Observer‑Mediated Canonical Identity (OMCI): A Framework‑Objective Theory of Identity Through Validated and Finalized Historical Recognition, with Graph‑Theoretic, Category‑Theoretic, and Higher‑Structural Extensions, and Applications to AI Systems

This paper introduces Observer‑Mediated Canonical Identity (OMCI) as a formal criterion for authoritative diachronic identity in governance‑sensitive systems. OMCI is designed for contexts in which identity cannot be adequately grounded either in presumed access to an entity’s essence or in static identifiers such as names, labels, hashes, registration tokens, or snapshots. Instead, OMCI defines identity as the outcome of a governance‑regulated recognition process in which identity‑relevant information enters through observer‑indexed records, is subjected to validation, and authoritatively grounds identity only when it supports a unique finalized canonical path between states of an entity. OMCI is observer‑mediated but framework‑objective: observers supply evidence, yet identity assignment is deterministic for fixed governance conditions. We present the strict path‑based rule, sharpen it on governance‑filtered DAGs and restate it categorically via the singletonhood of the category of finalized canonical paths. We also introduce a Reality Observation Equation (ROE) as an observer‑level validation score (an optional OMCI observation layer) for soft‑finality/conditional views without altering the strict identity rule. Finally, we outline higher‑structural enrichments, governance reconciliation, distributed extensions, and applications to AI model lineage, high‑risk autonomy, knowledge systems, institutional continuity, and unresolved branching.