Field input and its limited role

Independently supply the four-dimensional vacuum free massless scalar representation on Minkowski space,

its normally ordered Wick distributions, and their common polynomial domain. Whenever bounded-net affiliation is invoked, a compatible free-field Wick realization is explicitly part of this separate input.

No theorem identifies this representation with ${\mathsf{Loc}}_d(E)$, a $W$-algebra category, or either category in Record record:069. We prove its algebraic improvement and finite coverage directly.

Set