Minkowski's zero-distribution discrepancy conjecture

Let $\mu$ be Minkowski's measure. For each $j$, let $\nu_j$ be the normalized zero-counting measure of its degree-$j$ orthogonal polynomial, and let $\nu_E$ be the equilibrium (Chebyshev) measure on $[0,1]$. Let $D(\nu_j,\nu_E)$ denote their discrepancy.

Minkowski's zero-distribution discrepancy conjecture. As $j$ tends to infinity,

$$D(\nu_j,\nu_E)\longrightarrow 0.$$

Moreover, there exist positive constants $A,B$ such that

$$D(\nu_j,\nu_E)\leq A j^{-B}.$$

This gives a quantitative form of convergence of the zero distributions to equilibrium and therefore supports regularity of Minkowski's measure. The source reports numerical evidence, not a proof.