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Can you explain why the signature matching one in the blockchain disproves the theory?

I imagine the signature must also be somehow related to his private/public key pair otherwise his blog is just junk cryptography and would have been easily debunked anyway?

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Signatures are unique to the message that's being signed, otherwise they'd be useless.

Signatures are only probably unique. Theoretically there can be collisions.

Granted, the likelihood that he inadvertently collided with a public transaction is astronomically small.

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