The Kaufman exceptional set conjecture for planar projections

Let $K\subset\mathbb{R}^{2}$ be a Borel set, and let $\pi_e\colon\mathbb{R}^{2}\to\mathbb{R}$ be the orthogonal projection $\pi_e(x)=x\cdot e$ for $e\in S^{1}$. Assume that $0\leq t/2\leq s\leq t\leq 1$ and $\dim_{\mathrm{H}}K\geq t$. Kaufman's exceptional set conjecture.

$$\dim_{\mathrm{H}}\{e\in S^{1}:\dim_{\mathrm{H}}\pi_e(K)<s\}\leq 2s-t.$$

This conjecture would improve Kaufman's bound for the exceptional directions when the set has Hausdorff dimension at least $t>s$. The bound is known to be sharp, but the general conjecture remains open.