The extremal PageRank distance conjecture

Let $G$ be any unweighted directed graph, possibly with loops and bidirected arcs, and let $\alpha_1$ and $\alpha_2$ be two jumping constants. For each jumping constant, write $\pi_{\alpha_i}$ for the corresponding PageRank vector. Extremal PageRank distance conjecture. For every such graph and every pair $\alpha_1,\alpha_2$,

$$\\|\pi_{\alpha_1}-\pi_{\alpha_2}\\| < \sqrt{\frac{67}{50}}.$$

The paper's main theorem constructs unweighted directed graphs whose PageRank distance approaches $\sqrt{67/50}$ from below, so this conjecture asserts that the limiting value is the best possible universal bound. Its status is not resolved by the supplied text.