The Measure Algebra of the Theory of Data

The Theory of Data treats a measure as a governed analytical object rather than as a numeric column plus an aggregation function. This paper reconstructs the finite Contract Calculus fragments G0, G1, and G2 as the operation layer over governed measures in the Version 6 ontology. The fragments provide typed pointwise formation, state-disciplined reduction, restriction, population carve, and relation-based expansion with explicit disposition. Read together under Theory of Data Version 6.1, they form the proved finite core of the Measure Algebra of the Theory of Data. The paper develops three consequences of this reading. Multi-measure operations must form the relationships they need at a common analytical location before reduction destroys those relationships. Value state and domain state have distinct sufficiency boundaries, so a materialization may retain enough information for one later derivation but not another. Analytical identity is also separate from displayed value, shared sufficient-state carriers, and executable backend behavior. The paper does not claim a complete normal form for every Theory-of-Data transformation. It identifies a proved finite algebraic core, shows how Version 6 broadens its state-law interpretation, and marks the extension boundaries that remain open.