This is my first post on the forum, please be kind
I recently read up about impossibility of proof of stake and nothing at stake problem. I still do not follow what is so fundamental about it. Why can't we have a 'rule' that a node can generate only one block at given height and a running 'black-list' of public keys to enforce that rule. We can have black-listing someone as a mining operation with rewards several times block reward so that black-listing would be an equilibrium strategy.
One node can have as many public keys as it wants. Public keys are not assigned to nodes.