The impossibility of perfect forgeries?

I think the author is trying to say that there is a concept of knowledge that is inherent to words "perfect forgery". That either someone knows the origin of an object and therefore it is not a perfect forgery, or all such knowledge has been erased and now there is no way to say that an object is not authentic.

I think this is something of a straw man argument. There is an entirely satisfactory functional definition for "perfect forgery" which is that an object is a perfect forgery if it cannot be distinguished from an authentic object by someone with no prior knowledge of the object's origin. This is what I believe common intuition would determine the word "forgery" to mean. An object does not fail to be a perfect forgery because its creator knows it is not real. It is a perfect forgery if it can fool everyone else into believing it is real.

Making zero knowledge of authenticity a prerequisite for a "perfect forgery" is to neglect that there are multiple independent minds in the world with their own viewpoints. I can know "that is a perfect forgery" if I know it will fool anyone without my private knowledge. Such knowledge is not incompatible with the object being a perfect forgery, because the most sensible definition of "perfect forgery" is that it would fool anyone else, not that it has already fooled everyone including me.

When we talk about whether something is real or a forgery, I don't think we really care what it is composed of, we care about its provenance. The composition is really just a shortcut often used to help us identify obviously fake provenance; if something is not composed of the same stuff as the real thing, well then we can disqualify it from being real. I don't think anyone should suppose that identical composition is sufficient to guarantee real provenance though.

For perfect forgery detection, I think you need a complete and unimpeachable record of where each bill has been at each moment of its existence. The current physical properties of the item are just not enough. Obviously that is infeasible, though I guess crypto-currencies basically do that.

Isn’t this just saying that not all proofs are constructive? That is, just because you can prove the existence of an object doesn’t mean you necessarily have a method for identifying it.

Also, there is some vague appeal to a substructural logic here, since by mixing up the forgery with the genuine article, you’re destroying the information about their origins, which is what prevents you from identifying the forgery afterward.

I’m not up on my modal logic, but I think this can be expressed as ◻∃x.P(x) ↛ ∃x.◻P(x)—proving the existence of some x for which P is true does not imply that there exists any particular x for which P is provable.

In other words, to have a perfect forgery you must not know it is a forgery. If you could screen for knowing that a bill is a forgery, it would be useless to make one (since you could not spend it, since you knew it was a forgery). Bummer we can't. /s