What supported Green agreement actually implies

I-B-G's supported-transfer result concerns retarded and advanced scalar operations in a signed arrival window, with independent retained-shadow and compact-reserve conditions CheungIBG (:transfer, :transfer-contract). The corresponding ST sheets retain those support obligations CheungXAST,CheungIXAST.

It is not a theorem that $W_{\beta }=W_{\mathrm{flat}}$ in that window. Already for $\beta =0$, the regular diagonal difference is

which is nonzero for $0<\alpha <1$ CheungIBVP (:phi2). Thus exact covariance equality would contradict the regular-part Wick square.

The correct local statement is

on a sufficiently small developing product neighbourhood, and on any further specified pair region where the direct singularity has been subtracted and no additional front is met. The explicit kernel and Theorem thm:main, not a state-transfer inference, justify that assertion.