Awesome to see the PS4 scene progressing well, heres the latest news:

Developer Wildcard has updated his kernel dumper for the PS4. The tool supports firmware 4.05, 4.55, and 5.05.
For those of you interested in digging into the PS4 Firmware, youíll want to have a look into this tool which lets you dump the PS4 kernel for further analysis. This includes, but is not restricted to, looking for vulnerabilities in the firmware. (And if thatís your thing, youíll probably want to have a look at Belf, the recently released ida pro loader for PS4 Elfs)
Since some people were apparently having issues dumping the kernel through the original technique of a network socket, Wildcard has added direct support for dumping on the usb drive.
Thereís no compiled payload release though, so youíll have to build the payload yourself from source.