Earlier quoted context omitted.
I've thought about the high-jacking of reasoning-chains as a potential vector, but never saw a proven implementation in american models since, from my understanding, all major vendors throw out the reasoning tokens between turns.
For Claude, at least, "throw out the reasoning tokens" is only true when a session has been idle for more than an hour, and is new since March. The basic concept is that for a session active recently, interleaved thinking tokens are already in KV cache, so it's more efficient to keep using them than not! But when resuming an older session where KV cache has been evicted, it's more expensive to restore the thinking to…
Imagine a conversation with turns X, Y, and Z. When the LLM "reasons" about the next token A it does: P(A | X,Y,Z) and then P(B | X,Y,Z,A), etc. It will eventually produce a result P(D | X,Y,Z,A,B,C). Instead of continuing the context from X,Y,Z,A,B,C it continues it from X,Y,Z so you have P(N | X,Y,Z,D). This is what is meant by dropping the reasoning. This is done to save cache context for the session.
This is a different thing than preserving the K/V state of P(N | X,Y,Z,D).