Liu's exceptional-set conjecture for radial projections

Let $E\subset\mathbb{R}^d$ be a Borel set with $\dim_{\mathcal{H}} E\in(k-1,k]$, where $k=0,1,\dots,d-1$. For $y\in\mathbb{R}^d$, let $\pi^y(x)=(x-y)/|x-y|$ be the radial projection. Liu's conjecture.

\dim_{\mathcal{H}}\left\\{y\in\mathbb{R}^d:\dim_{\mathcal{H}}\pi^y(E)<\dim_{\mathcal{H}}E\right\\}\leqslant k.

The bound is generally sharp when $E$ lies in a $k$-dimensional affine subspace. The conjecture concerns the sharp exceptional-set estimate for radial projections when $\dim_{\mathcal{H}}E\leqslant d-1$, and the source states that it remains unknown in general.