Can one prove the discovery of a P versus NP solution without actually revealing it?
Or Meir’s comment is almost but not quite right, since it would be satisfied by a proof that P vs. NP is not independent even if the prover didn’t know which. A corrected version is “X is either the hash of a proof that P = NP or the hash of a proof that P $\ne$ NP”, where hash is SHA256, say.  Running that statement through a zero knowledge proof system gives the desired evidence.

However, if I was given such a proof, I would assign higher probability to someone having found a bug in the logical system being used.  It would be quite difficult to surmount that qualification in practice, since bugs in proof systems are fairly common.