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Ethereum is working on proof of stake, which boils down to "I believe that this future is what really happened, and to guarantee so, here's $1000 that you may destroy if it's not true."
https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQ
Key quote for me:
"in PoW, we are working directly with the laws of physics. In PoS, we are able to design the protocol in such a way that it has the precise properties that we want - in short, we can optimize the laws of physics in our favor. The "hidden trapdoor" that gives us (3) is the change in the security model, specifically the introduction of weak subjectivity."
Is a solution in which control of the network is secured through the same private keys that secure the stores of value an option?