The Prosperan Republic encompasses all worlds colonized and terraformed by humanity. As Prospectors claim there is no other intelligent life in the universe, Prospera claims essentially everything in the universe, up to and including other dimensions and theoretical existences.
The capital of the Republic is Prospera, and more specifically the capital of that world, Prospita. The government sits in this city, which includes The Council and The Senate, the upper and lower houses of government of Prospera.
The flag of the Republic is a simple bicolor with blue on the lower half and white on the upper half.
The Republic is organized in terms of 'Phases', and 'Sectors' within those. Each Phase denotes an era of colonization and distance from Prospera. Each phase could be defined as a sphere, and each phase outwards is a larger sphere around the smaller ones, centralized on Prospera. Societies in outer phase worlds begin as the same as the origin of the colony ships, but eventually begin to develop their own local culture. As communication technology gets more advanced and ships get faster, colonies closer to Prospera begin to be integrated and grow more and more like the homeworld.
Within each phase are four distinct sectors. Each sector is about 10x10 parsecs in size. However, most of that space is empty, and on average a sector contains 20-30 worlds. One world is always designated as a sector capital, and it is mandated that a Prospector sit in that world as a regional governor to manage the rest of the sector from a closer location. This Prospector has many duties, including the development of lagging colonies and peacekeeping duties. However, Prospectors often neglect or ignore their duties, and there is very little accountability from The Council.
All humans are automatically citizens of Prospera. Prospectors maintain a healthy respectable distance between themselves and the overall government at all times, preferring to avoid bureaucracy and policy. While they can do whatever they want, most Prospectors stay out and do only research and development, though there are exceptions. For example, certain theocracies, and The Council.