A scalar pairing is definable once its data are chosen

For a specified scalar two-point distribution ${\mathsf{H}}_2\in {\mathcal{D}}^{\prime }(M^2;\mathbb{C})$ and fixed frequencies $\lambda ,\mu$, the numerical expression

is well defined: the tensor product is a compact smooth test density in the fixed volume convention. No product of two singular distributions is required for this particular scalar pairing.

This observation is a definability statement, not a chosen quantum contraction. No ${\mathsf{H}}_2$ is selected; no Hadamard condition, state, positivity requirement, or time-ordering prescription is imposed here. It also does not construct contractions of the full cubic kernel with interaction kernels.

No prepared quantum product, singular locus, extension, scaling degree, counterterm, or Ward defect is constructed. Those tasks require specified quantum data and their own distributional proofs.

The sharp-width limit, ultraviolet completion, and all-orders finite-parameter renormalizability remain outside scope.