Proposition: Necessary physical positivity condition

If a positive physical state has exact two-point restriction $W_{\mathcal{B}}$ on the invariant observables, then

Its value must also be independent of the representative of the class in (eq:quotient).

Proof. The field associated with $f$ is a physical observable. Positivity applied to its adjoint times itself gives (eq:physicalpositive). Quotient relations require representative independence.