Statewise versus operator Bell causality in finite quantum sequential growth: exact separation and recovery at dimension two

Abstract

We present a bounded analysis of the finite, nonsingular, occurrence-ON quantum sequential-growth presentation at dimension d=2 and source stages n<=4. The preprint records five ledger-bound results: a frozen strong/strong commutativity baseline; an exact rational fixed-vector/general-covariance and reachable-state/martingale witness of noncommutativity; a source-native Eq. (120) lemma; commutativity on a proper reconstruction slice; and conditional statewise-to-operator recovery lemmas. Its purpose is to make the distinction between statewise and operator semantics auditable, rather than to classify all finite semantics. In particular, it does not claim the full 955 or 721 profiles, a complete finite occurrence-ON classification, or a reachable-visible witness. The bounded U2 auxiliary-ideal investigation is retained as a reproducibility and resource-boundary record, not as a unit-ideal theorem.