In Satoshis case, I think the proof of his identity would require more evidence: It would be necessary but not sufficient that he provide a cryptographically signed proof. It is unlikely, but possible that someone may have stolen Satoshis private keys.
This is an important point to be made, and it's
a point I've made before.
Until someone can provide some sort of cryptographic evidence (sign from an early address, moving coins, PGP, etc.), then what they say can be rightly ridiculed. If they
can provide such evidence, then that doesn't automatically make them Satoshi, but it does warrant further discussion and examination. Signing a message proves ownership; it does not prove identity.
Given CSW's endless list of lies, his repeated scam attempts, all his faked "evidence", his poor technical knowledge regarding bitcoin and cryptography, his complete lack of understanding regarding code he supposedly wrote, even his writing style and general philosophies regarding privacy, even if he did manage to sign a message or similar, I still wouldn't believe he was Satoshi.
In the interest of providing people with talking points, as much as it pains me to link to a BCH subreddit, I'll share this link:
https://www.reddit.com/r/btc/comments/b479rk/please_excuse_the_craig_wright_spam_but_this_is/ej4oxvj/