Continuing the discussion from Oberth cylinders ("oneills") for Imperial capitals:
The fundamental bedrock of the Treaty of Luna is that each colony is sovereign and has jurisdiction inside the Kármán line around its planet, i.e. where aerodynamic flight is possible (or tunnelling, shipping, etc.), and the Empire is sovereign and has jurisdiction in places that are outside the Kármán line of all inhabited planets. Like many fundamental bedrocks, that is impractical in some situations and requires exceptions, the exceptions being the causes of continual difficulties and complications. The major categories of exceptions are as follows:
The Empire has prerogative jurisdiction concerning Eichberger drives, CT weapons (same thing), interstellar travel, weapons of mass destruction, and mass destruction. They are fanatics about it. This jurisdiction just couldn’t be taken away from them.
The Independent Commission for Justice
The Independent Commission for Justice has statutory jurisdiction to enforce the Imperial Crimes Act everywhere. The includes within colonial sovereign jurisdiction and within Imperial sovereign jurisdiction on the same terms. The Commission for Justice was established by an act of the Imperial Senate, and it is not under the authority of the Imperial Council. It is however funded by the Eichberger Foundation…. Whether this counts as Imperial jurisdiction or not depends on the rhetorical and political purposes of the speaker.
Imperial residence enclaves
Each colony grants the Empire an extraterritorial enclave in which to construct an Imperial Residence, which acts as a base for its quasi-diplomatic representative (the Resident Commissioner a.k.a. Imperial Resident), headquarters for its operations in the colony, etc… These Imperial enclaves are limited by the Treaty of Luna to 256 square kilometres, no more, and are sometimes smaller.
If no other provisions were made, then as soon as the first settler arrived on a new world, not an employee of the Empire and intending permanent residence, that would would become a sovereign colony, abolishing ability of the Empire to continue terraformation and settlement, with the right to appoint a senator and make laws e.g. expropriating land. To allow settlement to proceed, the Senate passes an ad hoc intervention act specifying a provisional government for fifty years and the staged handover of government functions in that time. Until the Establishment Crisis of 580–584 establishment acts specified the Empire as interim government handing over to a liberal representative democracy; since the Compromise of '84 intervention acts have chartered independent provisional governments with statutory obligations to the Eichberger Realty Company. But the colonies with the old arrangement have not become independent yet (it starts happening on 1 January 607 ADT), so there is a collection of planets in which the Empire rules the hinterlands under the authority of old establishment acts.
Orbital operations for peaceful purposes
Colonies with unified space traffic control (single-government planets and Tau Ceti) are entitled by the Treaty of Luna to conduct “orbital operations for peaceful purposes” even though their orbital space between the Kármán line and the Hill sphere radius are by treaty Imperial sovereign territory. This allows them to build orbital habitats to conduct their own space industries so long as those are in orbit around their planets. (They could build purely residential habitats under this rubric, but there is limited enthusiasm because of the memory of hte Formation Wars.) The Imperial Navy gets to inspect the facilities to make sure that they pursue no non-peaceful purposes; some have an Imperial inspector in permanent residence. But the governments of the colonies get to apply their own laws etc.
Note that the right of the colonies to build facilities and conduct operations in orbit between the Kármán line and the Hill sphere radius does not exclude the Empire from doing the same alongside them. The orbital component of a type O spaceport, or a type T spaceport, can be either a colonial or an Imperial structure.
Licensed operations in deep space
Once you get outside the Hill sphere of an inhabited planet the Empire’s sovereignty is legally unqualified. However, it does not have sufficient staff to exploit all the resources there, nor even to provide government services to all the people employed in exploiting them. And for that matter a lot of colonial workers would balk at having their children raised in Imperial schools, for instance. The Empire doesn’t want to give rough characters free access to its peaceful and orderly residential habitats where they might disturb its servants; they don’t want to live under its company-town/garrison-state regime. So what the Empire does is to charter free habitats with the right to live under the laws of the nearby colony and to govern themselves, terms specified in the charter after negotiation.
Such habitats of course include some population that is not directly engaged in space industries, including in some cases people who are effectively exiles or refugees living in their own culture and under their own laws but with the rigours of their native government tempered by the charter and self-government arrangements.
