I'm a little confused about the comment about the mirror rectifications. The author seems to claim that the other versions in the paper are "mathematically correct versions". But the label says that those are rectifications applied to the image with different assumptions about the mirror shape.

None of the rectifications are "remarkably correct" in my opinion. As in, they don't result in an image that looks completely undistributed. Most easily seen at the table end in the mirror. The horizontally drawn line of the table end is clearly wrong. It would only be correct if it were at the center-line of the mirror, but it's well below.

But being 100% mathematically isn't really important for the painting I would argue. It captures the effect of the mirror as it "appears to the observer" perfectly in my opinion.