Come to think of it, to build a pole-tower, (crucible inside middle of the space escalator)
it can simply use the sea mining method I re-drew yesterday.
Instead hollow tower, crucibles, taking a small portion of the cross (+) lines of the frame-pyramid.
And then, send in tiny balls of metal, heat the crucibles, melt them, liquid level should go down from the top as they melt, then add in more metal balls from the top, calculate stability weight that is required at the bottom base of it, and to what shape, and crucibles that extends up should be connected to it.
So that base crucibles, which goes underground, can be built just after the frame-pyramid lines (+) is completed.
This saves volume. And material costs.
Can it be done with primal space escalator? 1.5km (max human tolerance in elevation for residence without discomfort to the body) vs. 100km reaching the atmosphere.
I would say, technically yes, but not a good idea. The risks are too high for instability over time, deterioration of structural volume (lack there of) and the method of build is a drop from top to bottom, like the first iteration of the space escalator, meaning it would take forever to build. And unpredictable, more complex in automation by machines. But from base ground, to incremental up, stacking up all surface areas, covering them all layer by layer and moving up from that, is quite easy.
So. It must be differentiated what is possible and practical, and what isn't.