Proposition: Failure of scalar generator absorption

Suppose the only uncertain force source is the white support amplitude $S_u$, shared across stages. Suppose gravity contributes $-\lambda A_{r_{\mathrm{c}}}[x,[x,\cdot ]]$ with $\lambda A_{r_{\mathrm{c}}}>0$ throughout a nonzero flat interval. Changing $S_u$ cannot match the two total generators on that interval, and hence cannot match them across the complete protocol by the scalar absorption construction of En01-B.

Proof. On the flat interval, the support-noise coefficient is zero for every value of $S_u$, while the gravity coefficient is positive. The double commutator is a nonzero superoperator on its admitted domain. Thus the generators cannot coincide there.