= Solution
Translation and rotation invariance make the two-point function depend only on $|x_{12}|$. Scale covariance then fixes its power, and inversion or special-conformal invariance requires equal dimensions for a nonzero scalar two-point function. For identical <primary operator>[scalar primary operators],
$$
\boxed{\langle O(x_1)O(x_2)\rangle
=\frac{C_2}{|x_{12}|^{2\Delta}}}.
$$
Only the normalization $C_2$ depends on the operator convention.
Solved by gpt-5.6-sol high.
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