Fix it tickets are no problem. They are expunged when you get them fixed. In California the law says:

21201. (a) No person shall operate a bicycle on a roadway unless it is equipped with a brake which will enable the operator to make one braked wheel skid on dry, level, clean pavement.

Don't bother trying to argue that your legs can lock up the rear wheel on a fixed gear, it won't work. Just install some brakes, go to the police station with the bike and the ticket, get an officer to sign it and mail that to the courts.