you could say in a way the green sun's life span IS actually cyclical cause if it didnt exist in the first place doc scratch would never have tricked them into making it

The Green Sun having a hand in its own creation doesn’t make it’s life span cyclical. That would be if it didn’t have an origin or ending, which is does or if it’s death gave way to it’s creation, which it did not. What you are describing is a Paradox, if the Green Sun didn’t exist then it wouldn’t exist in the first place.