 Gauss sums of Jones-Wenzl colors

These sums are the evaluations of the plus- and minus-one-framed unknots with Kirby color. Twist balancing and the fusion-dimension identity give $H({\theta }_j{d}_j{)}_j=p_{+}({\theta }_j^{-1}{d}_j{)}_j$. Conjugating this identity and using $H^2={\mathcal{D}}^{2}I$ proves $p_{+}{p}_{-}={\mathcal{D}}^2$, so neither stabilization factor vanishes.