"Take the idea of proof-of-stake as a base layer consensus mechanism, and throw the idea away for right now. That's not what this is, and the problems that need to be solved to enable proof-of-stake as a second layer system instead of a stand alone base layer are not the same. Proof-of-stake is essentially a federation, but where anyone can join and can't be stopped from doing so, and with a mechanism to punish members for acting malicious. As a base layer that creates all kinds of existential issues, like the objectivity of a slashing penalty. Proof-of-stake as a second layer does not have that problem when the bonds for slashing are on the mainchain, governed by proof-of-work."

SPIDERCHAINS: A PROOF OF STAKE SECOND LAYER FOR BITCOIN

Botanix Labs has designed a mechanism for governing a two-way pegged Bitcoin sidechain system with proof-of-stake collateralized with BTC.