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The blockchain is the oracle. (Note that a DHT can be the oracle too)

Can you explain what the problem is exactly? The infinitely small possibility that the same ID is generated for two different people?

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The Oracle problem is defined as the inability for blockchain solutions to validate their data with the real world. In this case it’s that any specific ID is actually a singular human, and not a bot, sock puppet, etc. Note this means any one person cannot get two or more IDs.

How would you implement a system that issued such IDs?

It might be possible to have a multi-layer identity system, where at the top level we have face matching and social vouching to implement uniqueness, and then we add a layer of zero knowledge proofs to allow people to mint new identities for themselves which can share reputation or attestations.

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