I understand that this is a general proof that will invalidate any attempt at a non evidenced based logical argument because if such a thing were possible that would imply that phase space volume decreases. In theory this should not invalidate someone saying that there is a perfect representation of (part of) the world inside the world, as this will not decrease the net entropy since the entropy of the representation is equal to the entropy of that world (the phase space volume will be lower but that isn’t a problem since we only care about the phase space volume changing, not just being lower but stable).

Therefore if someone says that they can prove without evidence that they were born with only correct beliefs this argument should not be able to a priori show that this is impossible?

(Obviously, my priors for someone believing all the right things without evidence will be exactly equal to chance which is basically zero, but that doesn’t mean it is impossible for it to happen in a way that can be proven for our laws of physics, just that we can’t believe that it happened before we see the proof)