The famous Hacking Group „fail0verflow“ has ported the Linux Kernel to make it compatible for the PS4. Their Fork is in progress and it is based on the Kernel Source of Software-Developer Linus Torvalds.
If you want to run a Final Version on your Console, you need a PS4 with Firmware 1.76 and WebKit Exploitation to entry the System. Also you will need more Exploits on your Console.