Remark: Classical closure is not quantum closure

The proof uses exterior tensor products of coefficient kernels, not contractions of two singular kernels at identified variables. It establishes pointwise multiplication only.

In particular, neither ${\mathcal{P}}_{\mathrm{gen}}$ nor ${\mathcal{P}}_{\Sigma }$ is asserted to be closed under the fixed Wick product. Arbitrarily long classical words have a place to live; their quantum products remain to be defined.