> The CoT might "in English", but is it really

Yes, it really is. It's emitting literal English text in patterns that have been coaxed through RL into doing some kind of useful fuzzy computation.

> is the CoT just another presentation layer over the actual weights?

What does this mean? Which part of the forward pass are you talking about here?

> What I think the author (and I) are wondering about, is whether instructions like these might influence not _only_ the final output, but also the way it got there.

Sure, LLMs are chaotic. If I mention as a casual aside that the sky is blue, I'll get a different answer, even when my query has nothing to do with the colour of the sky. The fact that style instructions compete for attention with more concrete instructions is probably the one part of the author's post that I agree with. Different doesn't mean worse; if I run with greedy sampling (so deterministic) then minor punctuation differences in my query still produce completely different answers.

My reading is that they are actually making a more concrete point, which is: requesting a simpler style compresses the output, and this causes loss of fidelity in future turns. I think this is something you would have to demonstrate instead of hand-waving. I'm happy to be corrected on specifics.