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There are solutions which don’t require a third party. These would be guaranteed to survive in case a third party shuts down with a long duration.

Paper: https://docs.google.com/document/d/e/2PACX-1vQe-OF0Lw9lutf6a...

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The solution in that paper does require third parties, except the parties are unknown, the amount of parties is unknown, and the system breaks down if insufficient people are interested in running the chain.

I’m really not convinced that solution is better is any way. If your adversary has the resources to coerce the “leave of entropy” in the OP, cracking that blockchain implementation will be trivial.

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