My PS4 just hard shutdown while playing Anthem, then I saw this post. It then had issues restarting. It'd come on briefly then shutdown a couple times.
I was alone, in a dungeon in freeplay when the game froze then the PS4 shutdown. Before anyone says, this is not a heat problem (at least in my case). Shutdowns due to heat have their own specific error code.
Also, my PS4 is 'somewhat' modded for extra cooling. I've re-applied Thermal Paste to the APU. Applied Thermal Pads to the Memory Chips. Have a custom top shell for extra ventilation and a small fan blowing over the chip.
I got System Software Error CE-36329-3 when my PS4 finally turned back on. It did a System Storage check and then gave me an error code, then afterwards repaired my SSD because "it was unplugged improperly". I've never had this sort of issue in any game I've played, never had a game shutdown my PS4, never had a system software error, nothing like that.
Edit: Confirmed by myself, my brother and another person in the comments, this can also occur if you shutdown your Console while Anthem is still running. After doing so, sometimes when you try to turn your Console back on, it will not respond to 'controller-input' power on. Then when touching the power button, it will have the same power cycling issue and subsequent system check and error message.