Regular-part agreement and supported laboratories

Every test supported in $\{r\ge r_0>0\}$ sees exactly the regular one-point functions, for all $c,\tau ,w,L$. No extension parameter alters the Friedrichs wave operator, the regular spectral state, or its local Hadamard subtraction.

The supported-transfer theorem of I-B-G concerns scalar retarded and advanced operators, with both the additional-arrival window and the independent retained-shadow reserve CheungIBG (:transfer, :transfer-contract). The X-A-ST and X-B-ST supported-chart contracts remain separate CheungXAST,CheungXBST. Neither Green-operator agreement nor a local developing chart transfers a vacuum covariance or selects apex contacts. No comparison with a flat-completion state is used in the proofs above.