The Gryphus Tech Corporation is present in many universes each with variations of the main characters. The core elements are usually present: the name, leader (they are all the same even if their names vary) and political system (one absolute leader).
The Gryphus Tech Corporation present in the Warframe Universe is depicted as a orokin monopoly. The core members of that monopoly were frozen after a certain incident and lost their memories due to prolonged stasis but due to the nature of their cryopods, they still have memories concerning the Gryphus Tech Corporation.
Using those memories, they rebuild the once prosper organization. The leader's (referred to as the Warlord) name is Gryphticon.
The Gryphus Tech Corporation in this universe is depicted as a military organization independant from the government that took control of the democratic Aurion Empire and turned it into a militaristic
society using the power of the VCore (Viridite Core) technology embedded inside each Auraframe.
The empire resulting from that coup d'etat advanced technology at a unprecedented speed which in turn allowed it to observe and control everything hapenning in the universe and literally predict the future. The advancement of technology at a high speed is in part caused by discovery of time rewind technology which allowed scientists to send technology to the past which would then am
eliorate current technologies.
Their current ennemies are the "Light", beings with technology comparable to that of the empire who reigned on the Universe long before Aurion . Both Aurion and the Light are now engaged in a endless war destroying worlds, creating cataclysm in planets light years away from the battle and anhilihating galaxies. Civilizations knowing about the war refer to it as "The War of the Gods" due to the nature of that war which was fought everywhere in the universe.