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Do bitcoin nodes or miners have ids that can be used to identify them. Like how do we know if it is the same miner that has added several blocks consecutively? Or how can I identify a node uniquely?

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Neither nodes nor miners have unique ids at the protocol level, by design.

Some miners however do voluntarily put messages in the blocks they produce, which allows identification (but, those could also easily be faked, if anyone was so inclined).

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    Some mining pools also reuse the same payout address, which could only be faked by forfeiting the block reward. Aug 28 at 16:51
  • @Pieter Wuille, when you say by design do you mean it can be designed so that miners and nodes have unique ids. Let us say you want to create a protocol called "proof-of-consistency"(bare with me please. :) I do not know much about this,). Can you create a protocol that checks how consistent a node or a miner has been in submitting truthful information to the blockchain for example like timestamp and reward them for it?
    – YulePale
    Aug 30 at 4:32
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When creating hashpower pools you're miner (rig ) is associated as having a miner address which is the same as you're wallet address so technically no the miner itself has no id bit uses the wallet address to be identified when assigning jobs and pools.

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