It doesn’t even do that. You can easily have one unique NFT claiming it represents ownership of the Mona Lisa, and another, unique and distinct NFT, also claiming ownership of the Mona Lisa. Besides ownership being unenforced, uniqueness is also unenforced.

But that's not how NFTs are being used now. For one, who would issue the Mona Lisa NFT, the Louvre, or Leonardo's family, or the family of his patron at the time? An NFT can't clear up a murky issue anymore than me writing you a paper receipt would.

But, a paper receipt is all that differentiates print #1 from #1005, and #1 is usually more prestigious. And even if those prints came off the machine in the other order, the actual artist is still attaching significance to one of them over the others.

NFTs are a way of saying that my identical print (file) is really the special one. Or that I'm special for having it. Or whatever.

It’s just like you having a paper receipt with #1 on it, and me also having a receipt with #1 on it. Both can be on the same blockchain at the same time, issued by different NFT ‘creators’. Or maybe on different blockchain... Which one is the ‘real’ one? No-one can say.

Do you not crypto? It's clear which address mints an NFT, and that address can be provably linked to the party with the keys. And they can put that proof on their website. You do know your favorite artists website, right?

So yeah, by looking at both NFTs we can clearly determine which is authentic.

If they're supposed to be unique, as opposed to 'we both sponsored the same art', then there are easy ways to ensure that.

For this reason, blockchains are not used that way - it does not track ownership of physical objects, it tracks ownerships of digital ones. If the blockchain says you own the only digital edition that Beeple created for his artwork, then this is so, because the blockchain states this.

If Beeple creates another NFT referring to the same work, then he is simply creating a second edition, in the same way that an artist can create a run of prints limited to 10, and later decide to create 10 further prints.

If someone else creates an NFT claiming to represent Beeples work, then this is like me selling my own unauthorized Robert Rauschenberg print, which I might find difficult to find a buyer for, though with enough talent, maybe not impossible.

In any case, the NFT is merely a digital equivalent of a print.

A digital equivalent of a print is an image file. The NFT has no real-world equivalent. Purportedly it "represents" the artwork, somehow, but in reality it's just a digital token with no connection whatsoever with the artwork.