The one positive thing I can say about Bitcoin is that it gives someone who is factually Satoshi an extremely easy way to prove that fact in a way which is extremely difficult for anyone else in the world to forge. Wright hasn’t because he can’t because he isn’t.
Tangent: that link shows exactly what's wrong with the current state of public-key cryptography: there are too many ways to get it wrong, and no broadly used standard tooling that's foolproof enough for the average person to be confident that they did it right.
This is the problem that Keybase is trying to solve, though I don't have enough experience with their system to know how well they succeeded.
Satoshi is known to have mined the first several blocks for Bitcoin. Each of those blocks has a coinbase address where the miner fee was deposited; each address encodes a public key.
Write a message like “I am Satoshi. Here’s a boring detail which proves this message was created on demand.”, sign with corresponding private key, post the ~10 lines of OpenSSL commands which verify that the signature matches. The end.