re: It's elevating
Let's assume it is buildable, with what ever new material yet to come, what do you do about all the satellites, rocket boosters and other space junk that would eventually smash into the tower even during it's construction. Let's face it. It's inevitable that something will hit the tower. They would have to deorbit all objects below the towers summit before they could start construction. Even then you would have to worry about meteorites coming in from outer space.