@spartacus,
We need also to elaborate more on your idea about data being distributed between users instead of replicated in nodes.
Although your proposed algorithm/protocol does not exactly comply with this idea as users need to disclose the data eventually and it should go to the blockchain and stay there permanently, hence replicated, it would be important to understand what this idea actually implies: Sharding of the state!
The data under consideration is nothing other than a part of the bitcoin state machine: which nested outputs of this output are still unspent? Trying to keep this data out of traditional full nodes, is such a concept. But we know that it is not the original design target and we are not in such a context. It is why I strongly recommend dropping such an idea and remaining focused on the core Spartacus Nested Output Protocol, SNOP. Invented this term right now
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