It hasn't been smooth sailing for the stock Android device. The update to Android 4.1 was not exactly a timely one which didn't make sense since the phone does not have the TouchWiz UI running on top of Android. The software version is GJ04 and will be sent out randomly via an OTA update to Samsung GALAXY Nexus handsets within the next 10 to 21 days.
Just yesterday, another Samsung device, the Samsung Galaxy S4, started to receive Android 4.3 along with the Premium Suite update that allows the phone to be compatible with the Galaxy Gear smartwatch.
source: Sprint via AndroidAuthority