No disagreement, although the sampling + search procedure is obviously adding quite a lot to the capabilities of the system as a whole, so it really should be c

No disagreement, although the sampling + search procedure is obviously adding quite a lot to the capabilities of the system as a whole, so it really should be considered as part of the architecture. It's a bit like AlphaGo or AlphaZero - generating potential moves (cf LLM) is only a component of the overall solution architecture, and the MCTS sampling/search is equally (or more) important.