= Solution
A momentum-shell <renormalization group> step has three parts:
1. Split the field into slow modes $\phi^-$ with $|k|<\Lambda/\zeta$ and fast modes $\phi^+$ with $\Lambda/\zeta<|k|<\Lambda$, then integrate out $\phi^+$ to obtain a <Wilsonian effective action> for $\phi^-$.
2. Rescale momenta by $k'=\zeta k$, equivalently coordinates by $x'=x/\zeta$, so the reduced cutoff returns from $\Lambda/\zeta$ to $\Lambda$.
3. Rescale the field, at the Gaussian fixed point by $\phi'(x')=\zeta^{(d-2)/2}\phi^-(x)$, so the coefficient of $(\nabla\phi)^2/2$ retains its chosen normalization.
The resulting functional has the original cutoff but changed coefficients. Iterating the operation gives a <renormalization-group flow> on masses and interaction couplings.
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