The contiguous-path conjecture for translation sequences

Let $F_N$ be the new facet in a translation sequence of a polytope, and let $x,y$ be the vertices defining the paths under consideration. Contiguous-path conjecture. Every edge adjacent to the new facet $F_N$ in a translation sequence is a member of some shortest path from $x$ to $y$. The source presents this as a sufficient statement for proving the $d$-step conjecture and says that the property is not generally known.