The Theory of Data

The Theory of Data is a foundation for governing analytical identity, derivability, and consistency independently of physical storage and execution. Version 8.2 retains the distinction between continuation-bearing measure families and governed analytical expressions and adds a compact value-state model over analytical points established by the universe. At every existing point, a governed analytical object has exactly one value state: Value(v), NA for non-applicability, or None for applicability without an established value. Point nonexistence is a fact of the universe rather than a fourth value state. Special mathematical results such as zero, empty values, infinity, and 0/0 remain values when admitted by the governing law. The revision locates missingness as a theory concerning None and distinguishes missingness mechanism from lawful missing-value treatment, including the requirement that treatments which alter a dependent expression's basis apply coherently across its required roles.Version 8.1 refines the Version 8.0 foundation in four closely related areas. First, it makes dependent sufficient basis explicit: composite constructions such as MEAN require their basis components to be established over the same governed analytical population. Second, it clarifies participation totality: participation must be resolved over the candidate analytical points required for a target result rather than inferred from whichever material observations happen to survive execution. Third, it clarifies the universe existence law as the source of analytical extent; geometry organizes governed points but material row presence does not create them. Fourth, it introduces an explicit missingness law for measure families, separating participation, support, missingness mechanism, and missingness treatment. The revision also clarifies the relation between universe and family participation: the universe establishes the admissible population, while a family may further restrict participation within that population. Missing-data mechanisms such as MCAR, MAR, and MNAR are treated as governed statistical claims or assumptions rather than conclusions inferred from observed missingness alone. Missingness treatment is kept distinct from mechanism. Dropping unsupported participating points changes the basis used by an analysis without rewriting participation; imputation creates constructed analytical state whose method, assumptions, and lineage must remain explicit. Version 8.1 preserves the central Version 8 distinction between continuation-bearing measure families and governed expressions. A measure retains the identity form F@A, while expressions remain governed analytical constructions whose results do not acquire family-continuation rights merely through computation or materialization. The Theory of Data remains independent of any particular database, query language, semantic layer, or implementation. Its purpose is to state the analytical objects and laws that those systems may realize.