I know a lot of really want a CFW for the PS4 but that’s not going to happen for a while as there’s a lot more to it than just having an exploit. There’s been a lot of progress going on when it comes to PS4 scene, as a lot of skilled full dev’s have been adding more tools and documentation all the time. Now the last piece of the puzzle has come together to run Linux on your PS4 with FW1.76.
https://twitter.com/psxdev/status/707736540131291136
https://twitter.com/psxdev/status/711700946292776960
https://twitter.com/zecoxao/status/707728349796368385
https://twitter.com/zecoxao/status/716040640753246211
Yesterday zecoxao pointed out a fully implemented PS4 dlclose exploit for FW 1.76 on git hub from kR105, “now you will need to add your own payload code to make it do anything useful“. 
“You will also need to compile it with CTurt’s PS4 SDK which you can get here”. https://github.com/CTurt/PS4-SDK.
Download: PS4 dlclose exploit
Download: PS4 Linux (needs to be compiled)
Download: A Compiled distro of Linux for the PS4
(Quote from wololo) Update: As pointed out by CTurt, you can simply download the compiled Linux files, put them on a FAT32 USB stick that you’ll connect to your 1.76 PS4, and test directly by going to the PS4 Playground live Demo here.