The external residual program

For a fully measured qubit,

The phase is absent from each classical marginal but retained jointly. The carrier $K$ in this coherent dilation is a quantum system; its observable $\mathsf{Bit}$ interface arises after $E$ is omitted.

This complete apparatus ledger is the distinction emphasized in CheungHawk04B,CheungEm03C. Operational discard may move a record carrier to an inaccessible environment in a unitary realization; it does not remove that environment from the complete preservation claim.