With Ethereum proof of stake, is transaction finality/settlement finality finally possible / within reach?

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It's in reach as much as it is theoretically possible: it can provide theoretical finality guarantees if more than 2/3 of participants are honest. These are the safety guarantees that Byzantine Fault Tolerant systems like Casper can offer, so much of the work is on attempting to discourage byzantine behaviour and minimising the damage when finality fails (e.g. economic or probabilistic finality.)

There have been several versions, and the protocol is still being worked on, but finality will still require >2/3 honest validators to provide 100% theoretical consistency, which in practice cannot be proven and double-finality will have a non-zero probability of occuring.

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