Generalized Borel conjecture for algebraically independent base-$b$ expansions

Let $b\geq 2$ be an integer base, and let $(\alpha_1,\ldots,\alpha_n)$ be an $n$-tuple of real numbers. Writing their base-$b$ expansions in aligned columns, call the tuple normal to base $b$ if every $n\times m$ digit matrix occurs with frequency $1/b^{mn}$ for every $m\geq 1$. Generalized Borel conjecture. If $\alpha_1,\ldots,\alpha_n$ are algebraic numbers and $1,\alpha_1,\ldots,\alpha_n$ are linearly independent over $\mathbb{Q}$, then $(\alpha_1,\ldots,\alpha_n)$ is normal to base $b$. Almost all tuples are normal, but this algebraic case remains open; the stated linear-independence condition is necessary according to the source.