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Yes, you can also easily prove the wrong thing.

That's why it doesn't suffice for only LLMs to know the relevant stuff.

You can't have a zoo run by animals.

Aren't all zoos technically run by animals? :D.
apt, as we try to contain the complexity of our designs while being ourselves panarchical hyper-systems
Unrelated but "Panarchical Hypersystems" makes for a great company name
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Lower intelligence animals....oh wait
I once saw an interview with a guy that designed garbage cans for National Parks. When asked what the hardest part of the job was he said, “accounting for the considerable overlap between the dumbest humans and the smartest bears”.
For months after some researchers “proved” our code signing system sound I was still finding security holes in the system. To this day I’m not sure what they proved. That the architecture worked? We’d already proven that to a hundred people.
Correct, because when there was no LLMs all code was perfect and bug free.