qwertyoruiopz made available a JailbreakMe PS4 4.0x Webkit exploit for OFW 3.55 through 4.07, and over this weekend he received an invite from the Rebug Team while sharing progress updates leading to confirmation of a 0day 4.50 kernel exploit obtaining R/W (Read / Write) access!
His latest JailbreakMe PS4 4.0x (Mirror via @X41) update states the exploit supports all non-4.50 Firmware, but specifically targets 4.06 currently due to ROP gadgets being hardcoded.
To recap, those on PS4 1.76 Firmware were able to make use of the Kernel Exploit Source Code that progressed to a PS4 BadIRET PoC finally leading to the 1.76 PS4 Dlclose Exploit.
For those on PS4 Firmware 4.07 or below you can use the JailbreakMe PS4 4.0x Exploit to gain userland access, and users on System Software 4.50 can rest assured a 0day 4.50 kernel exploit also exists although there is no user-level entry point for 4.50 OFW reported publicly as of yet.
Also keep in mind PlayStation 4 scene developers may decide to hold off disclosing the 0day PS4 4.50 kernel exploit much like the PS4 Pro 0day Exploit that was confirmed by Mathieulh until Sony patches it, so for the moment as usual the safest bet may be holding off making any System Software updates.
Finally keep an eye on the PS4 Dev Working Exploits page for an updated listing of PlayStation 4 WebKit / Userland and Kernel Exploits.
Thanks to @DoxyMarket, @hyndrid, @joona70, @mcmrc1, @Plankton, @sealab, @vettegast, @X41 and @xxmcvapourxx for the tips in the PSXHAX Shoutbox!