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I'd imagine that the ability to fake and tell apart fakes will scale with computational resources, and so we will also have progressively stronger signatures that cost more computational power to generate.

This is basically already the premise of PoW -- it's hard to fake out the network and the chain of hashes show you exactly how much computational work was put into demonstrating veracity.

This doesn't remove the ability to fake things, but it imposes a price. If you really want to show something is real, dump a bunch of computation into computing hashes.