Renormalization Notes (Precise Statement)
Clarifying the order-by-order claim and the superficial degree of divergence.
Finite counterterm basis at fixed order
Claim (v2.1): For any fixed truncation order $k$ in a small-$|\lambda_c|$ expansion of the EFT,
the operator basis is finite and counterterms required to renormalize amplitudes up to that order form a finite set that preserves BRST identities.
Power counting
At the renormalizable truncation ($d\le 4$), divergent structures are restricted to 2-point and selected 3-point functions, consistent with standard EFT behavior.
Exponential term
Expanding $e^{\lambda_c N}$ in powers of $\lambda_c$ and truncating at order $k$ promotes a finite tower of Yukawa-like insertions at that order.
No all-orders finiteness is claimed; statements are confined to any fixed order $k$.