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From my understanding, when a new block is mined, the coinbase address's balance is incremented by the block reward amount. If this address had a zero balance before the block was mined and the block contains a transaction that spends funds from this address, would the block be considered valid?

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No, the reward is credited after all the transactions in the block are processed.

From the Yellow Paper section 11. Block Finalization

The process of finalising a block involves four stages:

  1. Validate (or, if mining, determine) ommers;
  2. validate (or, if mining, determine) transactions;
  3. apply rewards;
  4. verify (or, if mining, compute a valid) state and block nonce.

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