Pointwise asymptotic conjecture for the optimal Hardy weight

Let $P u=-\Delta u+V(x)u+u$ be subcritical in $\mathbb{R}^n$, and assume that

$$\lim_{x\to\infty}V(x)=0.$$

If $u$ is a positive solution of $Pu=0$ in $\mathbb{R}^n$ satisfying the stated condition, then let $W$ be the optimal Hardy weight associated to the pair $(u,G)$. Optimal Hardy-weight asymptotic conjecture. The weight $W$ satisfies

$$\lim_{x\to\infty}W(x)=1.$$

This conjecture predicts the pointwise behavior at infinity of the optimal Hardy weight for a subcritical Schrödinger operator whose potential tends to zero. The supplied source does not state whether the conjecture has been resolved.