Local Extrema and Infinite Derivatives of the Delange Function of Base 3

In the ternary Hamming cube $Q_n^3$, the smallest number $ξ_n(m)$ of edges leaving a set of $m$ vertices is $2(nm-S_3(m))$, where $S_3(m)=\sum_{j<m}s_3(j)$ and $s_3$ is the ternary digit sum. After rescaling, these numbers are the values at the points $m/3^n$ of a continuous function $T$ of Takagi t