With proof of stake, a complete chain history is not strictly required by validating nodes.
You don’t want everyone to delete it, but it’s not required for consensus.
The more ambitious variants are very mathematically rigorous but axiomatize a wall-clock oracle, as well as in some cases mathematically-interesting but practically absurd assumptions about synchronicity.
Hoff has deployed his private fortune doing (among other, uh, things) serious research on distributed Byzantine consensus.
If they’ve got it nailed down I missed the paper.