"The PlayStation 4 reserves 3.5GB of GDDR5 its 8GB memory for the operating system, leaving 4.5GB of space for game code, according to current documentation PS4 shown to Digital Foundry by a well-placed source in the studio. However, other sources suggest that an additional 1GB of "flexible memory" can be claimed of booking OS, based on availability."
Better link above.
Article's also unbacked, using only one dated source (Shadow Fall presentation back when there's only 4GB of RAM).
Won't be saying anything unless better sources are put into the article.
I find it a little hard to beileve that the PS4's OS will be as bloated as the XB1's Win8-based OS, which will also use over 3GB of the XB1's 8GB RAM.
Even on the PS3 (where RAM is at a premium from the get-go), the OS (XMB) shuts down to free up space for games/apps when you start something up. I imagine the PS4's OS will, at the very least, go into a hibernation mode where critical system information is transferred to the HDD 'swap file' when a game/app is started.
Still, with the speed that GDDR5 RAM operates at and the multi-thread bus that the PS4 will utilize between CPU/GPU and RAM, it may not matter.