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Rogue Rings
"overland distances of about a hundred AU."

What a peculiar phrase to realize you have just typed.
I can totally see this endeavor as counting with the involvement of Binah (MPA's SI:6 archai) with the (maybe not really) hidden motivation of serving as a possible backup for the MPA (and other sephirotics) intended to survive until it arrives at another galaxy/deep time. Maybe it was not em who started the project, but in face of the very fresh danger that the Oracle Machines posed, e could conceivably provide some level of support.
If you wanted to up the surface area, couldn't you just crinkle and wrinkle a smaller ring until it had similar overland distances?

To a certain extent...
That brings up a whole different aspect of this.  

The Rogue Ring is essentially an evolution of a (reasonably) well-understood ISO type that becomes possible if we abandon the idea of needing to be near a star.  

But the hoopworld is nowhere near being the only type of ISO that could evolve into something conceptually different if we don't have a central star.  

For example, what's the 'Rogue ISO' equivalent of a Dyson Swarm?

You could have a 'Rogue Swarm' like a Dyson swarm, that orbits a common center of gravity, with no star required.  Maybe there's a central Rogue Planet, and maybe not.  The orbital mechanics would be an intensely complex n-body problem with course corrections made by other objects changing the parameters somewhat every day.  But that's *almost* equally true of conventional Dyson Swarms.   In a Rogue Swarm you'd presumably have some stations operating nuclear power plants to sustain themselves, and other stations positioned where there is a gradient of infrared radiation (ie, between those nuclear-powered stations and the Outer Darkness) living off their waste heat.  So you have a central swarm of stations generating their own power, and the rest of the swarm operating as if those central stations were a very large, very diffuse, star - possibly living on radiation gradients that even most hiders would consider negligible.

The outer layers would have to be very very low-powered indeed.  But operating a small group of 15 or 20 modosophont AI, on the Infrared power harvested from several hundred square kilometers of collectors, is not too hard to imagine.  The little 'cabin in the woods' groups on the periphery would be isolated from their neighbors by lightspeed delay and limited in size by the amount of power available, making them a true 'hinterland' as an area where you can't really have significant population density - and a fair number of people would probably like that.
Perhaps some variants of a “rogue Dyson” might have more chaotic orbits, resembling those seen in a globular cluster.
You may have heard of Birch's Supraself concept, which is a bunch of dynamically supported shells supported over their own centre of gravity. A Supraself could mass as much as a galaxy, in which case it would have some ferocious relativistic time dilation effects in the lower levels.
I've included an extragalactic one in OA, here

It's probably best if we describe the larger hypermegastructures as existing outside our galaxy, since they would seriously skew the political balance in the Terragen Sphere or the Milky Way as a whole...
Yeah, I can see it as a "between galaxies" phenomenon.

There could be some Rogue Swarms slowly developing in undisturbed places, at or outside the galactic rim, or above or below the galactic plane - very very sparse, several times as wide as but probably comprising less than one percent of the mass, of a "typical" Dyson Swarm, with dynamics such that, if anything were around long enough to complete an orbit, it would take millions of years.

But places near the center of the swarm can already be known as spots where the infrared environment makes it impossible to *passively* radiate away enough heat to stay at a comfortable-to-unmodified temperature. Any nebs who want to live there need to run heat pumps and keep radiators running just so they don't get too hot. And further out, there could already be stations living on the infrared from the center.

It might be well-understood that there are no problems with scaling it up, but it would probably be something that grows very slowly or stays fairly small for thousands of years just because not very many people want to live there. The idea of living off the infrared emanations of powered stations seems like an idea that would originate with Hiders.

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