Traffic cops lie, and the Judges are there for screw kids like you that go to court without a Lawyer.
The system thrives on people that "Just Pay the ticket". The whole system revolves around revenue, not safety.
Get a lawyer. I know in most of the South, they do this stuff where you can get probation for a year. If you do not get another ticket, the original ticket is dropped.
Keeping the points off of your liscence will save you big on Insurance down the road.
For example, in NJ, the simple $100 ticket can cost you $300 a year for three years in insurance surcharges.
Hey BMWlawman - If you caught another officer doing this, would you ticket them