Eleisya, the megastructure that took generations in the making, is a world-ship which functions as the apparatus of government across the Hegemony. This immense space-habitat features a model city, a space-borne environmental habitat, and of course the Capitol of the Hegemony, featuring the Mandate's Capital Complex and the Grand Master's Estates.
The important feature of Eleisya is that it is always moving. Gathering resources as it moves through systems to help ensure its self-sustainability as it continues to tour around the Hegemony. Making the central apparatus of Government a difficult target to find and catch for any that wish to. Allegedly also during times of crisis, the world-ship will hide itself in hidden systems within nebulae or in empty space.
It is worth noting that the world-ship does still maintain an impressive shipyard and military bastion to ensure it's safety if it is ever caught up to.