= Full-sky cubic bispectrum estimator
{title2=$\hat f_{\mathrm{NL}}=(6F)^{-1}\sum b^1\mathcal G\Theta_1\Theta_2\Theta_3/(C_1C_2C_3)$}
For an isotropic, full-sky temperature map with a fixed bispectrum template $b=f_{\mathrm{NL}}b^1$, the inverse-variance-weighted cubic statistic has normalization $F=\frac16\sum (b^1)^2\mathcal G^2/(C_1C_2C_3)$ over ordered triples. It is unbiased under the linear template relation and has Gaussian <cosmic variance> $1/F$. The factor $1/6$ counts the six cross-triple <Wick contractions>. A removed monopole cancels the nine internal-pairing terms; incomplete sky coverage or anisotropic noise generally require a linear correction.
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