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It turns out that 2*N btc has been sent.
Is it possible to have below zero balance on my btc balance becouse of double spending?
you said "Theoretically...", so you haven't actually done this yet?
if you managed to broadcast 2*N BTC with the same utxo used, you didn't actually send 2*N BTC out of your wallet
if those 2 txs has different txid, you were simply doing a double spend attempt and only one will be confirmed
"a below zero balance" is only temporary, it will get corrected after your wallet is synchronized correctly
I assumed that someone had more than 50% hashrate in order to make it possible. Anyway thanks a lot!