Numerical observables are not automatically stress-energy

Process positivity concerns an operator on the process input/output spaces. It does not identify those spaces with tangent directions or assign energy, momentum, local density, or volume.

For example, XXII-C proves $\mathrm{Tr}W=8$. The normalized operator $W/8$ can be used to form mathematical expectation values. That normalization does not identify it as a matter state on an extracted spacetime CheungXXIIC (lem:base).