Ah! Thank you for the correction. Much appreciated!

Although the magnetic interaction, i.e. the normal load between the two layers monotonically decreases with increasing h, 〈Fₓ〉exhibits a clear peak around h₀ = 9 mm. This is in strong contradiction with Amonton's empirical first law, which claims that sliding friction is proportional to the load ^33^.

Given that they use an array of magnets that can rotate freely, it's not "breaking" the law. At a distance the magnets are random and exert a force to lateral movement. Move the magnet array closer and the magnets align to the magnet below and the force changes.

It's like saying a ball on a hill violates Amonton's law. At the top of the hill you can push it easily. Push a little more such that it rolls down the hill and now in the valley of the hill you need more force to move it because pushing sideways means you are trying also push it uphill.

The magnets once flipped do not unflip when pulled back from the magnetic surface.

Given they are using an array of freely floating magnets it doesn't seem like a big "breaking". It's possible to create normal mechanical systems that also "breaks" Amontons' first law. For example, imagine a surface with an array of spring loaded pegs poking out of holes on a teflon surface. At light loads the object will have to slide against the pegs. But push a little harder and the pegs will push down into the holes of the surface and the object is now sliding on teflon.