I'll try and get through these arguments logically, however Trash, either you have poor reading comprehension skills, or you are doing nothing more than picking points and attempting to refute them with the flimsiest of assumptions. I'm not trying to insult you, but I'd like to see you put down counter-arguments that at least show you have done more than skim a post. Your main responses to everything said so far are all based on "The GTVA is BIGGER and BETTER than Sol", without much to really support this premise. Just a repetition of the same thing slightly rephrased. You can do better.
Now, down to the important stuff:
Given the rate of population growth, the available space and number of colonies, it's more likely the population of the colonies is greater than Sol
After all, the habitat in Sol is limited, the 20+ planets have more than enough room.
Let's also not forget that the population on Earth has increased from less than a billion to more than 6 billion in less than 100 years.
You are ignoring the likelihood that Sol is the oldest center of human settlement. There are likely numerous extraterrestrial colonies within Sol, such as Mars, Luna, Ceres, perhaps moons of other planets. There may even be terraforming which has rendered Venus a viable habitat. This is to say nothing of the likelihood of numerous installations within the solar system not based on existing solar bodies. Much of this possible colonization probably was well established before the discovery of subspace. This points to the likelihood that the population of Sol would be signifigantly larger than that of the GTVA before the node was closed., Since humans like to reproduce, this would likely have remained a constant factor.
The CURRENT population of Terra alone is enormous, which you've chosen to ignore. Yes, the population increased enormously in 100 years. A century is signifigantly longer than a mere three to four decades, which is all the GTVA would have in our Knossos reopening scenario to increase their populace.
We also know that Sol had research outposts all over the GTA, the techroom confirms that. Thus, there were more than enough scientists spread around and colonies would also have schools and universities, they won't be confined to Earth.
Nobody has denied this, however the backstory also confirms that the lion's share of the R&D and production industry is located in Sol itself. Not all certainly, but a hell of a lot of it. Sol would easily have plenty of technical ability to catch and probably outstrip the GTVA's production and research establishment.
GTVA has acess to Ancient ruins, the Knossos, scans and parts of numerous shivan vessels of which many are the newest and latest designs. That is a BIG bonus in terms of tech development for them.
And 20+ systems have the abilty to support a much bigger war machine, not to mention that the Capella BBQ might push the GTVA into a large military production more than any Lucy would. 80 Saths parading recently are a reason for fear - 1 Lucy parading 40 years ago really isn't.
Some access yes, of which all collected data from any discoveries would have been passed on to Terra up to the point of the node collapse. Yes, they would not have had access to the latest appearing Shivan ships, nor the Knossos. I do not believe it to be that big an advantage for the GTVA. For the most part GTVA tech was equivalent to their Shivan counterparts in the second incurision. In fact, in many ways it was superior. The newer Shivan units seemed like fairly minor variations of their older designs. The beam cannon was the greatest achievement for the GTVA, and it was matched up by the Shivans. It is unlikely that the engineers in Sol would not have come up with this tech, not to mention possibly surpass the level of the GTVA.
You are again insisting that the rest of the GTVA had a larger population than Sol. In fact the reverse is more likely from the reasons I've stated.
80 Sathanas class juggernauts would be a cause of concern, however they seem to have used the destruction of Capella as a means of boosting their ability to travel. They did not attack the rest of the GTVA - only the one star system. Rather than going into a frenzied military build up, the reverse is more likely: most avaricious politicians want the military budget for their own pet projects and social plans with nothing more at heart than the desire to keep their constituents happy, thus ensuring their continued share of the public trough. They are very fast to purport the belief that the enemy has gone away and public safety is assured.
The Colossus was intended to take on the Lucifer class destroyer by hopefully mounting weaponry strong enough to pierce its shields, on a platform strong enough to withstand the beating it would likely suffer in such a slugfest. It was not intended to take on its opposite number in a duel. The Colossus was not really suited for this role, thus its destruction in battle with a Sathanas without any supporting units for backup. Both of these ship types represented a total brute force approach to ship design. There is little finesse involved in their designs. Just the 'bigger is better' approach.
The Lucifer on the other hand seems to be based on the idea that the best defense is in itself a terrific offense. You don't need more than a few really powerful weapons on a vessel that cannot be harmed by enemy fire. Yes, this type of ship is indeed a serious concern.
After all, let's say Sol had been biulding up it's military. After 30 years of peace and no shivies in sight, do you really think they will keep up the pace?
I can't say for sure about the pace of their buildup, however the knowledge that your home is safe only so long as it remains isolated would be a continuing incentive to build up your defenses with the best you can possibly produce. Not neccesarily at a fever pitch, but at least a continuous effort. A political entity that has at least the illusion of its continued safety does not have that incentive.
Last, but not least - isn't the USA the military and economicly most powerul nation in the world? Cut it off them the rest of the world - who will be hit worse by that cut - the US or the rest of the world? The US f'course. Being the biggest means you also export and outsource the most, and then you're also affected the most by a collapse like that.
In the short term, yes, however it does not usually take an enormous ammount of time for humans to adapt to their situation and get things up and running again. In your example you have a prosperous country with a large, well educated population, and a great deal of natural resources at its disposal. After a decade or so it would recover and become its own self contained 'world'. Also, the US has an enormous influence on the rest of the world. I have little doubt that its sudden removal from the world scene would cause an awful lot of economic issues, not to mention military and political. The rest of the world also would survive, but they would not be very happy for a signifigant ammount of time.