Supported Green replacement does not replace the state

In an angularly small chart

I-B-G defines an additional-arrival threshold $T_{\mathrm{arr}}(x,x^{\prime })$ and proves

Replacing an intrinsic retarded or advanced scalar operation by a completion operation requires its signed pair window, a local parallel frame, and the independent retained-shadow and compact-reserve conditions CheungIBG (:transfer, :transfer-contract). The ST scalar sheets retain these support obligations CheungXAST,CheungXBST,CheungXCST.

This theorem does not transfer a symmetric covariance or a vacuum state. In particular, it does not imply that the current must vanish in a short laboratory window. The current is a local observable of a globally specified spectral state, not a retarded signal with a newly assigned emission event.

XI-E's named polynomial Hadamard domain CheungXIE (:domain, :star) has its own flat-background multiplet and product. It does not select the present positive state or construct a conical interacting algebra. Conversely, evaluating the one-point current does not transfer that multiplet or establish interacting gauge closure.