The Physically Admissible System Cut: Exact and approximate subsystem reduction

Every use of an open quantum system presupposes a cut, but a tensor factorization of a Hilbert space is not yet the constitution of a physical subsystem. This paper derives the physical subsystem criterion within the full LP architecture, retaining the links to emergence and coarse graining. A named candidate cut must first carry a complete constituted bearer: role completeness, profile completeness, global composition and constitution identity are fixed before Transformation is evaluated. Only then can one ask whether the unchanged global dynamics descends to a representative-independent reduced dynamics and whether the reduction preserves the existence and identity verdicts of that bearer. We derive a joint cut theorem: on a declared domain, an exact physical subsystem cut exists exactly when constitution labels, retained verdict labels and reduced futures are constant on reduction fibres, with all constitutive external coupling either retained in the carrier or explicitly fixed in the admissibility profile. This strengthens dynamic congruence without replacing it. A reduced baseline can be dynamically closed while erasing distinct physical coupling profiles; a CNOT-conjugated two-qubit factorization gives the complementary failure in which the reduced present state hides different futures. The autonomy defect remains the quantitative obstruction to exact closure, with the two-sided best-error bound and additive finite-horizon accumulation retained. Verdict margins are now typed after constitution: profile identity, persistence-class identity and existence can lose certification at different resolutions, while a constitution-changing perturbation triggers Constitution re-entry rather than being misreported as ordinary reduced-state error. The result places the system cut as the common reduction theorem underlying emergence, admissible coarse-graining and later classicality analyses. It adds no dynamics, no interaction and no physical constant; it states the conditions under which a mathematical subsystem description is sufficient for the physical whole it claims to describe.