The amount of detail on that site is breathtaking. Beautifully done, really.

However, on the question at hand, it mostly says:

>Bicycle stability can’t be explained using just one or two mechanisms. It’s a combination of many different intertwined factors, like the mass distribution of individual components, size of the tires, geometry of the frame, and others. [...] What keeps bicycles balanced with or without a rider is still an active area of research, and even the seemingly basic idea that, for a bicycle to be self-stable, it needs to turn the handlebars into the fall, has not yet been proven.