The Theory of Data — A Foundations Note

We propose that data constitutes an autonomous abstract realm with intrinsic laws — not an epiphenomenon of the physical world. The note gives the realm a two-level structure (the particle, a key–value pair; the atom, an anchor–vector pair — a column as a function from anchor instances to values), its dynamics (two primitive morphisms classified by anchor behavior — the mapper and the reducer — and an aggregator algebra whose composition-stability failures reproduce the classic silent analytical errors as theorems), and its declared law (the V/M/B anchor triad, measure families, corroborated dimension hierarchies, universes, basis), closing on a decidable definition of lawful transformation. Meaning is defined as a two-arrow mapping — expression → declared model → the world of particles — with refusal as the absence of an arrow into the lawful world. Epistemic rank is stated honestly: a working theory, externally confirmed by independent rediscovery in four traditions, with a named falsifiable edge. Companion system: Columna (Apache-2.0), pip install columna.v1.1 corrects the particle's semantic status, gives the universe its law of existence, folds basis into operator-indexed B-anchor rules, and states the layered calculus — aligned with the technical companion, DOI 10.5281/zenodo.21707018.