Well, I agree that the geometry is more important in general to stability, because of the self stabilizing nature of a wheel with front trail, where it's lowest center of gravity is found at the straight fork position. It is indeed a myth that gyroscopes stabilize bikes (gyroscopes don't stabilize Segway's, either, at least not directly). However, the current discussion is in relation to countersteer, which does have a tie to precession, even on a bicycle.

The two models for countersteering (not general stability) are outtracking, which suggests that as you press the left-hand bar, the contact patch moves to the left, which now places your CG to the right of the contract line, hence, you begin to fall to the right, initiating a lean. But as that happens, traditional stability geometry kicks in, the wheel attempts to return to its position under the CG, and you turn right. Centripetal forces keep you generally upright during this whole procedure.

The other model is the precession model, which suggests that as you press on the left-hand bar, gyroscopic precession changes the direction of the force, IE, it translates a horizontal rotation into a tilt, which inititates a lean. As the wheel attempts to move back under the CG, the entire machine turns to the right.

Both explanations rely heavily on the geometry of the bicycle, which is very important. I believe that, having ridden bicycles and motorcycles of all sizes and shapes, that it is really the harmonious interaction of both outtracking and precession that result in countersteer. If you get a wheel spinning in your hand and countersteer with it, you really must fight the thing, precession is very efficient way of translating the direction of force, and countersteering a quickly moving vehicle requires a fair quantity of force, more than enough to 'push' the bike into a lean. Imagine someone in a car moving alongside you, and pushing your top tube to the right, this would initiate a turn. The amount of force they'd have to exert on your top tube would be very similar to the amount of force you'd need to exert on your handle bar to inititate a lean through precession.

Interestingly, in the paper you cite, the concept of the chopper is not well discussed. I've seen choppers with many many feet of trail, that remain rideable, though their handling is indeed quite questionable. He accidentally creates a chopper on his own, though he clearly didn't get the cultural implications.

As an experiment, I'd like to build a bike with no trail, and play around with countersteer. I've ridden a few tall bikes with incredibly little trail, and they do indeed handle in a very squirrely manner, but it is still possible to countersteer them. Maybe that should be one of my next mutants... The quest for the unridable bike often creates some of the most amazing mutant bikes, like Chunk 666's springy bike, which is a bike completely cut in two at the top tube and down tube, and reattached with about 6 inches of heavy steel spring, so they are only loosely coupled to each other. Apparently it is ridable, just incredibly difficult. I'm amazed at what the human body can convince to stay stable.

peace,
sam