Remark: Residuals and the observation boundary

The accessible algebra is $\mathrm{Diag}(C)\otimes \mathcal{L}({\mathcal{H}}_S)$ if a spectator $S$ is supplied. Source purifications, random-kick labels, and detector complements are not observer assistance. A conditional spectator or reference state can change when a record is selected, although (eq:reference-marginal) preserves its unconditional marginal.

Consumption does not imply destruction of all microscopic information, nor does it forbid an unmeasured spectator from undergoing later dynamics. This is the residual distinction in Landmark I and En09-A@1 CheungI,CheungEn09A.