I don't have any papers off the top of my head, but it's all about pressure. You know the saying "many hands make light work" ? This is what it's all about.
If one person can carry one heavy box, then a couple people can lift a litter to carry a person.
If you have an object that is ten times as heavy, you need ten times as many people to lift it. Many many people can lift a house and move it.
(video in
this link here)
If you'd like to find some reading, try searching for "pressure" and learn about force per area. You can also look for "spring constant" to learn about how far a spring will compress based on how much force is pressed against it (or in this case how far foam will compress based on how much weight is above it).
This falls under the physics branch of school, specifically the "mechanics" branch of physics which is usually the first class in the physics series. The other classes cover electricity, magnetism, light and optics, heat transfer, and so on. My favorite physics teacher is Walter Lewin. He is a treasure and has posted dozens of amazing lectures and smaller videos on his channel. The one blow is all about springs:
Here is another on simple harmonic oscillators which is the fundamental theory of the report I made in the first post above.
Finally, a practical experiment you can try that is really easy:
Take something squishy like a yoga mat (or a bed mattress) and stand on it with your feet. Notice how far your feet will sink into the material. Then place a piece of wood on top and stand on the piece of wood. Notice how far the wood sinks into the material.
Your feet will sink in much deeper than the wood. This is because the same amount of weight is being applied (you) however the weight is being spread out over a larger area when you use the piece of wood. If you were to get a couple friends to stand on a small piece of wood with you, then it would sink in deeper because you're increasing the pressure by adding more weight while keeping the surface area the same.
This is the same effect as growing or shrinking the size of the vinyl in my experiment because I would have to grow or shrink the size of the foam underneath it by the same amount. The added weight of the vinyl would be cancelled about by the added surface area of the additional foam and the performance of the system as a whole would be the same.