I'm afraid I don't have mathematical proof of this, but can confidently assert that stitching the lining to the dress all around the hem will produce puckers and bulges. I believe the problem is caused by unequal stretching of fabrics.

Far better to hem each separately, then swing tack at the seams.

He suggests turning the dress before stitching the arm holes, which is possible, but it still leaves visible stitch lines at the hem. Much neater to leave it open at the side seam and pull through that, and then stitch that up whilst putting in the zip (stitching would be generally hidden by the arm).

Indeed, dear ladies, as you point out the problem is more complicated. You talk about stretching. That's the difference between mathematics and physics and engineering. How much of a complication you are willing to take into account and your approach to solving the problem is different for each branch of science.

Indeed, Ms. Steiconi, in fact he did consider stretching, but he considered stretching of one type material, when you really have two materials.

The discussion on topology he gave was strictly a "geometric" discussion. No real physics involved at all. He did cover stretching of fabric, but did it in just an "introductory" manner, justifying why he cut patterns the way he did, and thereafter no discussion on actual stretching and limits of stretching.

The actual mathematical problem should not just deal with topological possibilities and the mathematics of quadric surfaces (made from magic unstretchable strings), but take into account the mechanical material properties that he vaguely touched on. Rayon vs Nylon. Linen vs Cotton. Spandex vs. Polyester. And that means discussing the difference between liner and exterior, and how they interact with one another.

The issue is not that you can't obtain a mathematical proof, but rather, you need a mathematical description, and it's usually a very complicated description, perhaps only expressible as an approximation or computer model as opposed to analytical mathematical equations.

https://en.wikipedia.org/wiki/Cloth_modelingPS. Right now I'm getting some self-education on the subject of corset/waist cincher physics with a dash of cloth economics. Lesson 1: creases bad. Lesson 2: you get what you pay for