Some colonies have treaties with the Empire that guarantee them the right to licenses on specified terms, which were negotiated as supplements to the Treaty of Luna as additional inducements to get them to sign,
Imperial Direct Jurisdiction
The Empire builds habitats in space: administrative centres such as the Capitol and its sector HQs, space dockyards and naval bases, orbital manufacturing facilities, asteroid mines and refineries, bases on uninhabitable planets and moons, residential habitats for its employees and their families. In such habitats the Empire provides the structure, the utilities including energy, communications, water, and air, it provides the education system, the health care system, and all the primary employment. In those habitats the peace is kept and the laws are enforced by Home Office police, disputes are settled and accusations tried by Home Office courts.
The Empire builds residences in its enclaves on inhabited planets and moons, quasi-embassies for its resident commissioners and their staffs, HQs for its operations in colonies, type G spaceports and the ground component of type O or T spaceports, residential buildings for its employees and their families, with supporting infrastructure such as schools. It supplies the structure, communications, power, water, etc. in those places too, and because of its extraterritorial jurisdiction there H.O. police and courts have jurisdiction, Imperial civil and criminal laws apply, not colonial laws.
The ordinary civil and criminal laws of the Empire also apply in interstellar spacecraft, even if they are docked to colonial orbital ports.
Warships of the Imperial Navy (including Imperial marines’ troop ships) are not throng with Home Office police. The Home Office doesn’t supply the structure, energy, air, or water in them. Little occurs that requires civil law, and matters of a criminal nature are generally dealt with by military provosts, JAG officers, and the chain of command enforcing the Imperial Code of Military Justice through courts martial.
These are the places where the Empire exerts ordinary jurisdiction directly itself. If you get to grow up here, it is overwhelmingly likely because at least one of your parents is an Imperial servant; you go to an Imperial school. If you are resident here and did not grow up here, it is because you are an Imperial servant or retired Imperial servant. If you get sick or injured you will be treated at an Imperial hospital. You walk on an Imperial deck, breathe Imperial air, drink Imperial water, take your entertainment through the Imperial infonet, and participate in the culture and social life of off-duty Imperial servants. If you get in trouble and you don’t know what to do the Home Office will be along directly to sort things out for you. You are an Imperial.
Note By act of the Senate, no colony may end the citizenship nor abridge the citizen rights of any person on account of their serving the Empire or going and residing where service to the Empire takes them. Recruits to the Imperial Service from the colonies have domicile in their home colonies and only temporary residency in IDJ. This includes preserving the jus sanguinis rights of the children of Imperial servants. So a lot of Imperials have citizenship of the colony of their birth, or of the colony or colonies of a parent’s or their parents’ birth. Whereas on the other hand there is no citizenship of the Empire or of IDJ*, the legal status of Imperials is temporary or permanent residency.
Imperial Indirect Jurisdiction
The Empire is sovereign on new worlds that have not yet signed the Treaty of Luna, in all spaceships travelling at above escape velocity of their planet, and in space habitats that are not in orbit around an inhabited planet or moon. But it doesn’t supply structure, energy, comms, air, water, sewerage, drainage, police, or courts there, nor hospitals, schools, courts, nor police, and it doesn’t enforce its own civil and criminal laws. The legal technicality is that the Empire has delegated its jurisdiction over those place to some other authority, and that the laws of the relevant colony apply on the authority of Imperial sovereignty, as set out in an Imperial charter. This is a case of delegated authorities exercising Imperial jurisdiction to enforce colonial laws and definitely not™ a precedent for a colony exercising its own jurisdiction in deep space.
On an inhabited planet or moon, inside its Kármán line (except in an enclave where extraterritoriality provisions apply, and except in the case of a new world under Imperial administration under the provisions of a pre-580 Establishment Act), and in an orbital habitat or licensed non-interstellar spaceship that is orbiting an inhabited planet, that is colonial jurisdiction. The fact that the ICfJ can investigate and prosecute breaches of the Imperial Crimes Act and the face that Imperial Marines will drop from orbit and wreck your day if you build an Eichberger device does not make it Imperial jurisdiction. If you are an Imperial servant here you must obey the local law and pay the penalties if you breach it.
* There are some Imperials who if pushed on the subject of their lack of citizenship will rather icily tell you that they are citizens of Mayflower by jus sanguinis. This is tantamount to saying that your grandpappy murdered their grandpappy and that you had better watch your mouth.