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What calculation/process is being carried out within the gui, regarding the syncing process of the block chain for running a full node?

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The main things going on are:

  1. Getting block information from connected peers
  2. Building/Verifying the blockchain starting with the Genesis Block (block 0) and verifying each block and all transactions in the blocks follow consensus (which changes at various block heights based on historical hard forks) and building a block tree.
  3. Storing the verified blockchain in an LMDB database.

So it is doing network connections/downloading, verifying hashes, and writing to disk.

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