Light Cone Consistency: Closure, Ordering, and the Single-Observer Boundary

Abstract

Every distributed system is a message-passing system, and every message-passing system is a growing causal DAG observed by a set of observers. We treat each observer's consistency as two operators on its visible sub-DAG (a causal-closure filter $C$, fixing which dependencies it must have seen, and a fork resolution $O$, ordering the concurrent forks the filter admits) and give the resulting space the structure the flat catalog of named models lacks. The operators are coupled, asymmetrically: an order that refines causality supplies closure its filter never demanded. That coupling yields a decidable readability order (which configuration's data another can read honestly) with a factoring dichotomy: the order splits across the $C$ and $O$ axes exactly when ordering does not refine causality, and refuses to when it does, the cross-axis gap being the closure ordering supplies. On that order sit a consistency ratchet (a level lost under migration is never regained) and a Detection = Prevention bound: a system can tell its order inverted causality only if it retained exactly what would have prevented the inversion. The classical results land at clean coordinates in the same system, not as new claims: resolving a fork demands retaining the causal history that distinguishes its branches (database folklore, here an impossibility for every message-passing system) and linearizability resolves as a composite of two systems, a store and a global real-time serializer supplying an order no single observer's light cone can. The named models are configurations of $(C, O)$, exact over the standard-safety fragment and generative past it, predicting configurations the catalog has not named. LCC is a formalization of the observer-relative consistency model of Burgess and Gerlits.