Four declared structures

A fixed classical history has one normalized pure state on its complete live quantum names. Unitary gates and pure allocations preserve this property. At a rank-one destructive readout, each supported outcome has a normalized pure residual. Density operators and recorded channels describe ensembles, inaccessible restrictions, and complete input–output comparisons; they do not assert that a classical mixture is one pure branch.

An untouched reference $E$ may be included in a complete input. It has no available control or communication wire. Its storage is listed separately from the laboratory storage.