The sign conjecture for Conway polynomial coefficients of positive links

Let $L\subset S^3$ be an $m$-component link in the class $\mathcal{P}_0$, and write its Conway polynomial as

$$\nabla_L(z)=z^{m-1}\left(a_kz^{2k}+a_{k+1}z^{2k+2}+\cdots\right),$$

where $a_k\neq 0$ is the first non-vanishing coefficient. Here $k$ is the leading degree parameter and $m$ is the number of components.

Conway coefficient sign conjecture. The conclusion of the two-component obstruction holds whenever $L\in\mathcal{P}_0$: in general, the sign $(-1)^k$ is replaced by $(-1)^{s(k,m)}$ for some function $s(k,m)$ depending on $k$ and $m$.

For two-component links slice in a punctured $\mathbb{C}P^2$, the paper proves $(-1)^ka_k\leq 0$. The conjecture seeks an analogous sign rule for every link in $\mathcal{P}_0$, but does not specify the function $s(k,m)$.