White paper disproving perpetual motion? Well science doesn't work like that way either. It's not up to me to disprove such a thing, it's up to you to prove it. Not being a smart ass, it's just that way.
That said, I will give a VERY quick answer assuming you probably skipped HS physics. There is no real "free energy", so from a start, energy comes from somewhere. Charged capacitor is a good example. So charge from home AC, fine. Set bike in motion, with your scenario - let me ask you - have you spun an alternator under load? Takes a decent amount of energy, plus getting you going and keeping you in motion on the bike. The power from an alternator to the motor via a controller is not lossless.
Answer: Friction and other (electrical) losses - ie the first and/or second law of thermodynamics. We have yet to find a lossless system.
https://en.wikipedia.org/wiki/Perpetual_motion
