The Continuum Hypothesis conjecture on nontrivial corona automorphisms

Let $\mathcal{A}$ be a separable, nonunital C*-algebra, and let its corona be the quotient $\mathcal{Q}(\mathcal{A})=\mathcal{M}(\mathcal{A})/\mathcal{A}$ of its multiplier algebra by $\mathcal{A}$. An automorphism of $\mathcal{Q}(\mathcal{A})$ is trivial when its graph, pulled back to the unit balls of the multiplier algebras, is Borel in the strict topologies. Continuum Hypothesis conjecture. The Continuum Hypothesis implies that $\mathcal{Q}(\mathcal{A})$ has a nontrivial automorphism. This conjecture predicts abundant nontrivial automorphisms of corona algebras under the Continuum Hypothesis, extending known results for examples such as $C(\beta\mathbb{N}\setminus\mathbb{N})$ and the Calkin algebra; its resolution is not specified in the source.