The Theory of Data: A Foundational Framework for Governed Analytical Data, Lawful Transformation, and Certification

Abstract

The Theory of Data develops a foundational framework for governed analytical data, lawful transformation, and certification. A datum is one typed value at one anchor point. A member is a homogeneous typed partial function binding datums over one anchor within one universe. A measure is a stable governed family whose laws determine which anchored members share one analytical identity. The framework distinguishes coordinate structure, universe, regime, observation, provenance, and epistemic evidence. Event and spine are the two foundational universe types; regime is an orthogonal value-generation dimension. Version 5.0 makes explicit the consequences of the event/spine distinction for extent, missing points, readings of absence, sparse fill rules, and foreign-extent evaluation, and introduces regime-sensitive member identity and cross-regime passage. The Theory separates value operations from structural transformations and distinguishes result-frame evaluation, local member-contract certification, same-measure member closure, and new-measure synthesis. It develops mappers, reducers, sufficient-state aggregation, anchor and universe calculus, observation-process contracts, evidence propagation, lawfulness, faithfulness, and analytical certification. The broad framework is distinguished from its proved finite kernel. The companion Contract Calculus establishes results for the nested fragments G0, G1, and G2; Version 5's extent and regime additions remain framework definitions, propositions, design constraints, adequacy premises, or open formal extensions unless separately proved.