Barge-ins were handled symmetrically. When Flux detects that the user starts speaking, the agent pipeline is immediately cancelled: in-flight LLM generation is stopped, TTS is torn down, and a clear message is sent to Twilio to flush any queued audio. The agent falls silent instantly, and Flux resumes listening for the next end-of-turn.
Using the Lagrange basis, we can get a much nicer matrix representation
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