I am running Mavericks on a late 2012 Mini (2.3 GHz Intel Core i7, 16 GB RAM, Intel HD Graphics 4000 1024 MB), so I was not expecting the pixel clock patch to work. I booted from an external drive running Mountain Lion 10.8.5, applied the pixel clock patch, and connected to the Seiki via the Accell Mini DisplayPort to HDMI active adapter. I can confirm that 3840 x 2160 @ 30Hz comes up as the default resolution, without using SwitchResX. Everything looks fine, with the exception of the menubar which is far too small (all other elements of the GUI can be altered as far as size is concerned). To get around that problem, I enabled 1920 x 1080 HiDPI mode; "About This Mac" reports the VRAM allocation as 768 MB under Mountain Lion.
I also tried running Windows 7 via Boot Camp, and had no problems and didn't need the adapter...the connection was solid with no artifacts via just the HDMI connector. Perhaps the HDMI firmware for the Minis is set for v1.0? 4K capability has been standard since v1.3, so Mavericks should theoreticaly allow 3840 x 2160 @ 30Hz output via HDMI on the latest Mac Mini.