Distinguishability Regimes: A Diagnostic Ontology for Governed Systems and Distinction-Collapse Failures

Software and institutional systems are usually described with operational vocabulary — state, event, transition, validation, approval, logging, workflow, effect, execution. That vocabulary is locally useful but tends to compress several distinct settlement questions into a single operational surface: a validator can accept while meaning is unsettled, a workflow can advance while obligations remain, an approval can exist without a reconstructible authority chain, a model can answer while inference, evidence, adoption, and authority stay entangled. This paper is the ontological and diagnostic entry point of the Distinguishability Regimes Theory (DRT) series. It reads governed systems as regimes that settle distinctions, and it names a recurring, hard-to-see failure — distinction-collapse — in which operational success is presented as settlement while a distinction that should have been preserved, residualized, externalized, forbidden, or made traceable is silently collapsed. More sharply, it foregrounds unauthorized settlability: material made to look eligible for settlement before the relevant regime has made the required recognition, projectability, authority, and trace conditions reconstructible. The paper provides a vocabulary in which that diagnostic question can be asked precisely. It fixes a five-core ontology (distinction; Carrier, i.e. settlement-facing material; κ, a regime-local settlement coordinate; settlement; and trace), the non-core judgement-context structures needed to use it (regime, authority, witness, recognition, projectability, residual, projection), a general settlement judgement form R ; κ ⊢ Δ ⇓ M, a working taxonomy of settlement modalities (value, transition, residual, externalized, forbidden, incoherent, nonprojectable), a set of basic settlement constraints with their sources made explicit, and three governing disciplines: no premature closure, projection is not authority, and self-description is not self-authorization. The intended contribution is not to replace state machines, workflow engines, authorization logics, audit systems, or runtime architectures, but to give designers, auditors, and researchers a way to locate where such mechanisms have let an unsettled distinction masquerade as settled — a concern that is increasingly pointed for AI and agentic systems, where fluent output is easily mistaken for warranted settlement. DRT is an ontology and diagnostic discipline, not a programming language, workflow engine, audit system, legal or political theory, AI-alignment solution, or runtime architecture. This paper is self-contained and can be read without its companions: Paper 02 specializes the ontology into an operator-level judgement (Close_κ), and Paper 03 gives the conditions under which a software runtime can be said to materialize it. An accompanying open-source implementation of the series (GugenKoubou/Distinguishability-Regimes-Theory, release v0.1.0, https://github.com/GugenKoubou/Distinguishability-Regimes-Theory) is available as a feasibility witness for these runtime-facing consequences — an implementation-shaped demonstration only, not a reference API, conformance suite, or proof of the theory.