Infinitely many odd-superbridge knots conjecture

A knot $K$ has superbridge index $s[K]$, the minimum, over all knots $K'$ isotopic to $K$, of the maximum bridge number over unit directions. A knot with superbridge index $m$ is called an $m$-superbridge knot.

Odd-superbridge knots conjecture. There are infinitely many $(2n-1)$-superbridge knots for any positive integer $n\ge3$.

Nontrivial knots have superbridge index at least $3$, and the paper establishes that only finitely many $3$-superbridge knots exist, while infinitely many even-superbridge knots are known. This conjecture concerns the existence of infinitely many knots at every higher odd superbridge index.