Hausdorff dimension of level sets of the ternary Delange function

Determine whether every level set L(y)={x∈[0,1]:T(x)=y} of the base-3 Delange function T has Hausdorff dimension at most log 2/log 9.

Background

The paper constructs a subset E of the level set L(3/4) with Hausdorff dimension log 2/log 9. It then asks whether this dimension is an upper bound for every level set of T, generalizing known results for level sets of Takagi’s function.

References

We do not know whether every level set of T has Hausdorff dimension at most $\log2/\log9$, or whether $L(y)$ is finite for almost every $y$.

— Local Extrema and Infinite Derivatives of the Delange Function of Base 3  (2610.21265 - Zhu, 15 Oct 2026) in Section “Other bases and further questions”