Missingness Has a Universe: A Typed and Compositional Foundation for Missing-Data Research

Version 1.1 is a vocabulary revision, content-preserving: aligned with The Theory of Data, Version 4.0 — a measure is the governed family; a member of a measure is a governed series; a series is a typed binding of datums over one anchor. Nothing is altered in substance.Modern missing-data theory has developed powerful accounts of missingness mechanisms, ignorability, recoverability, testability, imputation, sensitivity analysis, and nonresponse. Yet most of this work begins after a data foundation has already been fixed: units, variables, observation opportunities, coordinate alignment, and population membership are treated as given by the complete-data model. In real analytical systems these are among the main sources of ambiguity and error, and an incorrect complete-data object cannot be repaired by a correct missingness model. This paper proposes a data-foundational account of missingness derived from the Theory of Data. A typed value lives at a typed anchor point inside a universe whose existence law determines which points belong to the population; an event universe is generated by occurrences, while a spine universe establishes expected points independently of value presence. Missingness becomes defined only after an eligible universe point has been established. For a target atom member, the paper introduces an M-contract with four determinant classes — functionally reachable coordinates, lawfully transported observed determinants, the unobserved target value itself, and latent determinants — with a functional-reachability admission rule for the M-anchor. MCAR, MAR, self-dependent MNAR, and latent-dependent MNAR become derived properties of the complete contract rather than primitive labels on a rectangular dataset. The deeper contribution is compositional: missingness is a law that must transform with the member under mapping, reduction, alignment, restriction, lag, expansion, and universe crossing. Part of that program is already formal — the population, support, and coverage rules specialize transformation rules proved in the accompanying Contract Calculus — and the paper specifies the remaining extension as the G_M program. The framework does not solve the classical identification problem; it exposes the premises conventional analyses must already make, gives them typed locations, and makes their consequences available to analytical computation.