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This may be a dumb and newb question but.....When you buy btc from an exchange i.e. coinbase, kraken, robinhood how do we know that it is actual btc being transacted thru the blockchain to an external wallet? From my understanding btc are just inputs and outputs (randomly generated numbers). So wouldnt you be able to spoof numbers and add in "fake" btc? Plz lemme know if I'm understanding this correctly.

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When you withdraw, if it shows up in your wallet, its real.
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A spoof/invalid transaction would never get mined or accepted by the network.

All coins are initially created when they're awarded to a miner as a block reward. Because the chain is a bunch of blocks linearly connected to each other, you can trace all bitcoins back to their original birth place (a mining reward in some past block).

The inputs or unspent transaction outputs (UTXOs) are always traceable.
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Wallets can't send or receive "non-actual" bitcoins. It's software with specific functionality. It won't recognize "fake" BTC.
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the Bitcoin in your exchange account only becomes REAL and more importantly YOURS when you transfer it out of the exchange and to your own non-custodial wallet.  When you are buying and selling Bitcoin at an exchange, you are really just moving numbers around in their private database, it does not involve the Bitcoin blockchain at all.  You are right, they may or may not actually have any Bitcoin.  That is why it is so important that if you want to make that Bitcoin yours, you transfer it to your own non-custodial wallet, this forces the exchange to actually engage with the Bitcoin blockchain and send you what is rightfully yours.  Now you know what it means by that saying I'm sure you have heard here... NYKNYB Not Your Keys Not Your Bitcoin.
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The only way to really tell: Send it to your own (hardware) wallet.
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It’s on the blockchain baby
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Send it to your ledger if you want to find out
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Are you talking about tainted coins that are flagged?

They wouldn't be on exchange for trade in the first place (I would hope at least..)   


If you just mean about ownership, just withdraw it to your own wallet.   
It's VERY real when you self custody... no such thing as fractional reserve IOUs that you can move off exchange. Anything transferred will be real BTC

It's why there is a special day each year where the community withdraws huge amounts of BTC (and shitcoins) to stress test exchanges to make sure they aren't abusing fractional reserves and issuing more BTC than they can reliably service.
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You only know when you withdraw to a wallet. There's a good chance that those exchanges aren't fully backed.
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I expect any trading on centralised exchanges uses an exchange-specific local “ledger” (a DB basically).
Only when you withdraw does the exchange create an on-chain tx using BTC funds they have in their pool.

So the “not your keys; not your bitcoin” is 100% accurate.

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