 Kirby killing property

In a modular tensor category, a loop with the normalized Kirby color encircling a charge-$x$ strand projects onto the vacuum anyon charge and multiplies it by $\mathcal{D}$. Indeed, the encircling scalar is ${\mathcal{D}}^{-1}{\sum }_a{d}_a{S}_{ax}/S_{1x}$, which equals $\mathcal{D}{\delta }_{x1}$ by unitary matrix orthogonality for the modular S-matrix.