Split-Buffer Principle: Swap-Defect Diagnostics for Operational Subsystem Geometry

Local von Neumann algebras in relativistic QFT are typically type III, obstructingnaive subsystem factorization even when observables commute at spacelike separation.The split property resolves this by inserting a type I factor as a collar/buffer betweennested local algebras, enabling operational independence (independent preparationand measurement) in a way strictly stronger than microcausality. We formalizethis principle in the background-free “admissible family” framework (Papers 1–3)and extract two diagnostics. First, split inclusions canonically induce a spatialtensor-product implementation for suitable commuting pairs, giving an intrinsicoperational meaning of “buffer.” Second (new discovery), we introduce the swap-defectinvariant δswap, an operational obstruction to splitness based on (approximate) innerimplementability of the flip automorphism on two copies of the inner algebra usingonly collar resources. Exact vanishing recovers splitness via the classical flip criterion,while small δswap defines an ε-split regime suitable for emergent-geometry diagnostics.