Dell has announced that they're going to release a 4k monitor under $1000 in the beginning of 2014, and also has a 24" 4k monitor around $1300. The product page for the 24" one mentions:
Optimal resolution:
3840 x 21601 at 60 Hz (DP1.2*)
3840 x 21601 at 30 Hz HDMI
The superscript 1 displays this warning:
Important Details
In order to display the 3840 x 2160 native resolution, please ensure the graphic card and its drivers used on the PC/Laptop is capable of supporting resolutions up to 3840 x 2160 at 60Hz via DisplayPort connectivity.
So the question is: Can the video card and Thunderbolt ports on a 2013 Macbook Air 13" support resolutions up to 3840 x 2160 at 60Hz via DisplayPort connectivity?
The EveryMac page for this model says it may be able to drive two daisy-chained 2560×1600 Thunderbolt monitors, and this ars report claims that two TB monitors was possible on the 2012 models. So, I'm hopeful that the laptop should be able to drive that many pixels, but I'm not sure whether the Thunderbolt ports, in mini-DP mode, speak the DP1.2 standard necessary to drive this monitor at 60Hz.
Best Answer
No, it won't support it. The Thunderbolt 1 controller in the Air only supports DisplayPort 1.1 and you need DisplayPort 1.2 to get 4K support, as you mention in your question.
Check out http://www.anandtech.com/show/7049/intel-thunderbolt-2-everything-you-need-to-know and http://en.wikipedia.org/wiki/Thunderbolt_(interface)#Thunderbolt_2