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I would know what does Bitcoin verify when you download a block.

Are the transactions verified too, or not? If they are, will it be the case for their signatures?

Best wishes.

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It depends what kind of software you're talking about.

A full node, by definition, verifies all consensus rules for newly received blocks and their transactions, including:

  • Proof of work
  • Difficulty adjustment
  • Subsidy (do miners not print too much money)
  • Double spending (do transactions not spend anything already spent)
  • Transaction balance (do transactions not spend more than they send)
  • Resource limits (block weight limit, op count limits)
  • Signature validity
  • ...

Other software that interacts with the Bitcoin network may verify whatever it likes - ranging from all of the above, to some subset, or nothing at all and just trusting what other nodes or servers give it.

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