Hosted large language models are increasingly accessed through remote APIs, but the API boundary still offers little direct evidence that a returned output actually corresponds to the client-visible request. Recent audits of shadow APIs show that unofficial or intermediary endpoints can diverge from claimed behavior, while existing approaches such as fingerprinting, model-equality testing, verifiable inference, and TEE attestation either remain inferential or answer different questions. We propose AEX, a non-intrusive attestation extension for existing JSON-based LLM APIs. AEX preserves request, response, tool-calling, streaming, and error semantics, and instead adds a signed top-level attestation object that binds a client-visible request projection to either a complete response object or a committed streaming output. To support realistic deployments, AEX provides explicit request-binding modes, signed request-transform receipts for trusted intermediaries, and source-output / output-transform receipts for trusted output rewriting. For streaming, it separates checkpoint proofs for verified prefixes of an unmodified source stream from complete-output lineage for outputs that have been rewritten, buffered, aggregated, or re-packaged, preventing transformed outputs from being mistaken for source-stream prefixes. AEX therefore makes a deliberately narrow claim: a trusted issuer attests to a specific request-output relation, or to a specific complete-output lineage, at the API boundary. We present the protocol design, threat model, verification state machine, security and privacy analysis, an OpenAI-compatible chat-completions profile, and a reference TypeScript prototype with local conformance tests and microbenchmarks.