Almost-sure divergence of denominators in p-adic continued fractions

Let $p\geq 5$, and let $\{|B_n|\}_{n\in\mathbb{N}}$ be the sequence of denominators of convergents for Browkin I, Browkin II and Algorithm MR p-adic continued fractions. Denominator divergence conjecture. The sequence $|B_n|$ tends to $+\infty$ with probability $1$. Under the paper's uniform-distribution assumption for p-adic digits, the expected size of a Browkin I partial quotient grows linearly with $p$, motivating this almost-sure growth claim; no proof is supplied.