That would be surprising to me. The reasoning _is_ the model intelligence in a lot of respects, and so dropping those from the context would affect its output pretty significantly.
I assume that instead they just have a lot of guardrails in place and multiple runtime environments that an individual turns ping-pong between in order to dehydrate/rehydrate the reasoning to keep it hidden from the end user.
"Stripping extended thinking: Extended thinking blocks (shown in dark gray) are generated during each turn's output phase, but are not carried forward as input tokens for subsequent turns. You do not need to strip the thinking blocks yourself. The Claude API automatically does this for you if you pass them back."
It's more nuanced in the various modes, but i haven't seen it boil down towards Thinking Tokens surviving more than two turns.
default depends on the model class. Opus: Claude Opus 4.5 and later Opus models keep all prior thinking blocks; Claude Opus 4.1 (deprecated) and earlier Opus models keep only the last assistant turn's thinking. Sonnet: Claude Sonnet 4.6 and later Sonnet models keep all; Claude Sonnet 4.5 and earlier Sonnet models keep only the last turn. Haiku: all Haiku models through Claude Haiku 4.5 keep only the last turn. Claude Mythos Preview also keeps all prior thinking blocks.
That would also explain the issue I mention in my other comment. And would also reinforce how much output would degrade without this. Opus 4.5 was a step above previous models in my experience. At some point it degraded and only got better when I disabled adaptive thinking. Adaptive thinking is always on for 4.6 and above.
I also wonder if they actually do a hybrid of "standard reasoning" and then classify this stripped chain of thought as "extended thinking".