Corrections made to the proposed architecture

The following qualifications are necessary for the proof:

1. A noncommuting family has ordered Weyl correlations, not an automatically available joint spectral law.

2. Finite residual number expectation defines quadratic field moments, but does not automatically define every unsmeared operator product on every state vector. Covariances were defined by their quadratic forms.

3. Mean convergence and variance convergence are separate. Their conjunction is equivalent to convergence of the second moment about the named classical target.

4. The condition $ϵn_{ϵ}\to 0$ is sufficient, not necessary, and is a condition on residual occupation, not on the total displaced occupation.

5. Trace-norm convergence of residual states controls bounded Weyl functions, not unbounded moment convergence.

6. The test-gauge identity proves exact descent in this free scalar representation. It does not prove descent in an interacting joint gravitational quantum ideal.

7. Neither statements summarized for VII-I/VII-J nor a pre-existing free-product repair are needed to define the present scalar fields or their Weyl correlations.