The nonlinear benchmark

The observation interface of VII-E allows a coupling rule of the form

while leaving the matter state unchanged. VII-E explicitly notes that this need not be affine and is not thereby a quantum channel CheungVIIE (Definition def:rules and Remark rem:nonlinear).

A concrete benchmark is the rule called Option N in VIII-B:

Its domain requires the selected deficit to stay in the declared interval. The rule selects one definite geometric packet and does not acquire a stochastic measurement record. The finite source letter of VIII-C uses a supplied source token in a prescribed table-selection command, including the word

A promised token is not an instrument that extracts an expectation from unknown matter CheungVIIIB,CheungVIIIC.

We take these as named comparison targets, not as premises providing a joint completely positive evolution. Proposition prop:affine below identifies exactly why a nonconstant deterministic selection cannot simply be promoted to an unconditional affine channel.