3 problems

Subset-normal bound conjecture. The inequalities above hold.

Facet-normal characterization conjecture. The normals of $K$ are the same as either those of a simplex bounded by an extra facet, or those of a pyramid that is not a simplex.

Asymptotic Carathéodory-rank conjecture. The ratio $\operatorname{CR}(d)/d$ is monotonically converging to $2$ as $d\to\infty$. The source records a counterexample to the integral…