Actually, In the Official Code of Georgia, there is a written grace:
Title 40 Chapter 14 Article 2 Section 8 subsection (a)
40-14-8 - When case may be made and conviction had
(a) No county, city, or campus officer shall be allowed to make a case based on the use of any speed detection device, unless the speed of the vehicle exceeds the posted speed limit by more than ten miles per hour and no conviction shall be had thereon unless such speed is more than ten miles per hour above the posted speed limit.
Note that it does not specify the same restriction for Georgia State Patrol / Department of Public Safety. They're the only ones who can make a case for 1 MPH above the limit (but will usually not enforce and only provide warnings until 5+ mph due to possible speedometer calibration miss adjustments...or they're just having a bad day). The only noted exception to this limit on county, city, and campus officers is in marked historic districts, marked residential zones, or inside designated school zones during the time period of one hour before and one hour after the times that school is in normal operation (zone active times are normally posted or the reduced speed limit signs are equipped with flashing amber lights. In this case, speed limits are automatically reduced up to 20 mph lower than standard posted limits [65+ mph areas will have school zone limits no lower than 45 mph; 55 mph areas will have school zone limits no lower than 35 mph; 45 mph areas and lower will have school zone limits no lower than 25 mph]). Definitions of marked historical districts and marked residential zones are noted in other parts of the O.C.G.A.