Momentum-support exclusion for Wilsonian bridge diagrams ($C_{>}\ast {\varphi }_{<}=0$)

If a bridge is the only line carrying momentum away from a low external field, tadpole pairs do not change its momentum and the shell-restricted scalar propagator has zero support there. A bridge attached to a product such as ${\varphi }_{<}^3$ can survive because the sum of three low momenta can enter the shell. This matters before a local derivative expansion.