Complete quasi-equidistribution conjecture for van der Corput sequences in irrational bases

Let $p$ and $q$ be integers with $1\leq q\leq p$, and let $\gamma$ be the largest root of

$$x^2-px-q.$$

The van der Corput sequence in base $\gamma$ is completely quasi-equidistributed in base $(p+1)$ if, for every finite-dimensional truncation of the sequence and every multi-index $\mathbf{k}\in\mathbb{N}_0^d$, its pair-correlation quantity satisfies $C_{(p+1)}(\mathbf{k};P_N)\leq 1$.

Complete quasi-equidistribution conjecture. Let $\gamma$ be the largest root of the polynomial $x^2-px-q$ for $1\leq q\leq p$. The van der Corput sequence in base $\gamma$ is c.q.e. in base $(p+1)$.

This conjecture proposes a scrambling base for coordinates associated with an irrational base and is motivated by numerical investigation. The source gives no proof or resolution.