The asymptotic relation between degree-two and degree-three Vassiliev invariants of positive knots

Let $(K_i)$ be a sequence of pairwise distinct positive knots, all with the same given unknotting number. Let $V$ be the Jones polynomial and let $\Delta$ be the Alexander polynomial, and define the standardly normalized Vassiliev invariants

$$v_2=-\frac{1}{6}V”(1)=\frac{1}{2}\Delta”(1),\qquad v_3=-\frac{1}{12}V”(1)-\frac{1}{36}V”'(1).$$

Asymptotic Vassiliev-invariant conjecture. The numbers $\log_{v_2(K_i)}v_3(K_i)$, which are well-defined for $K_i\ne !3_1$, converge to $2$ as $i\to\infty$. This predicts a precise asymptotic relation between low-degree Vassiliev invariants along any such sequence of positive knots, and is posed as a further property of Vassiliev invariants for the ordinary unknotting operation; the supplied text gives no resolution.