The Galactic Zoo aliens take aluminosilicate space rocks apart with molecular nanotechnology and then put them together? Let's say it's the same as what we need to send a kilo to escape velocity- 8,000^2*2 = 128,000,000 J/kg is 128 W/mg. The 'Worm' model of Alien AlSiOMNT is a hexagonal cross-section of 7,500 elements, deposited, @ one million times per second, 1MHz, 133.333 layers per second. A 4,000 nm worm is 100 nm wide and 4,000 nm has a mining/depositing head at either end and replicates in 30 seconds. It mines faster than it lays down stuff, is 2.8 g/cc vs. 5.6 g/cc of AlSiO rock. A 'worm' butts up to a rock face and mines material at one end, 2 micrometers in 30 seconds while printing out another 4 micrometer worm at the other end, which whips around and finds an empty bit of rock to nosh on…
Energy may be a choke point. One billion 'worms' mass 10^9*(1/10^7)^2*3/4*4/10^6*10^9*2.8 = 0.084 mg of AlSiOMNT, which has an energy cost of .084*128 = 10.8 W over 30 seconds. At 100 W/m^2 per second, we need 10.8/100/30 = 0.0036 m^2, or .0036*100^2 = 36 cm^2 of surface to provide the energy. One billon worms is 10^9*4,000*100/(10^9)^2*100^2 = 4.0 cm^2, an order of magnitude less, nearly 5 minutes. Actually, it's twice as bad, because we need to break the rock apart first, transport it a little way and print it into the 2nd worm, so call it 10 minutes for a worm to replicate, 6 times per hour.
I'm probably being pessimistic about the energy cost and optimistic about the speed of assembly/disassembly, plus the feasibility of the aliens' AlSiOMNT, but that evens out. The real impossible thing is FTL… anyway, in the outer solar system, we'd expect them to power all this with fusion. Doubling six times per hour, 24/7, the 31 rings wouldn't take all that long to put together. A trillion 'worms' massing 84 grams (probably more like 84 tonnes! 8-) grows to 84*2^(6*24)/10^6 = 1E39 tonnes in 24 hours, when supplied with enough energy. Of course, it's physically impossible for something to grow that fast; 10^12*2^(6*24) = 2E55 worms need a rock face of 2E55*3/4/(10^7)^2/10^12 = 1E29 km^2, over 100 billion, *billion*, times the surface area of the Earth!
(12,760/3*1,000)^2/pi^11 = 6.15E7*10^3*31 = 1.91E12 tonnes, total.
1.91E12 tonnes divided by 84 grams is 1.91E12/84*10^6 = 2.27E16 fold increase, just over nine hours- 84/10^6*2^55 = 3.03E12 tonnes. That's a rock face of 10^12*2^55*3/4/(10^7)^2/10^12 = 270.2 m. km^2, which is a little over half the surface area of the Earth. Since the worms need to spread out over the surface of an Earth-sized body @ 12,760*pi/4 = 10,021.7 km over 600 seconds, or 10,021.7/600 = 16.7028 km/s, over twice orbital velocity, that is also unlikely.
Since three trillion tonnes is a rock 3.03E12/5.6 = 5.4107E11 m^3 in volume and a sphere (5.41E11*3/4/pi)^(1/3)*2 = 10,109.6 m across, 10,109.6/10^3 = 10.11 km. A mountain, in space, but not hard to find, or rip out of Ceres, Vesta or any random outer icy rock-ball moon like Saturn's' moon Phoebe. A couple of trillion tonnes is less than a tenth of a quarter of one percent of that moons' mass. The mass of 'worms' would probably have to physically bust up the rock to make for enough surface area to convert rock into stuff quickly, then launch it at the inner solar system.
For doing stuff, or moving around, the worms link up in sheets 4-8 one millionths of a meter thick and slide past each other. One m/s per sheet would be a laminar flow 2 mm thick with a difference 250 m/s between top and bottom, .25 km/s, 150 km in the 10 minutes it takes to replicate one worm.
Get the mass in transit, with fuel, and build the ring on the way, do the course corrections and terminal maneuvering, where the ring swaps 10 tonnes/m^2 of off-world mass for Earth stuff, lifts it to orbit and sends it on the way to the Galactic Zoo. On arrival, the 'worms' zip the strip into a cylinder which laps itself about 300 times, adds end-cones, heating, lighting, additional atmo and water, and joins each sample of Earth to the rest of the structure which makes up the Galactic Zoo.
Plus whatever other things which its' unknown masters require…