Yesterday we saw disclosure of a 4.05 PS4 Kexec, and combined with a Userland Exploit like JailbreakMe PS4 4.0x WebKit RCE the PlayStation 4 scene is eagerly awaiting a public PlayStation 4 Jailbreak for Firmware 4.05 to surface. :D
In the meantime, since Porting JailBreakMe and Breaking Down...