Building and stabilizing a SupraWorld.

Imagine a SupraWorld being built around a gas giant like Jupiter. To have a 1g gravity on the surface the resulting SupraWorld would have to be less than twice the radius of the giant (my calculation; could be wrong). I have unobtanium but it only provides impossible structural resistance and nothing else.

My civilization will start by placing a large hexagonal flat surface (where the colonists live) with very large walls to prevent the atmosphere from escaping. More will come; eventually all the hexagons will join in a ring (the walls remove periodically as two hexes join) and eventually they will "close" as a sphere(the finished SupraWorld).

How do I prevent the single "hexes" from falling into the planet? My idea was to have them at the top of a huge "tower", with the colony at one end and a large near vacuum spheroid or whatever at the other end, floating into the gas giant's metallic hydrogen ocean. Gyroscopes would stabilize the structure preventing it from flipping. How credible is that?

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Building and stabilizing a SupraWorld.

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