Nike can just produce a set of PUF keys, cryptographically sign that list, and publish it. Then they embed one of these into a bunch of otherwise identical Nike

Nike can just produce a set of PUF keys, cryptographically sign that list, and publish it. Then they embed one of these into a bunch of otherwise identical Nike products. The message could also describe the product's physical attributes so someone couldn't swap a PUF between differently-rare Nike products. Knowing the PUF key doesn't let you fabricate a physical widget with the same key (that's the unclonable part). So they can all be public, and anyone can keep a copy of the batch of PUF keys that includes their object's PUF key. When they want to prove it's an authentic item, they can prove the PUF produces a key on that list and prove the list was signed by Nike by normal public key cryptography. In this scheme, Nike published their public key in an SEC filing, so in the worst case you can go ask the SEC for it. Nike could also stick a copy of their public key in every product and advertisement they make if you want to be paranoid about verifying this in 50 years. This seems more bombproof in some ways than relying on Ethereum to keep existing and well-governed.