From my understanding Bitcoin solves the Byzantine's Generals Problem under the assumption that there's no attacker that control more than 50%+1 of the mining power and this has been studied and proved in academic papers.
But what about Proof-of-Stake? I see several crypto (not just Ethereum) using or planning to use PoS. But does it work? Has proof-of-stake been studied in scientific papers and proved to actually solve the same problem that Bitcoin solves? Under which assumptions?
I understand that PoS is not wasteful like PoW and that PoS apparently allows for faster blocks, but if PoW solves one problem that PoS doesn't solve, PoS ain't an option to replace PoW because they're simply not doing the same thing?