Countable-exceptional-set conjecture for projections of planar self-similar sets

Let $K$ be a self-similar set in the plane, and call a direction $\pi\in G(2,1)$ exceptional for orthogonal projections of $K$ if the projection dimension equality does not hold. Countable-exceptional-set conjecture. For any self-similar set in the plane, the exceptional set is at most countable and explicitly determinable. This conjecture strengthens Marstrand's theorem by predicting that the exceptional directions for planar self-similar sets are not merely a null set but countable and explicitly identifiable. When the self-similar construction involves irrational rotations, the conjecture was confirmed by Peres and Shmerkin; the parser reports the conjecture as resolved.