Jablan–Radović conjecture on rational knots and OGC knots

A knot diagram is straight if, after labeling its $n$ crossings in traversal order, its knot word has the form

$$(1,2,3,\ldots,n-1,n,\sigma(1),\sigma(2),\sigma(3),\ldots,\sigma(n-1),\sigma(n)),$$

where $\sigma\in S_n$; a straight number $\mathtt{str}(K)$ is the minimum crossing number of a straight diagram of $K$. An OGC knot is a knot admitting a straight diagram, equivalently a diagram with a short OGC Gauss code. Jablan–Radović conjecture. Every rational knot is an OGC knot. The statement concerns whether the class of rational knots is contained in the class of knots admitting such straight diagrams; the source provides no resolution status.