Vertex distortion characterizes the unknot

Let $[K]$ be the lattice-knot equivalence class of a knot $K$, let $[U]$ be the equivalence class of the unknot, and let $\delta_V$ denote vertex distortion. Unknot characterization conjecture.

$$\delta_V([K])=1 \iff [K]=[U].$$

This conjecture asserts that vertex distortion takes its minimal value exactly for the unknot; the supplied text gives no resolution or further evidence for the claim.