Non-Brjuno divergence conjecture for Bishop quadrics

Let $\mu$ be a complex number that is not a root of unity and $|\mu|=1$. A number $\mu$ is Brjuno when it satisfies the Brjuno condition referred to in the source. Let $Q_{\gamma}$ be the Bishop quadric with Moser–Webster invariant $\mu$. Non-Brjuno divergence conjecture. If $\mu$ is not a Brjuno number, there exists a real analytic surface $M$ in $\mathbb{C}^2$ that is formally but not holomorphically equivalent to $Q_{\gamma}$. This is an open problem about the optimal arithmetic condition for convergence of normal forms near CR singularities; the stated claim asks whether every non-Brjuno multiplier can occur for a formally but non-holomorphically equivalent real analytic surface.