What is a universe?

A universe is a population of records plus everything you can lawfully say about it. It’s the answer to a question every warehouse quietly dodges: when you ask for “revenue by category,” what world is that question even asked in?

Start with a population

Every fact table is about something. Cascadia’s transactions table is about sale lines — one row, one line sold: a customer, a store, a product, a day, an amount. Its eom_inventory table is about stock snapshots — one row per store per day, a level read off the shelves.

That “about” is the universe’s base. And bases differ in what absence means: a missing sale-line combination means nothing happened — an honest zero (an events base); a missing snapshot means a gap in a grid that should be complete — and answers over gaps must say so (a spine base). Same warehouse, two different kinds of nothing.

Grow it by the arrows that don’t lie

From the base, the universe grows along many-to-one arrows — the relationships where each thing has exactly one home. Every store has exactly one region. Every day sits in exactly one month; every month in one quarter. So from a sale line you can climb: store → region, day → month → quarter → year. Numbers climb these arrows safely — revenue by store rolls up to revenue by region and nothing is counted twice, because each store has one region to give its revenue to.

Everything reachable this way — the grains, and every attribute they carry — belongs to the universe. That’s the whole rule: a universe is a base plus its many-to-one closure. You don’t choose its size; the data’s own structure decides, and the model just writes it down.

And then the arrow that breaks

Cascadia’s products sit in up to three categories. Product → category is many-to-many: a product has no single category to give its revenue to. The climb fails — and with it, category falls outside the transaction universe. Not “hard to reach.” Outside.

This is the moment most stacks fumble silently: the join fans out, revenue multiplies, and “revenue by category” comes back 44% bigger than total revenue with nobody the wiser. Columna does something different: it declares the boundary. Category lives in its own small universe (twelve rows — each category’s priority rank and allocation weight), and the product↔category relationship is declared for what it is — a frontier, not a path.

Crossing, when you mean to

Between universes there are exactly two kinds of passage, and both are declared:

• Shared grains. Transactions and inventory both live on store and day — the same declared levels, presented twice. So revenue (from sales) and stock position (from snapshots) compose at store × month lawfully, with no ceremony: the identity of the grains is the license.
• Faces. Crossing the many-to-many frontier requires a declared face — each one named for what it does. Cascadia declares three: touch (revenue reaches every category a product sits in — deliberately multi-counted, 1.44× the total, and the answer says so), primary (each product’s top-priority category gets it — single-counted, 270 secondary memberships disclosed as unrepresented), split (a weighted spread that reconciles to the grand total to the cent — certified on the answer).

And if neither passage exists? The ask refuses, and says why. Ask this demo for stock by customer and you’ll get the honest answer: those live in different universes, and no declared passage connects them.

Why carve at all?

Because every silent double-count, every mystery join explosion, every “primary category” chosen by a forgotten ETL rule is the same event: a question crossing a boundary nobody declared. Universes make the boundaries visible; declared passages make the crossings lawful; and everything else refuses by name instead of guessing.

One warehouse. Three universes. Two kinds of passage. No third way through — and that’s the feature.

See it drawn — live, from the running system — in Figure 1 on the case page. Or run it: pip install columna, and ask for revenue by category three lawful ways.

The theory, in full: Multi-Universe Processing · The Two Great Sources.