A precisely declared homogeneous class

Let ${\mathcal{W}}_4$ consist of symmetric rank-two Wick polynomials:

1. homogeneous of scaling dimension four under $[\varphi ]=1$;

2. built from $\varphi$ and finitely many derivatives with constant real Poincaré-covariant coefficients;

3. containing no dimensionful parameter, external tensor, or new field;

4. identified modulo the free field equation and its derivatives.

Only tensor identities inside this class are asserted.