Agentic AI systems increasingly act through tools, sub-agents, and external services, but governance controls are still commonly attached to prompts, dashboards, or post-hoc documentation. This creates a structural mismatch in regulated settings: obligations that must constrain execution are often evaluated only after execution has occurred. We introduce SARC, a runtime governance architecture for tool-using agents that treats constraints as first-class specification objects alongside state, action space, and reward. A SARC specification declares each constraint's source, class, predicate, verification point, response protocol, and operating point, and compiles these into four enforcement sites in the agent loop: a Pre-Action Gate, an Action-Time Monitor, a Post-Action Auditor, and an Escalation Router. We formalize the minimal invariants required for specification-trace correspondence, show why finite reward penalties do not generally substitute for hard runtime constraints, and extend the architecture to multi-agent workflows through constraint propagation, authority intersection, and attribution-preserving trace trees. We implement a prototype audit checker and report a reproducible synthetic evaluation over 50 seeds comparing SARC against post-hoc audit, output filtering, workflow rules, and policy-as-code-only baselines on a procurement task. SARC executes zero hard-constraint violations under exact predicates; its declared PAA throttling response reduces soft-window overages by 89.5% relative to policy-as-code-only. Predicate-noise and enforcement-failure sweeps are consistent with the claim that residual hard violations under SARC scale with enforcement-stack error rather than environmental violation opportunity. SARC provides the architectural substrate through which obligations can be made executable, inspectable, and auditable at runtime.