(Update: After considering the comments that came to this post, and “having a Better Idea,” the culture described in this post will no longer be used under this name; see the replacement post. This post remains for historical interest, but is no longer accurate.)
The New Roman Empire is a political entity in the Shine Cycle. Its name is something of a misnomer, since it’s not really either Roman or an empire, but the name stuck.
Sometime in the 1600s or so, several groups of English Puritans (and, to a lesser extent, other Dissenters) stumbled through a portal and found themselves in a whole new world—on a planet far above the world with which the Shine Cycle is mostly concerned. For some reason, when they came to the realization that they were no longer on Earth, they named the planet New Rome. (Or perhaps the crew of the first spacecraft to visit the planet named it that.)
New Rome is both agriculturally fertile and (in places) very rich in minerals, so their population grew to every corner of the whole planet. And between the “Puritan work ethic,” a strong interest in science among some segments of the population, and the somewhat reduced gravity of the planet, they were making their first essays into space travel in only a few centuries.
The solar system in which New Rome circles has a couple of other habitable (if not quite as hospitable) planets (including moons of its gas giants), so once space travel was reasonably safe enterprising individuals and families set out to colonize those as well.
Eventually, with some scientific breakthroughs that (in the projection of our world’s future history that I’m using for the Shine Cycle) we won’t discover for more than four more centuries, they explored nearby star systems and sent colonists there too.
Politically, the “New Roman Empire” is in fact a commonwealth, not an empire at all. Each of the worlds has its own government, mostly very similar to that of the Plymouth Colony or Calvin’s Geneva, but some drawing greatest inspiration from the Roman Republic. When they encountered—or were encountered by—inhabitants of the flat world far below (from the Shine and Wild Empire, probably) or of worlds around other stars in its sky, a conclave of the governments’ leaders was established to determine such things as foreign policy and common defense—by consensus when possible.
As you might expect from such a loose commonwealth, each world has its own emphases for trade. New Rome exports food, but is also the technological and political leader, for example. There is a vibrant trade between them, and with their closest neighbors. When the spider-ship network reaches them, it enables them to develop ties with much more distant partners.
Because the “foreign policy” of the commonwealth is primarily determined by consensus, there is a strong tilt toward political and military isolation: not getting involved in conflicts unless the New Roman worlds (or their most immediate neighbors and closest trading partners) are attacked. But when war becomes necessary, each world has a large, well-equipped, and very well-trained militia, merchant marine, and planetary- and system-defense corps that make having a sizable standing military unnecessary.