No-Fork project, bicycle geometry hacked

what kind of "proof" are you looking for?

The kind that you've provided over your last few replies, thank you; however, you are doing yourself no favours with this kind of phrasing...

I can also see why it turns your otherwise comprehensible world upside down...

...because that is the language of snake-oil and perpetual-motion-machine salesmen the world over. From the bulk of the thread, it's really not been clear what you've been claiming. At some points it seemed like you were saying that you'd worked out how to run a canted wheel such that it produced no camber thrust, which is obviously not true. What is clear from your more recent posts is that what you've done is some calculations as to how to counteract it with a contrary steering force. On that topic, this is not clear to me:

Camber of wheel exerts a force on the wheel in the direction of the camber. Think of a circling coin. The camber force is directed to the center of the circle.
This camber force exerts on the trail. So if I have my wheel leaning to the left, the camberforce is directed to the left. But, the force is exterted on the trail! making the bike steer to the right. (this is counter intuitive)

The wheel is canted to the (rider's) left, this exerts a force to the left on the fork-ends, which are in front of the steerer-axis, so how does that produce a turning force to the right? The answer to this isn't really relevant to the explanation, since I (think I) understand that what you're doing is moving the contact patch out of the plane of the frame (in whichever direction is necessary) to counteract the camber force. This was not at all clear, since I thought you were working within the constraint that the contact patch had to stay in the plane of the frame.

In general it seems to be a really inelegant design solution to introduce a lateral force (camber force from the wheel canting) that you then have to counteract, when the lateral force could simply be omitted in the first place (by having the wheel in the plane of the frame). Having to balance the two opposing forces perfectly in order to produce a truly neutral bike just seems like a lash-up. More importantly I don't think you can prove that you have perfectly achieved it because riders are so good at subconsciously compensating for lateral forces. We do it all the time with less-than-perfectly true or badly seated wheels, asymmetric loads, road camber etc. I did it for 3 years without it feeling strange enough for me to do anything about, even though I could see that my front wheel was out of whack. As @mdcc_tester said, it's really a question of whether you can do it well enough for riders not to notice, not whether it will ever be perfect. On a normal (forked) bike any lateral force is wrong; on a no-fork bike it could just be due to poor resolution of two intentionally generated forces.

The requirement for precisely matching the opposing forces also raises further questions:

Your comment suggests that setting up needs to be done fairly precisely with regard to canting vs. offset. If you change tyre size, the wheel radius will change, which will change the offset, so the canting will then presumably need to be changed if you want to precisely match the opposing forces.

Camber force is also affected by loads of things including load and tyre pressure, so if these change the camber force will change. Will the counteracting force change in proportion for the handling to remain truly neutral, rather than just good enough?