Remark: What is untouched under reference extension

The operation acts as ${\mathrm{id}}_Q$, but the conditional reference state may change when a clock outcome is selected. Such steering is compatible with (eq:drop-record): the unconditional reference marginal is unchanged.

The relational-evolution assertion on $S\otimes Q$ additionally requires stationarity of the full preparation under $K\otimes I_Q$. Stationarity of the $CS$-marginal alone does not imply stationarity of every extension.