The Hausdorff-dimension conjecture for the exceptional set $\Theta$

Let $\Theta$ denote the set introduced in Theorem

of the paper. **Hausdorff-dimension conjecture for $\Theta$.** The set $\Theta$ in Theorem

has Hausdorff dimension at least $2/3$.

This is presented in the section on open problems as a metrical refinement suggested by the paper's proofs. The excerpt gives no resolution, so the conjecture remains open.