A Primer on the Theory of Data Applied

Analytics is full of familiar practical rules: do not sum inventory through time, watch out for fan-out after joins, and be careful with denominators when rows are missing. This primer asks whether such rules are primitive facts of analytics or symptoms of a smaller analytical grammar. Through three short cases—open-store denominators, join fan-out, and inventory across time—the paper introduces several applied consequences of the Theory of Data. A denominator is shown to be a governed population rather than a side effect of surviving rows; some fan-out failures arise because a claimed source measure or anchor was never established; and additivity is shown to depend on a particular reduction from a particular source anchor to a particular target anchor rather than on a metric label such as “stock” or “semi-additive” in isolation. The three examples motivate a compact dependency: B→F@B→B≻A→Γ(e)→sufficient state, expressing the idea that analytical validity can depend on source-anchor existence, measure identity, anchor geometry, transformation law, and retained state before aggregation itself is considered. The primer is intentionally not a shortened version of The Theory of Data Applied. It is an accessible signpost to the longer paper and to the broader Theory of Data framework.