PERMANENT SOLUTION (stays after turning off PS4) - No
DOWNGRADE AVAILABLE - No
FULL CUSTOM FIRMWARE AVAILABLE - No
UPDATE: July 2017
There has been a chip manufactured called the MTX Key that allows you to share games that you have actually purchased on PSN over an unlimited amount of Playstation 4 consoles (you have to share your PSN password with the other consoles) This is normally limited by Sony to 2 consoles. We have no plans to stock this chip currently.
E3 Tech revealed a chip similar to the MTX key
PS4Kit revealed a chip similar to the MTX Key
UPDATE: August 2017
Sony release firmware 4.73. First This update currently blocks MTX Key, E3 Share and PS4Kit
UPDATE: October 2017
Details released for a Jailbreak for firmwares 4.05 and lower. No complete jailbreak has been released to the public at this stage but will be soon. PS4 Latest firmware at this point is 5.00
UPDATE: December 2017
A Jailbreak for firmware 4.05 has been released. It is currently still in the early stages but looks very promising. We will do some testing over the holiday period. If you are on firmware 4.05 or lower and want to jailbreak your console do not update. If you are already on a firmware higher than 4.05 you will have to wait and hope that either a downgrade comes out or another exploit is released.
In our testing we have found the Jailbreak is very stable. For the end user it is a little bit pointless at the moment as we wait for homebrew to be released i.e. emulators etc. We will keep this post updated.
UPDATE: February 2018
Details for a Jailbreak for firmware 4.06 and 4.07 have been released. In theory this jailbreak could be used on up to firmware 4.55 but would require more work as the entry point used in 4.06 nd 4.07 has been blocked.
None of these jailbreaks are yet permanent so need to be reapplied after every reboot. But the PS4 scene is finally moving forward so hopefully we see custom firmware at some point in the near future.
UPDATE: A jailbreak for 4.55 has been released so if you are on firmware 4.55 or lower you can now enjoy jailbreaking your PS4. As with all PS4 jailbeaks so far they are not permanent so as soon as the PS4 is power cycled (turned off and back on) the jailbreak needs to be reapplied.