Capuano–Veneziano–Zannier conjecture on Ruban continued fractions

Let $\alpha^{(p)}$ be a p-adic quadratic irrational, and consider its Ruban continued fraction. Capuano–Veneziano–Zannier conjecture. The Ruban continued fraction of a quadratic irrational is either periodic or converges in $\mathbb{R}$ to a transcendental number. Capuano, Veneziano and Zannier proved that Ruban continued fractions of p-adic quadratic irrationals always converge in $\mathbb{R}$; the conjecture concerns the nature of the limit in the non-periodic case and remains open.