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The way I see the assets is they are a bit like civilisational-wide abilities, a bit like skills in a normal rpg eg you have points in lockpicking etc. So you are upgrading manufacturing as Archonal Grid this will give your civilisation permanent +10 build progress on construction related rolls.
But the mountain planet colony is stuck on a lower tier technology, upgrading it would take a lot - I will say a colony ship is 300 + 100 for each asset, so to bring your civilisation level manufacturing to this planet would then be at least 400 ISD. I imagine they would then also have access to any base level capabilities of your arcology and Archonal Grid Systems etc.
