Referential Regimes: Transformation-Invariant Identity for Neutral Substrates

Abstract

Data systems increasingly operate under persistent legal, political, and analytic disagreement, where no single interpretive authority can be assumed. A neutral substrate provides stable shared reference without requiring agreement about causal or normative interpretation: it fixes reference structurally and leaves interpretation to extension layers. This paper derives the identity structure such a substrate requires using a small transformation algebra. Identity is treated as transformation-invariance: a referent is individuated by the admissible operations that preserve it. Once routine record operations are fixed, individuation becomes a structural calculation. That calculation exposes a mismatch between reference kinds and identity regimes. An accountability substrate must refer to six carrier kinds: obligation-bearers, rules, occurrences, scopes, records, and plain referents. Three kinds have more than one admissible basis. A scope may be fixed by extension or structure; a rule by content or structure; a plain referent by locus or object. Decomposition separates the scope readings, refinement separates the rule readings, and forking separates the plain-referent readings. Counting reference kinds gives six, while transformation analysis forces at least nine identity regimes. The three additional regimes add no new kind to the inventory. They arise from identity behavior under ordinary operations, and any attempt to collapse them reappears as a hidden regime that persistent disagreement cannot hold fixed. The result is a conditional lower bound. A richer transformation basis may leave the bound unchanged or force further splits, but it cannot erase a distinction witnessed here. The additional regimes correspond to distinctions often handled by modeling convention, but such conventions cannot substitute for regime-level identity commitments under persistent disagreement.