Your class 3 definition is inaccurate. Class 3 is limited to 28mph and cannot have a throttle, only pedal assist.

Anything that doesn't fall in one of those classes is a motorcycle that is not street legal and can only be rudden of private property (unless you can convince your DMV to give you registration as a motor vehicle.)

This can vary somewhat from state to state, but most states have adopted or are moving to adopt these classes.