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AI losses that arise through an insured organization's generative or agentic AI system require state reconstruction, not merely event reconstruction, because the relevant state changes as the system reasons, retrieves, calls tools, and acts. The relevant question is not only what loss occurred, but what the system was allowed to do, what it actually did, and whether that reconstructed loss can support insurance claim recovery. This paper addresses losses in which the insured's AI system is in the causal chain, including externally triggered failures such as prompt injection, retrieval-augmented generation (RAG) poisoning, malicious tool output, credential misuse, and data poisoning. Specifically, this paper introduces CER, a use-case-level diagnostic for AI residual risk transfer. C (control boundary) asks whether the system had an enforceable operating envelope. E (evidence reconstruction) asks whether the system state and causal chain can be reconstructed from retained artifacts. R (insurance response) asks whether the reconstructed loss is insured: whether insurance coverage is available in the market and placed for the insured, together with the proof needed to support insurance claim recovery. The paper makes three contributions: it defines the AI-specific reconstruction problem, operationalizes that problem through CER, and specifies claim-grade evidence for AI reconstruction. Public examples include the reported PocketOS and Replit agentic database-deletion incidents and Moffatt v. Air Canada as an adjudicated output/reliance case. Keywords: AI systems; CER framework; residual risk transfer; agentic AI; generative AI; AI insurance; evidence reconstruction.