Minkowski's measure power-law Jacobi convergence conjecture

Let $\mu$ be Minkowski's measure, and let $a_j$ be the out-diagonal Jacobi matrix elements associated with its orthogonal polynomials.

Minkowski's measure power-law Jacobi convergence conjecture. There exist two positive constants $A,B$ such that

$$\left|a_j-\frac14\right|<A j^{-B}.$$

This is a stronger quantitative version of the Nevai-class conjecture. The source describes it as based on numerical data and gives it with less confidence than its other numerical estimates; no proof is supplied.