Intel HD4000 with 4k HDMI output on Linux
Solution 1:
4K output with Intel HD 4000 graphics via HDMI 1.4 works for me. Both under Win10, as well as Ubuntu 15.
In Win 10 you have to force the graphics to use the stock Microsoft driver (graphic card settings - update driver - choose from disk - Microsoft) NOT the Intel driver which gets enabled by default. Intel Corp. is capping the max resolution, forcing you to buy new hardware. That is unnecessary for the usual web browsing / text / pic editing jobs. The stock MS driver has poor performance though, be warned.
In Ubuntu 15 the 4k output via HDMI works beautifully, both with the stock driver and the proprietary Intel driver. I strongly recommend installing Ubuntu system to use Intel HD graphics and UHD / 4K monitor.
Solution 2:
The HDMI 1.4 standards supports pixel clocks up to 340 MHz, and this is what allows it to display resolutions like 2560x1600@60Hz (268 MHz pixel clock) or 3840×2160@30Hz (297 MHz pixel clock). For 4k@60Hz, HDMI 2.0 and a 600 MHz clock is required.
The ThinkPad Edge 300's HDMI port, however seems to be limited to a 165 MHz (HDMI 1.0-1.1) pixel clock, while still offering the other HDMI 1.4 features according to Lenovo. This limits it to 1920x1200@60Hz.
Since HD4000 supports full HDMI 1.4 pixel clocks, the limit is typically caused by the TMDS bus driver chip used by the notebook or board manufacturer for the HDMI port. This information is then stored in the BIOS and used by the graphics driver to limit the resolutions available. In some cases, however, the BIOS limit is arbitrarily set to a low safe speed to avoid trouble with badly wired projectors in conference rooms and similar. People have some luck overriding the limit by using custom videomodes. YMMV.
Solution 3:
I also have intel HD4000, and I am running 3840x2160 at 24p Hz on windows, not sure about 30p Hz.
The tv I'm using as a monitor supports 4k@60hz, but I haven't been able to achieve that with this display card, I'm not sure if it is possible, and according to this guide (search for 2160), if it is possible looks like it might have to be done somehow through display port and not hdmi.
For windows users: user283110 said you need to force the graphics to use the Microsoft driver because you cant use the Intel driver. But you can actually use the intel driver by setting a custom resolution, click on your "search windows" and type: "CustomModeApp". Here are the full instructions