Remark: Correction relative to an earlier combined draft

An earlier IX-C-ST draft may display an “advanced trace formula” on the sharp source domain. If that formula is accepted as proved for the very same actual adjoint, on every source needed here, and with the local boundedness required in (TC), then it already supplies the certificate, up to the stated convention sign. In that reading the bridge must be marked proved, not simultaneously assumed and unverified.

If that operator/domain identification has not been established, the formula cannot be imported by notation alone. The weak inherited release retains that precise verification obligation. This distinction avoids both silently withdrawing an accepted premise and silently adding an unverified one.