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> has been offline for more than k blocks

These systems require you to be online at regular intervals for proper security guarantees.

Yes, as I mentioned users who don't have to sync back up have their vulnerabilities limited to stake grinding attacks.

So new users don't have proper security guarantees? That seems like a somewhat serious flaw.

Yes, this is the weakness of POS systems. Of course, with a POW system new users still need to get a trusted copy of the genesis block.

They don't, however, need trust to determine which chain has had the most work done on it. An alternative genesis with much less work done on it is suspect immediately.

New Bitcoin users also need to rely on trust to find out Bitcoin's genesis block. Yes it's trivially solved, but the same is true for PoS as long as the epochs are long enough.

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