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As per proof of transaction is, you do not need to send those tx to wallets X, Y, Z.
TX is send to the system (at all coins or almost all coins, back to next miner) not to the wallet of the person you send the coin.
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You can wire all the tx into your own wallet.
I dont really understood it, this means it works like proof of burn, or it means you can "send the transaction fee", without actually sending a transaction and so its basically proof of burn that instead of being frozen the coin goes back to the next miner?