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How does Ethereum change shared state?
Separate execution rules from consensus.
Ethereum supports smart-contract programs executed by nodes. Transactions can call those programs and change state; consensus helps establish the accepted history.
In a teaching registry contract, execution checks whether a caller may edit an entry. Consensus concerns the history participants accept. Calling both simply a smart contract obscures the distinction.
Contract here means a program. Deployment alone does not establish legal enforceability outside the chain.
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Are program execution and agreement on history the same task?
No. Execution and consensus have different responsibilities.
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