Radial projection exceptional-set conjecture above codimension one

Let $E\subset \mathbb{R}^d$ be a Borel set, let $\dim_H(E)>d-1$, and let $s\leq d-1$ be a real number. Radial projection exceptional-set conjecture.

$$\dim_H\{y\in\mathbb{R}^d:\dim_H\pi^y(E)<s\}\leq d-1+s-\dim_H(E).$$

This conjecture strengthens the Mattila–Orponen bound for points whose radial projection has zero $(d-1)$-dimensional Hausdorff measure, and concerns the size of exceptional centers producing projections of dimension below $s$.