Earlier quoted context omitted.
Maybe a real secure kernel, such as SeL4 or LynxOS.
The tipoff that it's not L4 is that it's a desktop OS that runs applications.
Sirrix TrustedDesktop on Turaya:
https://www.sirrix.com/content/pages/trusteddesktop_en.htm
Turaya's architecture:
http://www.perseus-os.org/content/pages/Overview.htm
FOSS alternative that they already use to develop itself: