Hysteresis model

Ok, check this out. If T = -T so the "-" vanishes, when you "rewrite" -T as T and the arrow changes direction this is equivalent to connecting the sides of a rectangle, first swapping left for right, i.e. a Moebius strip (just, you know, imagine that T is as long as you need it to be).

Transform T and voila, you are in Moebius land, going around a loop forever. If you travel along the median of the strip you can see a rectangle, with edges to your left and right, except the front and back look a bit curved...

With the T in hysteresis it's usually heat or electromagnetic energy, so abstracting this means going all the way to computational space and storage of charge or magnetic energy. Now we also have a combination optical/magnetic read and write device.

Any ways, the T and its inverse -T aren't hard to spot in a Rubik's computational model. Since in a single 4-cycle (i.e. only a single face, up to 4 permutations) there are 2xpairs of opposite edges, say, if you conventionally assign "1" to a restored cube, then -T has to be either the left-hand or right-hand motion in moving a _face group_ of elements. So then T[sup]2[/sup] = (-T)[sup]2[/sup].

So a 4-cycle in 1 letter is a form of reading and writing, then erasing again. You get to stay in one of 3 spaces, or "reset" the space - the branching factor is 3, with one letter algebras, which I will call "singular" 1-forms.