Definition: The Ward conclusion used in this paper

A local conformal Ward conclusion consists of:

1. an invariant dense field domain and continuous ordered joint field distributions;

2. a conserved current ${j_X}^{\mu }=t^{\mu \nu }{X}_{\nu }$;

3. a compact spacetime-smeared current whose commutator implements the declared infinitesimal transformation on every compactly localized Wick polynomial and every finite ordered product;

4. elementary and descendant contact distributions with the normalization calculated below;

5. compatibility of these actions with field relations and conformal Lie brackets.

It does not mean that every renormalized time-ordered product containing arbitrarily many stress tensors has been constructed.