Following their work-in-progress, PlayStation 4 developer zecoxao with help from droogie1xp, psxdev, VVildCard777, fx0code, CTurt for the exploit and kr105 for the payload have achieved kernel and code execution despite the Grey Screen of Death (GSoD) and fully implemented the Dlclose Exploit for PS4 Firmware 1.01 now! 
Download: PS4-dlclose-master.zip / GIT / PS4 Playground 1.01 Demo
From the README.md file, to quote: PS4-dlclose 1.01 Version
Fully implemented dlclose exploit for PS4 fw 1.01. Compile it with CTurt's.
This is the bare working exploit, you must add your own payload code to make it do anything useful. Enjoy!
Here's to hoping this PlayStation 4 kernel exploit port leads PS4 homebrew developers to uncovering more vulnerabilities and even some unknown goodies perhaps!
Patches for decrypt_pup_header (1.76):
Cheers to @CTurt, @kr105, @oneman123, @zecoxao and everyone idling in the PSXHAX Shoutbox this weekend! 
Download: PS4-dlclose-master.zip / GIT / PS4 Playground 1.01 Demo
From the README.md file, to quote: PS4-dlclose 1.01 Version
Fully implemented dlclose exploit for PS4 fw 1.01. Compile it with CTurt's.
This is the bare working exploit, you must add your own payload code to make it do anything useful. Enjoy!
Here's to hoping this PlayStation 4 kernel exploit port leads PS4 homebrew developers to uncovering more vulnerabilities and even some unknown goodies perhaps!
Code:
*(uint16_t *)0xFFFFFFFF827E31EE = 0x9090;
*(uint16_t *)0xFFFFFFFF827E31FD = 0x9090;
*(uint16_t *)0xFFFFFFFF827E3202 = 0x9090;
Code:
*(uint16_t *) 0xFFFFFFFF827C445C = 0x9090;
*(uint16_t *) 0xFFFFFFFF827C446B = 0x9090;
*(uint16_t *) 0xFFFFFFFF827C4470 = 0x9090;