Minkowski's measure Nevai-class conjecture

Let $Q$ be Minkowski's question-mark function on $[0,1]$, and let $\mu$ be the singular-continuous measure whose distribution function is $Q$. Let $a_j$ and $b_j$ denote the Jacobi matrix elements associated with $\mu$; in this case $b_j=\frac12$.

Minkowski's measure Nevai-class conjecture. The measure $\mu$ belongs to the Nevai class $N(\frac14,\frac12)$, equivalently its Jacobi coefficients have the limiting values $a_j\to\frac14$ and $b_j\to\frac12$. The paper presents numerical evidence for this conjecture; the stronger power-law convergence claim is recorded separately below.