Markovianity, the System Cut, and Q2-Identity: Why process memory is not identity - and when it is

Open-systems theory runs together two claims that this paper separates. The first is that Markovianity — the memorylessness of a reduced dynamics — is a property of the system. It is not: a single two-qubit exchange dynamics is non-CP-divisible on the reduced cut and exactly unitary-Markovian on the extended cut, so Markovianity is a property of the tuple (cut, preparation domain, intervention class, time range), fixed only once the cut is named. The second is that (non-)Markovianity decides identity, or that process memory is identity-relevant retained structure. It does not: a Markovian amplitude damping loses the record identity of a class with defect , while a non-Markovian process preserves a shielded identity frame exactly, so the memory coordinate and the identity coordinate are independent, and the correct test is the pair . The paper imports the domain machinery unchanged — CP-divisibility, the operational process-tensor Markov condition, and instrument-specific Markov order — and adds, from the identity architecture, the requirement that identity be judged on the maximal continuation quotient. It closes with the converse question: when is a memory back-path constitutive for identity? A back-path is a constitutive coupling if and only if a causally isolated interruption of it — a severing test — changes admissibility, , or ; and the size of the information backflow is neither necessary nor sufficient for this. What is not delivered is stated throughout: no system cut, no memory time, and no damping rate follows from the law, and the results are the finite-dimensional named-process sector.