It seems a lot of folk are confused about what the HDMI output of the D4 (and D800) is. The manuals aren't any help. The answer is a bit convoluted: it depends. If you take the cards out of the camera and use LiveView, you'll get uncompressed HDMI output (with audio) that matches the Movie Settings. No wrappers, no interpolation, but straight video matching what you selected. I hope you have a big storage device attached if you try that, as that's one heck of a lot of data coming down the pipe. Indeed, I'm not sure how I'd record that short of bringing a small and very fast RAID farm with me on location. Even just testing this in my office I chewed through a lot of drive space.
The better choice is to use an Aja Ki Pro Mini or an Atomos Ninja and record the HDMI uncompressed output directly into 4:2:2 ProRes (Apple's native compression for Final Cut Pro X, and a very high quality compressor). But you'll have to press a lot of buttons and jump through a lot of procedural hoops to do that (which is what books like mine are for ;~), plus you'll have an HDMI cable between the camera and the recorder. Who's going to do that? Dedicated high end videographers who post grade their footage. If you're never going to go beyond Blu-Ray quality and don't do a lot of post grading, then just record to the cards and use the built in AVC compression.