Certified Service Is Not Enough for Long-Running AGI

Certified service coverage is not sufficient for long-running artificial general intelligence. A workflow may pass service audits, preserve executable witnesses, and maintain reusable certified records, yet still fail as a responsible agent when it exercises delegated authority, self-modifies, accumulates persistent memory, generates new goals, recovers from incidents, or interacts with other agents. This paper develops an operational continuity theory for long-running AGI workflows under finite verification. It introduces continuity-certified AGI as robust certified service inside a multi-layer viability kernel covering recovery, authority, identity, mutation, goal commitment, memory integrity, federation, liability, trusted-base health, cross-layer consistency, and non-erasing critical-violation history. The framework formalizes external-effect release gates, impact-classifier certificates, risk-vector layer predicates, tiered dependency cones, authority-contained substrates, trace-complete effect monitoring, fail-closed recovery with controlled re-entry, revocation-safe authority planning, identity morphisms, self-modification certificates, goal-conflict lattices, memory metabolism, privacy and retrieval-governance constraints, robust federated-contagion bounds, enforceable liability ledgers, and validation channels treated as ordinary trusted-base components rather than privileged human exceptions. The main integration result is a structural risk-vector viability theorem. Under declared confidence events, structural identification support, calibrated risk certificates, open-world hazard charges, and robust drift certificates, a workflow can enter, remain in, or recurrently return to a continuity-certified regime when repair, audit, quarantine, authority control, memory governance, trusted-base maintenance, liability resolution, and consistency repair dominate novelty, contamination, communication hazards, unsupported risks, and cross-layer coupling. The paper also provides machine-readable continuity record requirements, schema-profile and migration semantics, a minimal continuity audit checklist, and a falsifiable deployment evaluation protocol. The goal is a theory that is not merely about model capability or certified skill libraries, but about responsibility-bearing, authority-constrained, self-modifying, memory-governed, trusted-base-aware, federated workflows that can operate under real-world verification limits.