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How does proof of stake organize validation?

Stake and protocol duties are different from identity authentication.

Proof of stake (PoS) uses assets committed as a security deposit to organize eligibility or weight for proposing, validating and voting on blocks. Ethereum validators must check blocks, and certain protocol violations can destroy part or all of their stake.

Putting up stake does not make every statement trustworthy. Nodes still validate transactions and blocks. Different PoS systems may use different selection, voting and finality rules.

Read the complete protocol rather than treating PoS as a label that guarantees every property.

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