Multi-Universe Processing: Territories, Frontiers, and the Lawful Passage of Meaning

Analytics practice treats a warehouse as one modeling space. We argue it is a federation of universes — territories of functional reachability — and that the decomposition is not a design choice but a derivation: a universe is the maximal closure of a base population under many-to-one edges, and the modeler records boundaries the data has already drawn. On this ontology we prove a Frontier Theorem: between universes there exist exactly two types of lawful passage — alignment at a grain whose identity is declared and proven, and crossing of a many-to-many frontier through a declared face — and, for a given pair, possibly none. The taxonomy is closed: there is no third type, and an ask licensed by neither refuses, naming the frontier. Faces decompose as driver × combinator, and the three combinators are classified by what a crossing does to conservation — touch exceeds, stating its fan-out; assign redistributes, stating its shadow; alloc commutes, certifying reconciliation on every answer. A two-mode traversal semantics settles non-additive measures at frontiers: reducers cross populations naturally; their resolved values do not combine. What distinguishes the account from its ancestors — summarizability conditions, non-strict hierarchies, bridge tables with weighting factors — is that prior work checks or documents what this paper declares, adjudicates, and serves: every passage is proven at publish and carries its own arithmetic on the answer. And all of it runs: the constructs ship in an open-source implementation whose demonstration warehouse serves a deliberate 1.44× over-count, a single-count with 270 memberships disclosed as unrepresented, and a weighted split reconciling to the grand total to the cent — each number regenerable by the reader in minutes.