  The first two authors introduced vertex distortion and showed that the vertex
distortion of the unknot is trivial. It was conjectured that the vertex
distortion of a knot is trivial if and only if the knot is trivial. We will use
Denne-Sullivan's bound on Gromov distortion to bound the vertex distortion of
nontrivial lattice knots. We will then conclude that trivial vertex distortion
implies the unknot, proving the conjecture. Additionally, the first conjecture
in vertex distortion's debut article is proven and a vertex distortion
calculator is given.
