The conjecture that all Takagi function graphs have Assouad dimension 2

Let $T_{a,b}$ be a Takagi function with $a,b\text{ in }\mathbb{R}^+$ and $ab>1$, and let $\Gamma_{T_{a,b}}$ denote its graph.

Assouad-dimension conjecture. For all such Takagi functions,

$$\dim_{\mathrm{A}} \Gamma_{T_{a,b}}=2.$$

The paper has not completely determined the Assouad dimension of any Takagi function, but proves that it can be strictly larger than the upper box dimension for graphs of Takagi functions. The conjecture is motivated by the fact that the graph of the Wiener process has Assouad dimension $2$ almost surely.