6 problems

Yu's conjecture. For every $\tfrac12<\lambda<1$,

For each integer $n$, define … Here $T_{1/2,n}$ is the generalized Takagi function considered in the source. Allaart–Kawamura maximum-growth conjecture. As $n\to\infty$, … This pre…

For each integer $n e 0$, let $T{1/2,n}$ be the corresponding generalized Takagi function on $[0,1]$, and consider its points of absolute maximum. Allaart–Kawamura conjecture.…

Let $T$ be the Takagi function, and let $L(y)$ denote its level set at height $y$. The Hausdorff dimension of $L(y)$ is bounded above by $0.668$ for every $y$, as follows from Madd…

Abscissa generic level sets. A full Lebesgue measure set of abscissa points $x\in[0,1]$ have level sets $L(\tau(x))$ that are uncountable and have Hausdorff dimension $0$.

Baba's maximal-dimension conjecture. The example $L(\frac{2}{3})$ achieves the largest possible Hausdorff dimension among all level sets $L(y)$; equivalently,