The DDS optimality conjecture for book crossing numbers of complete graphs

Let $K_n$ be the complete graph on $n$ vertices, let $u_k(K_n)$ denote its minimum number of crossings in a $k$-page book drawing, and let $Z_k(n)$ denote the number of crossings in the DDS construction of $K_n$ in $k$ pages. DDS optimality conjecture. For all positive integers $k$ and $n$,

$$\nu_k(K_n) = Z_k(n).$$

The conjecture asserts the optimality of the DDS construction for every number of pages and every complete graph. The paper presents this as a general conjecture; its $k=3$ case is supported by computations for all 8 values of $n\geq 7$ considered there.