The core idea is that every piece of gold would carry a digital signature, much like the certificate you get when buying gold.
Also, if your gold is stolen, they can't sell it since they don't have the crypto keys to transfer the owner of this item, with the help of government regulations it'll be much easier to find stolen gold.
What would create the signature in the gold?
Why couldn't I simply dissect or melt part of the gold to change the signature?
If you remove the gold signature then you've essential detached the piece of gold from blockchain, which means you won't be able to trade that gold any more (given that government enforces the blockchain).
If you're talking about changing the signature to match another existing signature so you can scam someone, it won't work, you certainly will show a signature that exists on blockchain and the buyer can validate it. However, when you try to sell it, you don't have the private key to transfer the ownership of this asset to another person.