Enterprise AI systems are increasingly deployed as delegated actors within governed enterprises rather than as conventional applications. This shift exposes a gap in the existing enterprise architecture (EA) toolchain: current frameworks describe components, viewpoints, methods, and risk vocabulary, but none specify the authority semantics by which an AI capability is allowed to act. The result is a recurring failure mode in which technical capability is conflated with operational authorization. Ordinal Systems Architecture (OrdSA) introduces a control grammar for that gap. It organises AI capability into seven ordinal layers (Enterprise Intent, an Enterprise AI Orchestrator, Capability Domain Orchestrators, Agents and Workflows, Tools and Execution Channels, a Data and Knowledge Substrate, and an Outcome–Audit–Feedback closure) and governs them with a single architectural principle: authority flows downward, evidence flows upward, and no lower ordinal layer may expand its own authority. OrdSA is canonicalised as a versioned, tool-neutral YAML schema rather than as prose, making conformance mechanically checkable and positioning the construct as complementary to TOGAF, the Unified Architecture Framework, ArchiMate, the NIST AI Risk Management Framework, Zero Trust Architecture, IAM/PAM, policy-as-code, and DevSecOps. This paper presents the construct, its governance principle, the schema-first canonical form, the five-rung execution-rights ladder applied at the tools layer, the related-work positioning, the conformance assertions a conforming deployment must demonstrate, and a worked scenario that traces an AI coding agent through allow, refuse, and escalate paths across the ordinal stack.

Version 1.0.0 of the OrdSA prime paper. Construct repository at github.com/osa-ai-org/ordsa-ai (v0.1.6 at time of paper publication). Paper drafted by JD Longmire and Micah Longmire with thinx-Claude as collaborative drafting assistant; construct independently maintained by OlogosAI under the prime/review governance arrangement (see cross-ai#20).