The very interesting Work of Jeffrey Cook

[BEP]

Vector math and calculus won't answer how rotation of the magnet is achieved unless you blow out the generalities.

Notice how the spin axis of the magnets are not all perpendicular to the driving coil axis  

In order to 'pull' on one side of the magnet diameter more than the other side the proximity of the magnet diameter must be closer to the coil hollow core.

It doesn't really matter, does it? Hasn't it been proven that there is no fibroid like force connecting to something like an individual magnetic domain pole?

In accepted theories there is no way to rotate the magnet because the magnet's field is not anchored anywhere except the poles.

Now, if we stop thinking of possible interactions between A, H & B some useless baggage goes away. Think instead of Lorentz force on the electrons in the magnet and how torque could be applied to their trajectories just by them being in a time dependent magnetic field. I'm speaking of a single field that not only changes in density with each pulse but also changes between three angles.

As the pulse rises one half of the magnet N pole is repelled by the increasing coil field.
At the same time, the shorted gardener wire coil/core has an opposite magnetic field induced into it.
The other half of the magnet N pole diameter is attracted to the coil/core.

Doable?

[EMdevices]

WW,  the way this setup is analyzed is by integrating the forces generated on a sub volume dV of the magnet by the time varrying magnetic field at that location, and vector calculus is needed.  All analysis problems have some assumptions made so we need to be careful.  If the axis of rotation of the magnet wobbles, or theres nonlinear impact with the axle because its diameter is smaller, then the kinematic analysis gets even more comples, and this can explain the spin perhaps, but not in the assembled unit with pulleys, because its a weaker force.

I've conducted experiments and theoretical analysis similar to this setup, but with static fields shaped to produce a perpetual torque, and it did't work, but my conclusion was that time varying magnetic fields were needed.  I was hoping that the magnet in a divergent field would spin, if shaped appropriately, but realized the field also produces a force on each domain, not just a torque, as each magnetic domain tries to align to the external field, and these forces when integrated and pivoted about an axis perfectly counteracted the torque.  Of cours this is a simplistic way of thinking about it.  I hope im making sense.

EM

[BEP]

You make perfect sense and calculus is needed but there two points not working in your hypothesis.

1. There wouldn't be forces on individual domains. I'm not saying there could not be. I'm saying that the accepted thoughts are that these forces would only be applied to the magnetic domain group making up the entire ferromagnetism of the magnet, with the exception of the few domains already not in-line with the majority.  What I do think is that the magnet must be looked at as a saturated core. Unless the external magnetic field is in either repulsion or attraction it should have no uni-directional effect upon the magnet. Surely, if we could polarize a toroid shaped magnet so that all field lines were closed within and around the toroid, like a saturated toroid core, it would be useless as a magnet but no magnet would stick to it  
2. From your posts on this I still have the impression that you aren't considering the third magnetic field being created between the core(iron coil - induced field), the normally expected field from the coil (copper) bottom and top and the normally unexpected  polarity shift perpendicular to the copper coil field.

We know what happens between opposing fields(copper coil vs. the field induced in the iron wire core). In the area of opposition there is a radial magnetic field created. Since there is an existing radial field at right angles to the former, we have convergence of three radial fields all at right angles to one another. If all this is true, wouldn't we expect something unique?

Of course, none of the above would make sense unless you are convinced that a planar (and single layer) coil produces two magnetic fields opposing one another and on opposing sides of that layer (the same as a single layer solenoid coil does except the field is in the shape of a toroid and finally, a single field).
And, that there is no termination of a magnetic field line. Figurative or not, all magnetic field lines are closed loops with absolutely no termination point, unlike field lines of charge.

Sorry, that is a sticking point for me as I have never found a magnetic field simulator that will show the empirically proven dual radial fields of a simple planar coil. They all seem to show the field as a single compressed solenoid field. Stupid, in my opinion.

Edit>> In fact, there is no difference between a solenoid and planar coil magnetic field. The problem lies in the way the results are presented and generally understood. There isn't enough clarity. This leads folks to think that there is North at one end of the coil and South is at the other. It isn't that simple. At each end of a solenoid or planar coil there is a North & South. So, a planar coil (or the end surface of a Brook's type coil) there is a pole at the ID and the other pole is at the OD. The mirror opposite is at the other end of a Brook's type coil (or the other side of a planar coil)).

Magnetic field lines don't terminate anywhere and North/South is another construct only good for navigation.