= Nonvanishing of Kirby stabilization factors
{title2=$p_+p_-=\mathcal D^2$}
Let $H$ be the real <Hopf pairing of Jones-Wenzl colors> <matrix>, $d$ the dimension vector and $T$ the diagonal <matrix> of <Jones-Wenzl twist eigenvalues>. Twist balancing on the <fusion of Jones-Wenzl colors> gives $HTd=p_+T^{-1}d$, using $\sum_i d_iN_{ij}^k=d_jd_k$. Complex conjugation gives $HT^{-1}d=p_-Td$. Apply $H$ again and use finite sine orthogonality, $H^2=\mathcal D^2I$. Since $Td\ne0$, the displayed identity follows. Thus both factors used to normalize the <Jones polynomial surgery invariant> are nonzero.
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