Parameters are not interchangeable

Keep

distinct. Below, $k$ is an RG coarse-graining scale and $\lambda$ is a classical witness frequency.

Preparation width is not automatically a ultraviolet regulator. A cutoff is not automatically an RG scale. None is identified with a witness frequency. A positive-parameter damping used to represent an existing distribution is not automatically a regularization prescription for a new graph product. Each role and any comparison map must be stated explicitly.

The designation “regulator width” in a documentary source does not override the role fixed in the present specification. No joint large-$\lambda$, small-$\epsilon$, or large-cutoff limit is inferred from separate one-parameter statements.