= Two-strand Kirby projector
{title2=$K_\Omega(a,b)=\mathcal D P^{ab}_1$}
An encircling <normalized Kirby color> loop around two equally oriented <anyon> strands is $\mathcal D$ times the <orthogonal projection> onto their total <vacuum anyon> charge. In the <isotopy normalization of anyon diagrams>, erasing the vacuum edge writes this as $\delta_{b,\bar a}(\mathcal D/d_a)$ times the cup-cap diagram. The cup-cap squared is $d_a$ times the cup-cap, so $d_a^{-1}$ is essential.
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