Why: Interleaved-thinking models (MiniMax, DeepSeek R1) require the
assistant's thinking to be passed back verbatim in message history; dropping
it degrades later turns. The product's P2-I1 replayed thinking only into the
request-side rebuild; with the session transcript becoming the authoritative
context (quality P2-I2), capture must live in the kernel so thinking persists
in the transcript and replays on every request.
Evidence: SELF - TestReasoningCaptureAndReplay covers capture (SSE
reasoning_content into Message.Thinking, content unpolluted) and replay
(<think> prefix on thinking assistants, untouched non-thinking messages);
go vet + go test ./... pass.
Impact: sse.go accumulates reasoning deltas into the terminal message's
Thinking; client.go toProviderMessages renders captured thinking as a
<think> block prefix for assistant messages. Anthropic path unchanged;
messages without thinking serialize exactly as before.