The Theory of Data

A value becomes data only when it is bound to something it is about. The Theory of Data (ToD) develops a compact ontology for governed analytical objects. A universe establishes a governed root-point domain under an explicit existence law. An anchor is a governed partition of that universe. A measure family supplies analytical identity and family law. A measure is one family at one anchor, written F@A. Version 6.1 makes the identity criterion operationally explicit. Family identity is determined ex ante from a governed semantic signature, independently of agreement or disagreement among computed outputs. An implementation may assign an opaque immutable family_id to that signature; canonical names remain governed resolvable handles. Identity is therefore an input to a consistency test, never an inference from its result. The revision separates four locations for governance information: family identity, edge validity, certificate/materialization, and metadata. Meaning-bearing participation, multiplicity, unit, regime, and related semantics belong to family identity when they change the quantity or its declared family law. Edge predicates determine whether a particular derivation faithfully realizes that identity. Exactness, approximation, retained capability, and evidence grade belong to the certificate/materialization layer when the semantic target is unchanged. Inside a measure family, the central coherence theorem uses commutative-monoid sufficient state. The underlying algebra is standard; ToD's contribution is architectural: the state law is attached to family identity and edge contracts so that staging equivalence becomes a governed property. Version 6.1 adds a state-law taxonomy for commutative, order-sensitive, ordered/stateful, and non-decomposable cases. Partition anchors remain foundational. Many-to-many membership, overlapping cohorts, and fractional allocations are handled through governed assignment, allocation, expansion, or derived membership universes while partition geometry remains intact. Multi-parent lineage is illustrated with Average Order Value. A minimal conformance appendix shows how universes, anchors, families, edges, certificates, immutable IDs, and semantic signatures can be declared while keeping institutional authority outside the ontology. The claim remains narrow. ToD governs analytical identity, derivability, consistency, lineage, and materialized capability under declared premises. Empirical truth and statistical warrant require their own evidential grounds.