It's not necessary, but is significantly more radio-quiet than a lunar orbit. And secondly, though unfortunately not something we could really exploit this time, the stable temperatures of the lunar night greatly help with calibration for sensitive measurements like the 21cm Dark Ages signal
This is quite seriously missing the point: computational theorem-provers and contributions to mathlib (for Lean, anyway) allow for checking "correctness". The LLM is one of the many ways to search for tactics that help complete a proof for a theorem not yet in mathlib.
The LLM is not done until the theorem-prover says it is done - at which point we can be sure of the correctness of the assertion in the context. AFAIK there is no debate about inaccuracy with theorem-provers. Their real limitation continues to be converging in realistic timescales and efficient search over all combinations of proof tactics.
makes me wonder if a sufficiently large number of connected nodes can represent bits via their online/offline status, and their network graph representing "memory"
How was the interactivity achieved? Could you maybe link to the source so I can learn? I have been trying to get something like this working with quarto, but it is getting way too complicated.