An equation and a singularity condition do not select a state

The proposition assumes a scalar covariance for its comparison. It constructs no Einstein–scalar covariance for Em02-E. Additional invariance, infrared, decay, or state-selection conditions may eliminate some of the freedom; those conditions must be stated and proved.

Positivity also has a graded and gauge-qualified meaning in a gauge-fixed theory. One does not impose ordinary positive scalar state conditions on every ghost or unphysical metric component. The physical algebra, its involution, and its state must be identified.

Linearized Einstein–Klein–Gordon quantization on on-shell backgrounds has a separate construction with its own field and gauge hypotheses Hack. That reference does not choose the two-point matrix, initial state, or spatial-tail estimates for an independently specified original-rod lapse.