Authenticity has no real bearing on the argument.
In the case of the Mona Lisa, its perfect “clone” can be both authentic or inauthentic depending on the criteria you use to describe “authentic.”
If the two paintings are exactly alike then there is no measurable difference between the two—the new one would even have all the particles involved with the correct aging appearance and smell of the original. Therefore, to all outside observers who don’t know the history of each painting, they are identical and there is no difference between them.
But, just because you don’t know the difference between them doesn’t mean there isn’t a difference. They are indeed identical, but there is, at minimum, two important differences: 1) they inhabit two separate coordinates in space and they always have; 2) one was touched by da Vinci and the other was not. Two identical objects, with 2 differences.
If “touched by da Vinci” is the criteria that makes the painting authentic in your mind, then one is authentic and the other is not. But, remember, you are an outside observer; you’re not the Mona Lisa.
The Mona Lisa has no brain, so she doesn’t have self-awareness. Self-awareness is the only important criteria in this discussion.
Why can’t we apply the same logic to you and your perfect clone? You are both identical in every possible way to all outside observers, with no measurable difference (both are authentic depending on the criteria used). And we should all agree that there is one certain difference: you both occupy different coordinates in space and always have (assume the infinite universe scenario with no physical contact between you and your clone if that makes the point clearer).
If you’re willing to accept that two identical objects have one difference, why the resistance to accepting that there may be more than one difference?
In this case, the other difference is the PI/POV/qualia of you and your clone. I’m in the camp that believes the PI is not only different past the point of divergence (which we all agree on), but also at the point of convergence. Why? Two reasons: 1) it is how we perceive the world and our place in it. 2) It’s the simplest explanation. It feels right and it’s simple. Why complicate things?
What’s the second relevant difference between you and your clone? Just like only one Mona Lisa having a real history of physical contact with da Vinci, only one of you has a real history of continuous physical contact with the original you.
We all agree that you and your diverged clone have two separate PI’s. Why do some of you insist that you have only one PI when you were perfectly symmetrical, at or before the point of bifurcation? I believe you were always separate people (you never shared the same coordinates in space, did you?); some of you believe you were one person who became two. That’s illogical—it’s a paradox.
It may be more apparent if you reverse the arrow of time (it doesn’t break physical law to posit that). In this case, your conclusion is that two people became one? That’s even more bizarre.
Or, let’s take it to the extreme: two almost perfect clones become perfectly symmetrical for a period of time, then become asymmetrical once again. Two people become one, and then become two again. Where did that second guy go? Is the first second guy the same one that pops back out again? That’s beyond science fiction—it’s almost beyond fantasy.
My perfect clone doesn’t agree with me, but he sustained head trauma after divergence, so I don’t put much merit in his hypotheses.