Isaac's Condition (TU) is false

In 2006 Isaac reduced the simple normality to base $2$ of $\sqrt s$, for $s$ not a perfect square, to a property of dyadic expansions that he called Condition~(TU): the upper frequency of the digit~$1$ in $\sqrtν$, along any subsequence, depends only on the tail of the expansion of $ν$. We show that