4 problems

Lutz's dimension spectrum conjecture. For every line $L_{a,b}$, the spectrum $\operatorname{sp}(L_{a,b})$ contains a unit interval. The conjecture concerns which effective dimensio…

Let $gamma$ be the parameter in the definition of $gamma$-energy randomness, and let $Member_gamma$ denote the class defined by the source. Member characterization conjecture. A re…

A real is strongly $gamma$-random if it is strongly random with parameter $gamma$, and Hippocrates $gamma$-energy random if it satisfies the Hippocrates energy-randomness notion wi…

Let $B$ be a Martin-Löf random Brownian path, and let $Z_B$ denote its set of zeros. For a real $x$, write $\operatorname{cdim}(x)$ for its constructive dimension. Dimension-spectr…