Orponen's radial projection dimension conjecture

Let $X\subset\mathbb{R}^d$ be a Borel set, with $\operatorname{dim_H}(X)\leq d-1$, that is not contained in a hyperplane. For $y\in X$, let

$$\pi_y(X)=\left\{\frac{x-y}{\lvert x-y\rvert}:x\in X\setminus\\{y\\}\right\}$$

be the radial projection of $X$ from $y$ onto $S^{d-1}$. Orponen's radial projection conjecture.

$$\sup_{y\in X}\operatorname{dim_H}(\pi_y(X))=\operatorname{dim_H}(X).$$

This conjecture was stated in the planar case by Orponen and is presented as plausible for all dimensions; its resolution status is not specified in the source.