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Are transactions validated by recomputing the entire blockchain? If not, how else can it be confirmed that a bitcoin I'm attempting to transact is one that I actually had come into acquisition of previously and still have?

If yes on the other hand, how long does that recomputation typically take in practice, and does that pose a scalability risk in the potential for Bitcoin usage (and hence the length of the blockchain) to outpace Moore's law?

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No. The blockchain must be queried, but not recomputed. If you see a transaction that has two inputs, you will need to query to check if those outputs have been spent. You will also need their encumbrance scripts in order to check the spending transaction meets the required criteria. In essence, this is just a database lookup.

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A transaction is valid if it is signed by the private key of an address in the UTXO set. So it isn't a 'recomputation of the entire blockchain', its just querying against a database.

So in relation to your question, the size of the UTXO set is an important variable. Look up 'UTXO bloat' for more discussion on this.

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