The reconstructed record does not recover a second observable

This is a proved obstruction for a stated processing class and a stated output interface. It is not an obstruction to access to the full boundary quantum algebra. The same distinction underlies observable-algebra formulations of recovery BKK2007.

The effect $J$ is a finite-mode population effect. It is not called a black-hole interior observable. Neither the proposition nor the reference system constructs an interior partner.