2K or 4K DCP? Only Chuck Norris knows

All the projection systems can upscale or downscale a DCP with a different resolution than the projector has. FLAT (or F)  stands for 1.85:1 aspect ratio and SCOPE (or S) stands for 2.39:1 aspect ratio.

If your film is 2K there is no reason for a 4K DCP delivery. For example, if a film is 2K FLAT with a bitrate of 250Mbits/s that would mean 4.694bits/pixel.
The DCP of the same film in 4K FLAT at the maximum allowed bitrate of 250Mbits/s would be 1.173bits/pixel. One could observe that each pixel of a 4K DCP has the ¼ of the data compared to the 2K version of the same film. The bitrate remains the same but the compression factor is 4 times bigger.  

As a result, screening the 4K version of this 2K film in 2K cinemas, would mean a 75% loss of the initial data information. 

We always recommend the closest resolution and aspect ratio for your film.​