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I think that "LLMs can never X" is just always false.

LLM can never solve a halting problem (because no one can using a Turing machine).

A finite-size LLM can solve the finite-size halting problem, and an infinite-size LLM can solve the infinite-size halting problem

Halting problem input has finite size (i.e. it’s a Turing machine)

"LLMs can never predict the next word"