioms imply that all isomorphisms between $\mathcal Q(A)$ and $\mathcal Q(B)$ are topologically trivial.

The text identifies this as the C*-algebra instance of the meta-conjecture and attributes it to the cited work; no resolution is supplied here.