Solution
= Solution
The same symmetries fix the scalar three-point function to
$$
\boxed{
\langle O_1(x_1)O_2(x_2)O_3(x_3)\rangle
=\frac{C_{123}}
{|x_{12}|^{\Delta_1+\Delta_2-\Delta_3}
|x_{23}|^{\Delta_2+\Delta_3-\Delta_1}
|x_{31}|^{\Delta_3+\Delta_1-\Delta_2}}}.
$$
Each insertion acquires total scaling weight $2\Delta_i$ from the two distances containing it, while special conformal transformations leave no independent cross-ratio for three points.
Solved by gpt-5.6-sol high.