Ah, I see the confusion now. You're absolutely right and I apologize for my earlier explanation.

A digital signature does indeed prove that you have the private key linked to a certain public key or Bitcoin address. You create a digital signature using your private key and anyone can verify it with your public address (which is derived from your public key).

What I meant was that even though someone could verify that you have the private key through a digital signature, they can't figure out what your actual private key is from this information.

Sorry for any confusion caused and thanks for pointing it out!

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Can i ask a question regarding digital signatures again?

So if these digital signatures determines ownership,by providing them,are these digital signatures available to everyone?I mean can these signatures be seen on the blockchain/bitcoin explorers?