In this double dougnut world, the fundamental group would be the free group on two generators:
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What users experience as "responsiveness" is the time from when they stop speaking to when they hear the first syllable of the agent's response. That path runs through turn detection, transcription, LLM time-to-first-token, text-to-speech synthesis, outbound audio buffering, and network hops between all of them. You optimize this by identifying which stages sit on the critical path and making sure nothing blocks unnecessarily.