Trustless staking pools with a consensus layer and slashed pool participant replacement

When changing participants, is it possible to rotate the keys without changing the underlying secret? Also, is it possible to execute that without any coordinator ever having access to the full secret?

When a participant misbehaves, the Eth1 contract would have to believe other participants that the bad actor has done a penalizable action. I imagine there is no way that the Eth1 contract could in fact validate the offense is valid or invalid. In that case wouldn’t each participant have to trust a majority of other participants in order to not get evicted from the pool?

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