how do you know how many monero coins there are if the transaction history is erased

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Feel free to research. I ain't your bitch to run around educating you.

I did

u don't

Monero is unverifiable

Do you verify Bitcoin by checking every single input/output yourself for a billion+ transactions?

Or do you simply run a Bitcoin node?

You have your answer.

Consider a sealed box of chocolates where each chocolate has a unique weight. You can verify the total weight of the chocolates inside the box without seeing or counting each one individually. Similarly, Monero uses cryptographic techniques to ensure the total number of coins is correct without revealing individual transaction details.

There is also a tx_ sum commend that you can run so display total number of coins when you run a full node.