Is my brand new central air conditioner short cycling?

If you are at set point, it sounds like it's working correctly. Many of the newer high end thermostats have the ability to program maximum number of cycles per hour or minimum time between cycles, etc. varies by Tstat. You have to get into "installer setup" which requires the installer manual for directions and codes. But bear in mind, if you change some of those settings, you'll have wider temperature swings between cycles.

I'm not an expert in the calcs for HVAC, but your system might be a little over-sized. If it's oversized, it cools the space quickly, but doesn't have enough run time to dehumidify the space, leaving occupants with a cool, but clammy feeling.

I guess the most important question is: "Are you comfortable in the conditioned space?" If so, live and let live. For me personally, 68 would be way too cold, but that's just me.

Ed Beal may have other thoughts regarding the cycling rate and hope he'll chime in...I always learn something from him!

There could be any number of problems with your A/C unit. My recommendation is to have it serviced to make sure it is operating properly. Note, if the A/C does not cool to the setting of the thermostat then there is a problem that needs attention. Also, in a 2 story house the 2nd floor is usually warmer than the 1st floor since heat rises and cool air falls.