the operators in the CT Lagrangian, we need to solve a set of linear equations, it so happens that there are four linear Eqs. in the three unknowns and there still is a unique solution. Geometrically, this is like having four planes in the three dimensional Euclidean space and still they all passing through one common point. The choice of the renormalization conditions shall determine this point. This may raise the following concern: could it be that if we find $\tilde{\cal G}_{\rm 1-loop}$ for $\eta$ such that $-k \eta \gtrsim 1$, we end up having many more equations and only three unknowns? Would the solution be guaranteed to exist in that case?

But most importantly, in the limit $\eta \rightarrow 0$, only one divergent term is left and thus in taking this limit, we end up erasing the information about the form of CTs or their number completely. This is similar to what happens in e.g. spontaneous symmetry breaking. If we consider the $Z(2)$ symmetric renormalizable scalar field theory ${\cal L} = - \frac{1}{2} (\partial \phi)^2 - m^2 \phi^2 - \lambda \phi^4/24$. When $m^2 > 0$, three CTs are enough to absorb all the infinites in the theory. The same 