No collapse of governing authority; Sol was able to feed itself at the least. First Fleet moved quickly after the node shutdown to seize control of all military manufacturing assets and instituted personnel and ship rotation rules to prevent any particular regional faction from easily staging a rebellion. The ruling government is more military than civilian, but in general preserves most of the freedoms that were available under the GTA with the caveat that a developing large-scale military action suspends the government and places the entire system under martial law.
Their weaponry has evolved along heavy spinal-mount accelerators as weapons of decision, fast bombers to cripple enemy ship weapons, and missile-based antifighter systems with either massive but relatively short-ranged antimatter "screen" warheads intended to break up and destroy attacking bomber formations (that also make decent antiship weapons in a close fight) or small, fast, long-ranged missiles for engaging dispersed targets. Their ship designs show a much clearer and more direct Great War influence, with many Great War models being uprated or rebuilt and even brand-new ships being obvious descendants of older ones.
They've heard the GTVA's attempts to communicate with them, they just don't believe it. Sol believes itself alone in a Shivan-dominated universe, with a siege mentality to match: their society is effectively designed for total war at moment's notice. They maintain heavy mine grids at the previous locations of the jump nodes, compulsory military service, detailed plans for moving the economy onto a war footing as rapidly as possible, and deep reserves of military hardware, shipbuilding capacity, and munitions manufacturing that are maintained for use in wartime.