>>10931664Carbon nanotubes could build it. I've done the calculations.
Assuming the rather rosy statistics are accurate, Carbon Nanotubes are strong enough to reach "escape velocity", such that you can build an infinitely high tower. In other words, no matter how high, the tower's weight does not increase fast enough to ever overcome the breaking point of the wire.
If you had carbon nanotubes, you could build any inane structure you wanted with no regard to architectural constraints, without any fear it would collapse