Numerical observables are not automatically stress-energy

Standard stress-energy constructions use additional dynamical structure, for example a matter action and metric variation Tong (Section 4.5). In locally covariant quantum field theory, metric response through relative Cauchy evolution provides another precise framework BFV. Neither framework is already contained in a three-party process matrix.

If an action, generators, or response model are additionally assumed, that status must remain visible. If an operator-valued stress tensor is claimed, its field domain, state, composite-field prescription, and comparison with operational records require separate proofs. An equality of real expectation tensors is not an operator Einstein equation.