They gave their "logic", such as it is ... and it's utterly irrational.
Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems relevant.
A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'.
Counterexample: 35 + 6.
> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization
Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time.
> There's no reason to think that it won't provided if asked for
But they didn't provide it.
> There's no reason to think that it won't provided if asked for, but it hardly seems relevant.
My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.