The odd writhe formula for the zeroth Alexander polynomial of virtual knots

Let $K$ be a virtual knot. Let $\Delta_0(K)(u,v)$ denote the zeroth Alexander polynomial, and let $OW(K)$ denote the odd writhe of $K$. The odd writhe conjecture.

$$2\left\vert \Delta_0(K)(-1,-1) \right\vert=\left\vert OW(K) \right\vert.$$

The relationship is proved for the family of virtual twist knots and is conjectured here for all virtual knots. The formulation in the introduction uses a particular factor $\overline{\Delta}_0$ of $\Delta_0$, while the later conjecture and its virtual-twist-knot corollary state the displayed formula directly for $\Delta_0$.