Observable coefficients and physical states

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Every coefficient must distinguish quantum fields, classical backgrounds, and external preparation data. Smooth evaluation on one configuration is not a distributional definition on arbitrary joint tests.

Hadamard two-point data used to define products do not alone select a physical state. In a gauge-fixed theory, positivity must be formulated on an appropriate physical algebra or representation, not assumed for the full ghost–auxiliary multiplet FRBV,BFR,CheungXG. An expectation and a complete measurement output are different interfaces.