= Cubic dispersion symmetry with negative transport
{title2=$\nu_{1,2}=(-k\pm\sqrt{-3k^2-4})/2$}
For dispersion $w(k)=-i(k^3+k)$, the other roots of $w(\nu)=w(k)$ satisfy $\nu^2+k\nu+k^2+1=0$. In $D_+=\{\operatorname{Im}k>0,\operatorname{Re}w(k)<0\}$ both roots lie in the lower half-plane. Interpolating the unknown linear polynomial $G_2+i\nu G_1$ at them eliminates two boundary traces. The resulting symmetric expression has removable singularities where the roots coalesce.
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